id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1,964 | EP-158 | Erdős Problem #158 | Let $A\subset \mathbb{N}$ be an infinite set such that, for any $n$, there are most $2$ solutions to $a+b=n$ with $a\leq b$. Must\[\liminf_{N\to\infty}\frac{\lvert A\cap \{1,\ldots,N\}\rvert}{N^{1/2}}=0?\] | Erdős Problems (#158, https://www.erdosproblems.com/158). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.158). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/158",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/158 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,965 | EP-159 | Erdős Problem #159 | There exists some constant $c>0$ such that
$$R(C_4,K_n) \ll n^{2-c}.$$ | Erdős Problems (#159, https://www.erdosproblems.com/159). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.159). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/159",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/159 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,966 | EP-160 | Erdős Problem #160 | Let $h(N)$ be the smallest $k$ such that $\{1,\ldots,N\}$ can be coloured with $k$ colours so that every four-term arithmetic progression must contain at least three distinct colours. Estimate $h(N)$. | Erdős Problems (#160, https://www.erdosproblems.com/160). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.160). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/160",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/160 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,967 | EP-161 | Erdős Problem #161 | Let $\alpha\in[0,1/2)$ and $n,t\geq 1$. Let $F^{(t)}(n,\alpha)$ be the smallest $m$ such that we can $2$-colour the edges of the complete $t$-uniform hypergraph on $n$ vertices such that if $X\subseteq [n]$ with $\lvert X\rvert \geq m$ then there are at least $\alpha \binom{\lvert X\rvert}{t}$ many $t$-subsets of $X$ o... | Erdős Problems (#161, https://www.erdosproblems.com/161). Maintainer status: OPEN. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.161). | 1 | partially_solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/161",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"combinatorics",
"ramsey-theory",
"discrepancy",
"hypergraphs"
] | null | null | null | null | https://www.erdosproblems.com/161 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,968 | EP-162 | Erdős Problem #162 | Let $\alpha>0$ and $n\geq 1$. Let $F(n,\alpha)$ be the largest $k$ such that there exists some 2-colouring of the edges of $K_n$ in which any induced subgraph $H$ on at least $k$ vertices contains more than $\alpha\binom{\lvert H\rvert}{2}$ many edges of each colour.
Prove that for every fixed $0\leq \alpha \leq 1/2$,... | Erdős Problems (#162, https://www.erdosproblems.com/162). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.162). | 1 | partially_solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/162",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"combinatorics",
"ramsey-theory",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/162 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,969 | EP-165 | Erdős Problem #165 | Give an asymptotic formula for $R(3,k)$. | Erdős Problems (#165, https://www.erdosproblems.com/165). Maintainer status: OPEN. Erdős prize: $250. OEIS: A000791. | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/165",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/165 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,970 | EP-168 | Erdős Problem #168 | Let $F(N)$ be the size of the largest subset of $\{1,\ldots,N\}$ which does not contain any set of the form $\{n,2n,3n\}$. What is\[ \lim_{N\to \infty}\frac{F(N)}{N}?\]Is this limit irrational? | Erdős Problems (#168, https://www.erdosproblems.com/168). Maintainer status: OPEN. OEIS: A004059, A057561, A094708, A386439. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.168). | 1 | partially_solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/168",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/168 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,971 | EP-169 | Erdős Problem #169 | Let $k\geq 3$ and $f(k)$ be the supremum of $\sum_{n\in A}\frac{1}{n}$ as $A$ ranges over all sets of positive integers which do not contain a $k$-term arithmetic progression. Estimate $f(k)$.
Is\[\lim_{k\to \infty}\frac{f(k)}{\log W(k)}=\infty\]where $W(k)$ is the van der Waerden number? | Erdős Problems (#169, https://www.erdosproblems.com/169). Maintainer status: OPEN. OEIS: A005346. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/169",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/169 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,972 | EP-170 | Erdős Problem #170 | Let $F(N)$ be the smallest possible size of $A\subset \{0,1,\ldots,N\}$ such that $\{0,1,\ldots,N\}\subset A-A$. Find the value of\[\lim_{N\to \infty}\frac{F(N)}{N^{1/2}}.\] | Erdős Problems (#170, https://www.erdosproblems.com/170). Maintainer status: OPEN. sparse ruler problem OEIS: A046693. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.170). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/170",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | sparse ruler problem | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/170 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,973 | EP-172 | Erdős Problem #172 | Is it true that in any finite colouring of $\mathbb{N}$ there exist arbitrarily large finite $A$ such that all sums and products of distinct elements in $A$ are the same colour? | Erdős Problems (#172, https://www.erdosproblems.com/172). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.172). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/172",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/172 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,974 | EP-173 | Erdős Problem #173 | In any $2$-colouring of $\mathbb{R}^2$, for all but at most one triangle $T$, there is a monochromatic congruent copy of $T$. | Erdős Problems (#173, https://www.erdosproblems.com/173). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.173). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/173",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/173 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,975 | EP-174 | Erdős Problem #174 | A finite set $A\subset \mathbb{R}^n$ is called Ramsey if, for any $k\geq 1$, there exists some $d=d(A,k)$ such that in any $k$-colouring of $\mathbb{R}^d$ there exists a monochromatic copy of $A$. Characterise the Ramsey sets in $\mathbb{R}^n$. | Erdős Problems (#174, https://www.erdosproblems.com/174). Maintainer status: OPEN. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/174",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/174 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,976 | EP-176 | Erdős Problem #176 | Let $N(k,\ell)$ be the minimal $N$ such that for any $f:\{1,\ldots,N\}\to\{-1,1\}$ there must exist a $k$-term arithmetic progression $P$ such that\[ \left\lvert \sum_{n\in P}f(n)\right\rvert\geq \ell.\]Find good upper bounds for $N(k,\ell)$. Is it true that for any $c>0$ there exists some $C>1$ such that\[N(k,ck)\leq ... | Erdős Problems (#176, https://www.erdosproblems.com/176). Maintainer status: OPEN. | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/176",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/176 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,977 | EP-177 | Erdős Problem #177 | Find the smallest $h(d)$ such that the following holds. There exists a function $f:\mathbb{N}\to\{-1,1\}$ such that, for every $d\geq 1$,\[\max_{P_d}\left\lvert \sum_{n\in P_d}f(n)\right\rvert\leq h(d),\]where $P_d$ ranges over all finite arithmetic progressions with common difference $d$. | Erdős Problems (#177, https://www.erdosproblems.com/177). Maintainer status: OPEN. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/177",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"discrepancy",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/177 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,978 | EP-180 | Erdős Problem #180 | If $\mathcal{F}$ is a finite set of finite graphs then $\mathrm{ex}(n;\mathcal{F})$ is the maximum number of edges a graph on $n$ vertices can have without containing any subgraphs from $\mathcal{F}$. Note that it is trivial that $\mathrm{ex}(n;\mathcal{F})\leq \mathrm{ex}(n;G)$ for every $G\in\mathcal{F}$.
