id stringlengths 6 8 | alias stringlengths 24 50 | problem stringlengths 24 5.03k | answer int64 -16,384 80.2B | graph stringlengths 0 6.44k | domain stringclasses 4
values | secondary_domain stringclasses 4
values | goal stringclasses 4
values | evaluator_id stringclasses 1
value | root_lemma stringclasses 89
values | lemma_paths listlengths 0 5 | recipe_id stringlengths 0 6 | seed_template_id stringclasses 96
values | ending_id stringclasses 13
values | olympiad_level int64 2 9 | num_spawns int64 0 3 ⌀ | lemma_set listlengths 1 7 ⌀ | num_lemmas int64 1 7 ⌀ | generation_time float64 0 43.9 | created_at stringlengths 27 27 | verification dict | problem_hash stringlengths 6 6 | parent_id stringlengths 0 6 | variant stringclasses 3
values | license stringclasses 1
value | llm_solvers listlengths 1 13 ⌀ | solution_status int64 0 2 ⌀ | lemma_applicability listlengths 0 12 | irt_difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
58c0b0 | sequence_lucas_compute_v1_124444284_4323 | Let $n = \sum_{k=1}^{6} k$. Define $L_n$ to be the $n$-th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_m = L_{m-1} + L_{m-2}$ for $m \ge 3$. Find the remainder when $86713 \cdot L_n$ is divided by $85386$. | 32,972 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"_c": Const(86713),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(85386)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T05:55:18.108453Z | {
"verified": true,
"answer": 32972,
"timestamp": "2026-02-08T05:55:18.109268Z"
} | 45d52e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 925