Is it true... | Erdős Problems (#180, https://www.erdosproblems.com/180). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.180). | 1 | solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/180",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"turan-number"
] | The maintained Erdős Problems source lists problem 180 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/180",
"label": "Erdős Problems #180: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://hug... | 2026-09-27T00:00:00 | Erdős Problems #180: disproved (Lean): https://www.erdosproblems.com/180
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/180 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,979 | EP-181 | Erdős Problem #181 | Let $Q_n$ be the $n$-dimensional hypercube graph (so that $Q_n$ has $2^n$ vertices and $n2^{n-1}$ edges). Prove that\[R(Q_n) \ll 2^n.\] | Erdős Problems (#181, https://www.erdosproblems.com/181). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.181). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/181",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/181 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,980 | EP-183 | Erdős Problem #183 | Let $R(3;k)$ be the minimal $n$ such that if the edges of $K_n$ are coloured with $k$ colours then there must exist a monochromatic triangle. Determine\[\lim_{k\to \infty}R(3;k)^{1/k}.\] | Erdős Problems (#183, https://www.erdosproblems.com/183). Maintainer status: SOLVED (LEAN). Erdős prize: $250. OEIS: A003323. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.183). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/183",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | The maintained Erdős Problems source lists problem 183 as “solved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/183",
"label": "Erdős Problems #183: solved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #183: solved (Lean): https://www.erdosproblems.com/183
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/183 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,981 | EP-184 | Erdős Problem #184 | Any graph on $n$ vertices can be decomposed into $O(n)$ many edge-disjoint cycles and edges. | Erdős Problems (#184, https://www.erdosproblems.com/184). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.184). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/184",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | [Discussion #4 literature review, 2026-10-08] arXiv:1310.7082 is "Concentration of small Willmore spheres in Riemannian 3-manifolds" by P. Laurain and A. Mondino; cited paper (Conlon–Fox–Sudakov, "Cycle packing"): arXiv:1310.0632. | [
"erdos-problems",
"graph-theory",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/184 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,982 | EP-187 | Erdős Problem #187 | Find the best function $f(d)$ such that, in any 2-colouring of the integers, at least one colour class contains an arithmetic progression with common difference $d$ of length $f(d)$ for infinitely many $d$. | Erdős Problems (#187, https://www.erdosproblems.com/187). Maintainer status: OPEN. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/187",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"ramsey-theory",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/187 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,983 | EP-188 | Erdős Problem #188 | What is the smallest $k$ such that $\mathbb{R}^2$ can be red/blue coloured with no pair of red points unit distance apart, and no $k$-term arithmetic progression of blue points with distance $1$? | Erdős Problems (#188, https://www.erdosproblems.com/188). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.188). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/188",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/188 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,984 | EP-190 | Erdős Problem #190 | Let $H(k)$ be the smallest $N$ such that in any finite colouring of $\{1,\ldots,N\}$ (into any number of colours) there is always either a monochromatic $k$-term arithmetic progression or a rainbow arithmetic progression (i.e. all elements are different colours). Estimate $H(k)$. Is it true that\[H(k)^{1/k}/k \to \inft... | Erdős Problems (#190, https://www.erdosproblems.com/190). Maintainer status: SOLVED (LEAN). | 1 | solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/190",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | The maintained Erdős Problems source lists problem 190 as “solved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/190",
"label": "Erdős Problems #190: solved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #190: solved (Lean): https://www.erdosproblems.com/190
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/190 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,985 | EP-193 | Erdős Problem #193 | Let $S\subseteq \mathbb{Z}^3$ be a finite set and let $A=\{a_1,a_2,\ldots,\}\subset \mathbb{Z}^3$ be an infinite $S$-walk, so that $a_{i+1}-a_i\in S$ for all $i$. Must $A$ contain three collinear points? | Erdős Problems (#193, https://www.erdosproblems.com/193). Maintainer status: DISPROVED (LEAN). OEIS: A231255. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.193). | 1 | solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/193",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | The maintained Erdős Problems source lists problem 193 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/193",
"label": "Erdős Problems #193: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://hug... | 2026-09-27T00:00:00 | Erdős Problems #193: disproved (Lean): https://www.erdosproblems.com/193
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/193 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,986 | EP-195 | Erdős Problem #195 | What is the largest $k$ such that in any permutation of $\mathbb{Z}$ there must exist a monotone $k$-term arithmetic progression $x_1<\cdots<x_k$? | Erdős Problems (#195, https://www.erdosproblems.com/195). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.195). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/195",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/195 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,987 | EP-196 | Erdős Problem #196 | Must every permutation of $\mathbb{N}$ contain a monotone 4-term arithmetic progression? In other words, given a permutation $x$ of $\mathbb{N}$ must there be indices with either $i<j<k<l$ or $i>j>k>l$ such that $x_i,x_j,x_k,x_l$ are an arithmetic progression? | Erdős Problems (#196, https://www.erdosproblems.com/196). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.196). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/196",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/196 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,988 | EP-197 | Erdős Problem #197 | Can $\mathbb{N}$ be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions? | Erdős Problems (#197, https://www.erdosproblems.com/197). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.197). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/197",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/197 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,989 | EP-200 | Erdős Problem #200 | Does the longest arithmetic progression of primes in $\{1,\ldots,N\}$ have length $o(\log N)$? | Erdős Problems (#200, https://www.erdosproblems.com/200). Maintainer status: OPEN. OEIS: A005115. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.200). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/200",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"primes",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/200 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,990 | EP-201 | Erdős Problem #201 | Let $G_k(N)$ be such that any set of $N$ integers contains a subset of size at least $G_k(N)$ which does not contain a $k$-term arithmetic progression. Determine the size of $G_k(N)$. How does it relate to $R_k(N)$, the size of the largest subset of $\{1,\ldots,N\}$ without a $k$-term arithmetic progression? Is it true... | Erdős Problems (#201, https://www.erdosproblems.com/201). Maintainer status: OPEN. OEIS: A003002, A003003, A003004, A003005. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/201",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/201 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,991 | EP-202 | Erdős Problem #202 | Let $n_1<\cdots < n_r\leq N$ with associated $a_i\pmod{n_i}$ such that the congruence classes are disjoint (that is, every integer is $\equiv a_i\pmod{n_i}$ for at most one $1\leq i\leq r$). How large can $r$ be in terms of $N$? | Erdős Problems (#202, https://www.erdosproblems.com/202). Maintainer status: SOLVED (LEAN). OEIS: A389975. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.202). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/202",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"covering-systems"
] | The maintained Erdős Problems source lists problem 202 as “solved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/202",
"label": "Erdős Problems #202: solved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #202: solved (Lean): https://www.erdosproblems.com/202
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/202 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,992 | EP-203 | Erdős Problem #203 | Is there an integer $m\geq 1$ with $(m,6)=1$ such that none of $2^k3^\ell m+1$ are prime, for any $k,\ell\geq 0$? | Erdős Problems (#203, https://www.erdosproblems.com/203). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.203). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/203",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"primes",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/203 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,993 | EP-208 | Erdős Problem #208 | Let $s_1<s_2<\cdots$ be the sequence of squarefree numbers. Is it true that, for any $\epsilon>0$ and large $n$,\[s_{n+1}-s_n \ll_\epsilon s_n^{\epsilon}?\]Is it true that\[s_{n+1}-s_n \leq (1+o(1))\frac{\pi^2}{6}\frac{\log s_n}{\log\log s_n}?\] | Erdős Problems (#208, https://www.erdosproblems.com/208). Maintainer status: OPEN. OEIS: A005117, A076259. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.208). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/208",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/208 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,994 | EP-212 | Erdős Problem #212 | Is there a dense subset of $\mathbb{R}^2$ such that all pairwise distances are rational? | Erdős Problems (#212, https://www.erdosproblems.com/212). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.212). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/212",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/212 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,995 | EP-213 | Erdős Problem #213 | Let $n\geq 4$. Are there $n$ points in $\mathbb{R}^2$, no three on a line and no four on a circle, such that all pairwise distances are integers? | Erdős Problems (#213, https://www.erdosproblems.com/213). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.213). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/213",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/213 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,996 | EP-217 | Erdős Problem #217 | For which $n$ are there $n$ points in $\mathbb{R}^2$, no three on a line and no four on a circle, which determine $n-1$ distinct distances and so that (in some ordering of the distances) the $i$th distance occurs $i$ times? | Erdős Problems (#217, https://www.erdosproblems.com/217). Maintainer status: OPEN. | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/217",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/217 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,997 | EP-218 | Erdős Problem #218 | Let $d_n=p_{n+1}-p_n$. The set of $n$ such that $d_{n+1}\geq d_n$ has density $1/2$, and similarly for $d_{n+1}\leq d_n$. Furthermore, there are infinitely many $n$ such that $d_{n+1}=d_n$. | Erdős Problems (#218, https://www.erdosproblems.com/218). Maintainer status: OPEN. OEIS: A333230, A333231, A064113. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.218). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/218",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/218 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,998 | EP-222 | Erdős Problem #222 | Let $n_1<n_2<\cdots$ be the sequence of integers which are the sum of two squares. Explore the behaviour of (i.e. find good upper and lower bounds for) the consecutive differences $n_{k+1}-n_k$. | Erdős Problems (#222, https://www.erdosproblems.com/222). Maintainer status: OPEN. OEIS: A001481, A256435. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/222",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"squares"
] | null | null | null | null | https://www.erdosproblems.com/222 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,999 | EP-233 | Erdős Problem #233 | Let $d_n=p_{n+1}-p_n$, where $p_n$ is the $n$th prime. Prove that\[\sum_{1\leq n\leq N}d_n^2 \ll N(\log N)^2.\] | Erdős Problems (#233, https://www.erdosproblems.com/233). Maintainer status: OPEN. OEIS: A074741. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.233). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/233",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/233 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,000 | EP-234 | Erdős Problem #234 | For every $c\geq 0$ the density $f(c)$ of integers for which\[\frac{p_{n+1}-p_n}{\log n}< c\]exists and is a continuous function of $c$. | Erdős Problems (#234, https://www.erdosproblems.com/234). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.234). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/234",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/234 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,001 | EP-236 | Erdős Problem #236 | Let $f(n)$ count the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$. Is it true that $f(n)=o(\log n)$? | Erdős Problems (#236, https://www.erdosproblems.com/236). Maintainer status: OPEN. OEIS: A039669, A109925. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.236). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/236",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/236 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,002 | EP-238 | Erdős Problem #238 | Let $c_1,c_2>0$. Is it true that, for any sufficiently large $x$, there exist more than $c_1\log x$ many consecutive primes $\leq x$ such that the difference between any two is $>c_2$? | Erdős Problems (#238, https://www.erdosproblems.com/238). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.238). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/238",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/238 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,003 | EP-241 | Erdős Problem #241 | Let $f(N)$ be the maximum size of $A\subseteq \{1,\ldots,N\}$ such that the sums $a+b+c$ with $a,b,c\in A$ are all distinct (aside from the trivial coincidences). Is it true that\[ f(N)\sim N^{1/3}?\] | Erdős Problems (#241, https://www.erdosproblems.com/241). Maintainer status: OPEN. Erdős prize: $100. OEIS: A387704. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.241). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/241",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/241 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
2,004 | EP-243 | Erdős Problem #243 | Let $1\leq a_1<a_2<\cdots$ be a sequence of integers such that\[\lim_{n\to \infty}\frac{a_n}{a_{n-1}^2}=1\]and $\sum\frac{1}{a_n}\in \mathbb{Q}$. Then, for all sufficiently large $n\geq 1$,\[ a_n = a_{n-1}^2-a_{n-1}+1.\] | Erdős Problems (#243, https://www.erdosproblems.com/243). Maintainer status: OPEN. OEIS: A000058. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.243). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/243",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/243 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,005 | EP-244 | Erdős Problem #244 | Let $C>1$. Does the set of integers of the form $p+\lfloor C^k\rfloor$, for some prime $p$ and $k\geq 0$, have density $>0$? | Erdős Problems (#244, https://www.erdosproblems.com/244). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.244). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/244",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/244 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,006 | EP-247 | Erdős Problem #247 | Let $1\leq a_1<a_2<\cdots$ be a sequence of integers such that\[\limsup \frac{a_n}{n}=\infty.\]Is\[\sum_{n=1}^\infty \frac{1}{2^{a_n}}\]transcendental? | Erdős Problems (#247, https://www.erdosproblems.com/247). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.247). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/247",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/247 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,007 | EP-249 | Erdős Problem #249 | Is\[\sum_n \frac{\phi(n)}{2^n}\]irrational? Here $\phi$ is the Euler totient function. | Erdős Problems (#249, https://www.erdosproblems.com/249). Maintainer status: OPEN. OEIS: A256936. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.249). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/249",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/249 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,008 | EP-251 | Erdős Problem #251 | Is\[\sum \frac{p_n}{2^n}\]irrational? (Here $p_n$ is the $n$th prime.) | Erdős Problems (#251, https://www.erdosproblems.com/251). Maintainer status: OPEN. OEIS: A098990. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.251). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/251",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/251 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,009 | EP-252 | Erdős Problem #252 | Let $k\geq 1$ and $\sigma_k(n)=\sum_{d\mid n}d^k$. Is\[\sum \frac{\sigma_k(n)}{n!}\]irrational? | Erdős Problems (#252, https://www.erdosproblems.com/252). Maintainer status: OPEN. OEIS: A227988, A227989, A307036, A359060. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.252). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/252",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/252 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,010 | EP-254 | Erdős Problem #254 | Let $A\subseteq \mathbb{N}$ be such that\[\lvert A\cap [1,2x]\rvert -\lvert A\cap [1,x]\rvert \to \infty\textrm{ as }x\to \infty\]and\[\sum_{n\in A} \{ \theta n\}=\infty\]for every $\theta\in (0,1)$, where $\{x\}$ is the distance of $x$ from the nearest integer. Then every sufficiently large integer is the sum of disti... | Erdős Problems (#254, https://www.erdosproblems.com/254). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.254). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/254",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/254 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,011 | EP-256 | Erdős Problem #256 | Let $n\geq 1$ and $f(n)$ be maximal such that for any integers $1\leq a_1\leq \cdots \leq a_n$ we have\[\max_{\lvert z\rvert=1}\left\lvert \prod_{i}(1-z^{a_i})\right\rvert\geq f(n).\]Estimate $f(n)$ - in particular, is it true that there exists some constant $c>0$ such that\[\log f(n) \gg n^c?\] | Erdős Problems (#256, https://www.erdosproblems.com/256). Maintainer status: OPEN. | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/256",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/256 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,012 | EP-257 | Erdős Problem #257 | Let $A\subseteq \mathbb{N}$ be an infinite set. Is\[\sum_{n\in A}\frac{1}{2^n-1}\]irrational? | Erdős Problems (#257, https://www.erdosproblems.com/257). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.257). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/257",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/257 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,013 | EP-258 | Erdős Problem #258 | Let $a_1,a_2,\ldots$ be a sequence of positive integers with $a_n\to \infty$. Is\[\sum_{n} \frac{\tau(n)}{a_1\cdots a_n}\]irrational, where $\tau(n)$ is the number of divisors of $n$? | Erdős Problems (#258, https://www.erdosproblems.com/258). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.258). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/258",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | The maintained Erdős Problems source lists problem 258 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/258",
"label": "Erdős Problems #258: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #258: proved (Lean): https://www.erdosproblems.com/258
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/258 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,014 | EP-260 | Erdős Problem #260 | Let $a_1<a_2<\cdots$ be an increasing sequence such that $a_n/n\to \infty$. Is the sum\[\sum_n \frac{a_n}{2^{a_n}}\]irrational? | Erdős Problems (#260, https://www.erdosproblems.com/260). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.260). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/260",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/260 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,015 | EP-261 | Erdős Problem #261 | Are there infinitely many $n$ such that there exists some $t\geq 2$ and distinct integers $a_1,\ldots,a_t\geq 1$ such that\[\frac{n}{2^n}=\sum_{1\leq k\leq t}\frac{a_k}{2^{a_k}}?\]Is this true for all $n$? Is there a rational $x$ such that\[x = \sum_{k=1}^\infty \frac{a_k}{2^{a_k}}\]has at least $2^{\aleph_0}$ solution... | Erdős Problems (#261, https://www.erdosproblems.com/261). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.261). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/261",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/261 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,016 | EP-263 | Erdős Problem #263 | Let $a_n$ be an increasing sequence of positive integers such that for every sequence of positive integers $b_n$ with $b_n/a_n\to 1$ the sum\[\sum\frac{1}{b_n}\]is irrational. Is $a_n=2^{2^n}$ such a sequence? Must such a sequence satisfy $a_n^{1/n}\to \infty$? | Erdős Problems (#263, https://www.erdosproblems.com/263). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.263). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/263",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/263 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,017 | EP-264 | Erdős Problem #264 | Let $a_n$ be a sequence of positive integers such that for every bounded sequence of integers $b_n$ (with $a_n+b_n\neq 0$ and $b_n\neq 0$ for all $n$) the sum\[\sum \frac{1}{a_n+b_n}\]is irrational. Are $a_n=2^n$ or $a_n=n!$ examples of such a sequence? | Erdős Problems (#264, https://www.erdosproblems.com/264). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.264). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/264",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/264 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,018 | EP-265 | Erdős Problem #265 | Let $1\leq a_1<a_2<\cdots$ be an increasing sequence of integers. How fast can $a_n\to \infty$ grow if\[\sum\frac{1}{a_n}\quad\textrm{and}\quad\sum\frac{1}{a_n-1}\]are both rational? | Erdős Problems (#265, https://www.erdosproblems.com/265). Maintainer status: OPEN. ambiguous statement | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/265",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | ambiguous statement | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/265 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,019 | EP-267 | Erdős Problem #267 | Let $F_1=F_2=1$ and $F_{n+1}=F_n+F_{n-1}$ be the Fibonacci sequence. Let $n_1<n_2<\cdots $ be an infinite sequence with $n_{k+1}/n_k \geq c>1$. Must\[\sum_k\frac{1}{F_{n_k}}\]be irrational? | Erdős Problems (#267, https://www.erdosproblems.com/267). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.267). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/267",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/267 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,020 | EP-269 | Erdős Problem #269 | Let $P$ be a finite set of primes with $\lvert P\rvert \geq 2$ and let $\{a_1<a_2<\cdots\}=\{ n\in \mathbb{N}: \textrm{if }p\mid n\textrm{ then }p\in P\}$. Is the sum\[\sum_{n=1}^\infty \frac{1}{[a_1,\ldots,a_n]},\]where $[a_1,\ldots,a_n]$ is the lowest common multiple of $a_1,\ldots,a_n$, irrational? | Erdős Problems (#269, https://www.erdosproblems.com/269). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.269). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/269",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/269 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,021 | EP-271 | Erdős Problem #271 | Let $A(n)=\{a_0<a_1<\cdots\}$ be the sequence defined by $a_0=0$ and $a_1=n$, and for $k\geq 1$ define $a_{k+1}$ as the least positive integer such that there is no three-term arithmetic progression in $\{a_0,\ldots,a_{k+1}\}$.
Can the $a_k$ be explicitly determined? How fast do they grow? | Erdős Problems (#271, https://www.erdosproblems.com/271). Maintainer status: OPEN. Stanley sequences OEIS: A005487. | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/271",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | Stanley sequences | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/271 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,022 | EP-272 | Erdős Problem #272 | Let $N\geq 1$. What is the largest $t$ such that there are $A_1,\ldots,A_t\subseteq \{1,\ldots,N\}$ with $A_i\cap A_j$ a non-empty arithmetic progression for all $i\neq j$? | Erdős Problems (#272, https://www.erdosproblems.com/272). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.272). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/272",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/272 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,023 | EP-273 | Erdős Problem #273 | Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p\geq 5$? | Erdős Problems (#273, https://www.erdosproblems.com/273). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.273). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/273",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/273 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,024 | EP-274 | Erdős Problem #274 | If $G$ is a group then can there exist an exact covering of $G$ by more than one cosets of different sizes? (i.e. each element is contained in exactly one of the cosets) | Erdős Problems (#274, https://www.erdosproblems.com/274). Maintainer status: OPEN. Herzog-Schönheim conjecture Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.274). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/274",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | Herzog-Schönheim conjecture | [
"erdos-problems",
"group-theory",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/274 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,025 | EP-276 | Erdős Problem #276 | Is there an infinite Lucas sequence $a_0,a_1,\ldots$ where $a_{n+2}=a_{n+1}+a_n$ for $n\geq 0$ such that all $a_k$ are composite, and yet no integer has a common factor with every term of the sequence? | Erdős Problems (#276, https://www.erdosproblems.com/276). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.276). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/276",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/276 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,026 | EP-278 | Erdős Problem #278 | Let $A=\{n_1<\cdots<n_r\}$ be a finite set of positive integers. What is the maximum density of integers covered by a suitable choice of congruences $a_i\pmod{n_i}$?
Is the minimum density achieved when all the $a_i$ are equal? | Erdős Problems (#278, https://www.erdosproblems.com/278). Maintainer status: OPEN. | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/278",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | Maximum-density half: an exact characterisation and a fixed-parameter exact algorithm (2^{O(r^2)} poly(input)); the minimum half was settled by Simpson (1986). Whether an exact algorithm counts as an answer to 'what is the maximum density' is for the maintainers to judge. Alper Ferudun (2026), unrefereed preprint with ... | [
{
"url": "https://doi.org/10.5281/zenodo.22244392",
"label": "Alper Ferudun (2026), An Exact Fixed-Parameter Algorithm for Extremal Unions of Residue Classes — unrefereed preprint"
},
{
"url": "https://eulersolve.org/papers/ep-278/",
"label": "EulerSolve paper page and verification materials"
... | 2026-09-27T00:00:00 | null | https://www.erdosproblems.com/278 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,027 | EP-279 | Erdős Problem #279 | Let $k\geq 3$. Is there a choice of congruence classes $a_p\pmod{p}$ for every prime $p$ such that all sufficiently large integers can be written as $a_p+tp$ for some prime $p$ and integer $t\geq k$? | Erdős Problems (#279, https://www.erdosproblems.com/279). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.279). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/279",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/279 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,028 | EP-281 | Erdős Problem #281 | Let $n_1<n_2<\cdots$ be an infinite sequence such that, for any choice of congruence classes $a_i\pmod{n_i}$, the set of integers not satisfying any of the congruences $a_i\pmod{n_i}$ has density $0$.
Is it true that for every $\epsilon>0$ there exists some $k$ such that, for every choice of congruence classes $a_i$, ... | Erdős Problems (#281, https://www.erdosproblems.com/281). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.281). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/281",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | The maintained Erdős Problems source lists problem 281 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/281",
"label": "Erdős Problems #281: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #281: proved (Lean): https://www.erdosproblems.com/281
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/281 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,029 | EP-282 | Erdős Problem #282 | Let $A\subseteq \mathbb{N}$ be an infinite set and consider the following greedy algorithm for a rational $x\in (0,1)$: choose the minimal $n\in A$ such that $n\geq 1/x$ and repeat with $x$ replaced by $x-\frac{1}{n}$. If this terminates after finitely many steps then this produces a representation of $x$ as the sum of... | Erdős Problems (#282, https://www.erdosproblems.com/282). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.282). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/282",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/282 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,030 | EP-283 | Erdős Problem #283 | Let $p:\mathbb{Z}\to \mathbb{Z}$ be a polynomial whose leading coefficient is positive and such that there exists no $d\geq 2$ with $d\mid p(n)$ for all $n\geq 1$. Is it true that, for all sufficiently large $m$, there exist integers $1\leq n_1<\cdots <n_k$ such that\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}\]and\[m=p(n_1)... | Erdős Problems (#283, https://www.erdosproblems.com/283). Maintainer status: PROVED (LEAN). OEIS: A380791. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.283). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/283",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | The maintained Erdős Problems source lists problem 283 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/283",
"label": "Erdős Problems #283: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #283: proved (Lean): https://www.erdosproblems.com/283
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/283 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,031 | EP-288 | Erdős Problem #288 | Is it true that there are only finitely many pairs of intervals $I_1,I_2$ such that\[\sum_{n_1\in I_1}\frac{1}{n_1}+\sum_{n_2\in I_2}\frac{1}{n_2}\in \mathbb{N}?\] | Erdős Problems (#288, https://www.erdosproblems.com/288). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.288). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/288",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/288 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,032 | EP-289 | Erdős Problem #289 | Is it true that, for all sufficiently large $k$, there exist finite intervals $I_1,\ldots,I_k\subset \mathbb{N}$, distinct, not overlapping or adjacent, with $\lvert I_i\rvert \geq 2$ for $1\leq i\leq k$ such that\[1=\sum_{i=1}^k \sum_{n\in I_i}\frac{1}{n}?\] | Erdős Problems (#289, https://www.erdosproblems.com/289). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.289). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/289",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/289 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,033 | EP-291 | Erdős Problem #291 | Let $n\geq 1$ and define $L_n$ to be the least common multiple of $\{1,\ldots,n\}$ and $a_n$ by\[\sum_{1\leq k\leq n}\frac{1}{k}=\frac{a_n}{L_n}.\]Is it true that $(a_n,L_n)=1$ and $(a_n,L_n)>1$ both occur for infinitely many $n$? | Erdős Problems (#291, https://www.erdosproblems.com/291). Maintainer status: OPEN. OEIS: A110566. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.291). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/291",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/291 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,034 | EP-293 | Erdős Problem #293 | Let $k\geq 1$ and let $v(k)$ be the minimal integer which does not appear as some $n_i$ in a solution to\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}\]with $1\leq n_1<\cdots <n_k$. Estimate the growth of $v(k)$. | Erdős Problems (#293, https://www.erdosproblems.com/293). Maintainer status: OPEN. ambiguous statement | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/293",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | ambiguous statement | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/293 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,035 | EP-295 | Erdős Problem #295 | Let $N\geq 1$ and let $k(N)$ denote the smallest $k$ such that there exist $N\leq n_1<\cdots <n_k$ with\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}.\]Is it true that\[\lim_{N\to \infty} k(N)-(e-1)N=\infty?\] | Erdős Problems (#295, https://www.erdosproblems.com/295). Maintainer status: OPEN. OEIS: A192881. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.295). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/295",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/295 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,036 | EP-301 | Erdős Problem #301 | Let $f(N)$ be the size of the largest $A\subseteq \{1,\ldots,N\}$ such that there are no solutions to\[\frac{1}{a}= \frac{1}{b_1}+\cdots+\frac{1}{b_k}\]with distinct $a,b_1,\ldots,b_k\in A$?
Estimate $f(N)$. In particular, is it true that $f(N)=(\tfrac{1}{2}+o(1))N$? | Erdős Problems (#301, https://www.erdosproblems.com/301). Maintainer status: OPEN. OEIS: A390394. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/301",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/301 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,037 | EP-302 | Erdős Problem #302 | Let $f(N)$ be the size of the largest $A\subseteq \{1,\ldots,N\}$ such that there are no solutions to\[\frac{1}{a}= \frac{1}{b}+\frac{1}{c}\]with distinct $a,b,c\in A$?
Estimate $f(N)$. In particular, is $f(N)=(\tfrac{1}{2}+o(1))N$? | Erdős Problems (#302, https://www.erdosproblems.com/302). Maintainer status: OPEN. OEIS: A390395. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.302). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/302",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/302 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,038 | EP-304 | Erdős Problem #304 | For integers $1\leq a<b$ let $N(a,b)$ denote the minimal $k$ such that there exist integers $1<n_1<\cdots<n_k$ with\[\frac{a}{b}=\frac{1}{n_1}+\cdots+\frac{1}{n_k}.\]Estimate $N(b)=\max_{1\leq a<b}N(a,b)$. Is it true that $N(b) \ll \log\log b$? | Erdős Problems (#304, https://www.erdosproblems.com/304). Maintainer status: OPEN. OEIS: A097847, A097849. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.304). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/304",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/304 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,039 | EP-306 | Erdős Problem #306 | Let $a/b\in \mathbb{Q}_{>0}$ with $b$ squarefree. Are there integers $1<n_1<\cdots<n_k$, each the product of two distinct primes, such that\[\frac{a}{b}=\frac{1}{n_1}+\cdots+\frac{1}{n_k}?\] | Erdős Problems (#306, https://www.erdosproblems.com/306). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.306). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/306",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/306 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,040 | EP-311 | Erdős Problem #311 | Let $\delta(N)$ be the minimal non-zero value of $\lvert 1-\sum_{n\in A}\frac{1}{n}\rvert$ as $A$ ranges over all subsets of $\{1,\ldots,N\}$. Is it true that\[\delta(N)=e^{-(c+o(1))N}\]for some constant $c\in (0,1)$? | Erdős Problems (#311, https://www.erdosproblems.com/311). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.311). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/311",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/311 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,041 | EP-312 | Erdős Problem #312 | Does there exist some $c>0$ such that, for any $K>1$, whenever $A$ is a sufficiently large finite multiset of positive integers with $\sum_{n\in A}\frac{1}{n}>K$ there exists some $S\subseteq A$ such that\[1-e^{-cK} < \sum_{n\in S}\frac{1}{n}\leq 1?\] | Erdős Problems (#312, https://www.erdosproblems.com/312). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.312). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/312",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/312 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,042 | EP-313 | Erdős Problem #313 | Are there infinitely many solutions to\[\frac{1}{p_1}+\cdots+\frac{1}{p_k}=1-\frac{1}{m},\]where $m\geq 2$ is an integer and $p_1<\cdots<p_k$ are distinct primes? | Erdős Problems (#313, https://www.erdosproblems.com/313). Maintainer status: OPEN. OEIS: A054377. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.313). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/313",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/313 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,043 | EP-317 | Erdős Problem #317 | Is there some constant $c>0$ such that for every $n\geq 1$ there exists some $\delta_k\in \{-1,0,1\}$ for $1\leq k\leq n$ with\[0< \left\lvert \sum_{1\leq k\leq n}\frac{\delta_k}{k}\right\rvert < \frac{c}{2^n}?\]Is it true that for sufficiently large $n$, for any $\delta_k\in \{-1,0,1\}$,\[\left\lvert \sum_{1\leq k\leq... | Erdős Problems (#317, https://www.erdosproblems.com/317). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.317). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/317",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/317 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,044 | EP-318 | Erdős Problem #318 | Let $A\subseteq \mathbb{N}$ be an infinite arithmetic progression and $f:A\to \{-1,1\}$ be a non-constant function. Must there exist a finite non-empty $S\subset A$ such that\[\sum_{n\in S}\frac{f(n)}{n}=0?\]What about if $A$ is an arbitrary set of positive density? What if $A$ is the set of squares excluding $1$? | Erdős Problems (#318, https://www.erdosproblems.com/318). Maintainer status: SOLVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.318). | 1 | solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/318",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | The maintained Erdős Problems source lists problem 318 as “solved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/318",
"label": "Erdős Problems #318: solved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #318: solved (Lean): https://www.erdosproblems.com/318
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/318 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,045 | EP-319 | Erdős Problem #319 | What is the size of the largest $A\subseteq \{1,\ldots,N\}$ such that there is a function $\delta:A\to \{-1,1\}$ such that\[\sum_{n\in A}\frac{\delta_n}{n}=0\]and\[\sum_{n\in A'}\frac{\delta_n}{n}\neq 0\]for all non-empty $A'\subsetneq A$? | Erdős Problems (#319, https://www.erdosproblems.com/319). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.319). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/319",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/319 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,046 | EP-320 | Erdős Problem #320 | Let $S(N)$ count the number of distinct sums of the form $\sum_{n\in A}\frac{1}{n}$ for $A\subseteq \{1,\ldots,N\}$. Estimate $S(N)$. | Erdős Problems (#320, https://www.erdosproblems.com/320). Maintainer status: SOLVED. OEIS: A072207. | 1 | solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/320",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | The maintained Erdős Problems source lists problem 320 as “solved” on 2026-09-27. No Lean verification is inferred from the existence of a formalized statement.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/320",
"label": "Erdős Problems #320: solved"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggingface.c... | 2026-09-27T00:00:00 | Erdős Problems #320: solved: https://www.erdosproblems.com/320
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/320 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,047 | EP-321 | Erdős Problem #321 | What is the size of the largest $A\subseteq \{1,\ldots,N\}$ such that all sums $\sum_{n\in S}\frac{1}{n}$ are distinct for $S\subseteq A$? | Erdős Problems (#321, https://www.erdosproblems.com/321). Maintainer status: SOLVED. OEIS: A384927, A391592. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.321). | 1 | solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/321",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | The maintained Erdős Problems source lists problem 321 as “solved” on 2026-09-27. No Lean verification is inferred from the existence of a formalized statement.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/321",
"label": "Erdős Problems #321: solved"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggingface.c... | 2026-09-27T00:00:00 | Erdős Problems #321: solved: https://www.erdosproblems.com/321
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/321 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,048 | EP-322 | Erdős Problem #322 | Let $k\geq 3$ and $A\subset \mathbb{N}$ be the set of $k$th powers. What is the order of growth of $1_A^{(k)}(n)$, i.e. the number of representations of $n$ as the sum of $k$ many $k$th powers? Does there exist some $c>0$ and infinitely many $n$ such that\[1_A^{(k)}(n) >n^c?\] | Erdős Problems (#322, https://www.erdosproblems.com/322). Maintainer status: OPEN. OEIS: A025456, A025418. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.322). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/322",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powers"
] | null | null | null | null | https://www.erdosproblems.com/322 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,049 | EP-323 | Erdős Problem #323 | Let $1\leq m\leq k$ and $f_{k,m}(x)$ denote the number of integers $\leq x$ which are the sum of $m$ many nonnegative $k$th powers. Is it true that\[f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}\]for all $\epsilon>0$? Is it true that if $m<k$ then\[f_{k,m}(x) \gg x^{m/k}\]for sufficiently large $x$? | Erdős Problems (#323, https://www.erdosproblems.com/323). Maintainer status: OPEN. OEIS: A004825, A004831, A004832, A004833, A004842, A004843, A004844, A004845, A004857, A004869. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.323). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/323",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powers"
] | null | null | null | null | https://www.erdosproblems.com/323 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,050 | EP-324 | Erdős Problem #324 | Does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ such that all the sums $f(a)+f(b)$ with $a<b$ nonnegative integers are distinct? | Erdős Problems (#324, https://www.erdosproblems.com/324). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.324). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/324",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powers",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/324 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,051 | EP-325 | Erdős Problem #325 | Let $k\geq 3$ and $f_{k,3}(x)$ denote the number of integers $\leq x$ which are the sum of three nonnegative $k$th powers. Is it true that\[f_{k,3}(x) \gg x^{3/k}\]or even $\gg_\epsilon x^{3/k-\epsilon}$? | Erdős Problems (#325, https://www.erdosproblems.com/325). Maintainer status: OPEN. OEIS: A004825, A004832, A004843, A004854, A004865. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.325). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/325",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powers"
] | null | null | null | null | https://www.erdosproblems.com/325 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,052 | EP-326 | Erdős Problem #326 | Does there exist $A=\{a_1<a_2<\cdots\}\subset \mathbb{N}$ which is a minimal basis of order $2$ (i.e. every large integer is the sum of $2$ elements from $A$, and no proper subset of $A$ has this property), such that\[\lim_{k\to \infty}\frac{a_k}{k^2}=c\]for some $c\neq 0$? | Erdős Problems (#326, https://www.erdosproblems.com/326). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.326). | 1 | partially_solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/326",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/326 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,053 | EP-327 | Erdős Problem #327 | Suppose $A\subseteq \{1,\ldots,N\}$ is such that if $a,b\in A$ and $a\neq b$ then $a+b\nmid ab$. Can $A$ be 'substantially more' than the odd numbers?
What if $a,b\in A$ with $a\neq b$ implies $a+b\nmid 2ab$? Must $\lvert A\rvert=o(N)$? | Erdős Problems (#327, https://www.erdosproblems.com/327). Maintainer status: OPEN. OEIS: A384927. | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/327",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/327 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,054 | EP-329 | Erdős Problem #329 | Suppose $A\subseteq \mathbb{N}$ is a Sidon set. How large can\[\limsup_{N\to \infty}\frac{\lvert A\cap \{1,\ldots,N\}\rvert}{N^{1/2}}\]be? | Erdős Problems (#329, https://www.erdosproblems.com/329). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.329). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/329",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/329 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,055 | EP-330 | Erdős Problem #330 | Does there exist a minimal basis with positive density, say $A\subset\mathbb{N}$, such that for any $n\in A$ the (upper) density of integers which cannot be represented without using $n$ is positive? | Erdős Problems (#330, https://www.erdosproblems.com/330). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.330). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/330",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | The maintained Erdős Problems source lists problem 330 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/330",
"label": "Erdős Problems #330: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #330: proved (Lean): https://www.erdosproblems.com/330
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/330 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,056 | EP-332 | Erdős Problem #332 | Let $A\subseteq \mathbb{N}$ and $D(A)$ be the set of those numbers which occur infinitely often as $a_1-a_2$ with $a_1,a_2\in A$. What conditions on $A$ are sufficient to ensure $D(A)$ has bounded gaps? | Erdős Problems (#332, https://www.erdosproblems.com/332). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.332). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/332",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/332 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,057 | EP-334 | Erdős Problem #334 | Find the best function $f(n)$ such that every $n$ can be written as $n=a+b$ where both $a,b$ are $f(n)$-smooth (that is, are not divisible by any prime $p>f(n)$.) | Erdős Problems (#334, https://www.erdosproblems.com/334). Maintainer status: OPEN. OEIS: A062241, A045535. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/334",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/334 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,058 | EP-335 | Erdős Problem #335 | Let $d(A)$ denote the density of $A\subseteq \mathbb{N}$. Characterise those $A,B\subseteq \mathbb{N}$ with positive density such that\[d(A+B)=d(A)+d(B).\] | Erdős Problems (#335, https://www.erdosproblems.com/335). Maintainer status: OPEN. | 1 | partially_solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/335",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/335 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,059 | EP-336 | Erdős Problem #336 | For $r\geq 2$ let $h(r)$ be the maximal finite $k$ such that there exists a basis $A\subseteq \mathbb{N}$ of order $r$ (so every large integer is the sum of at most $r$ integers from $A$) and exact order $k$ (so every large integer is the sum of exactly $k$ integers from $A$).
Find the value of\[\lim_r \frac{h(r)}{r^2... | Erdős Problems (#336, https://www.erdosproblems.com/336). Maintainer status: OPEN. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/336",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/336 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,060 | EP-338 | Erdős Problem #338 | The restricted order of a basis is the least integer $t$ (if it exists) such that every large integer is the sum of at most $t$ distinct summands from $A$. What are necessary and sufficient conditions that this exists? Can it be bounded (when it exists) in terms of the order of the basis? What are necessary and suffici... | Erdős Problems (#338, https://www.erdosproblems.com/338). Maintainer status: OPEN. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/338",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/338 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,061 | EP-340 | Erdős Problem #340 | Let $A=\{1,2,4,8,13,21,31,45,66,81,97,\ldots\}$ be the greedy Sidon sequence: we begin with $1$ and iteratively include the next smallest integer that preserves the Sidon property (i.e. there are no non-trivial solutions to $a+b=c+d$). What is the order of growth of $A$? Is it true that\[\lvert A\cap \{1,\ldots,N\}\rve... | Erdős Problems (#340, https://www.erdosproblems.com/340). Maintainer status: OPEN. OEIS: A080200, A005282. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.340). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/340",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/340 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,062 | EP-341 | Erdős Problem #341 | Let $A=\{a_1<\cdots<a_k\}$ be a finite set of positive integers and extend it to an infinite sequence $\overline{A}=\{a_1<a_2<\cdots \}$ by defining $a_{n+1}$ for $n\geq k$ to be the least integer exceeding $a_n$ which is not of the form $a_i+a_j$ with $i,j\leq n$. Is it true that the sequence of differences $a_{m+1}-a... | Erdős Problems (#341, https://www.erdosproblems.com/341). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.341). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/341",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/341 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
2,063 | EP-342 | Erdős Problem #342 | With $a_1=1$ and $a_2=2$ let $a_{n+1}$ for $n\geq 2$ be the least integer $>a_n$ which can be expressed uniquely as $a_i+a_j$ for $i<j\leq n$.
What can be said about this sequence? Do infinitely many pairs $a,a+2$ occur? Does this sequence eventually have periodic differences? Is the density $0$? | Erdős Problems (#342, https://www.erdosproblems.com/342). Maintainer status: OPEN. OEIS: A002858. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.342). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/342",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/342 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
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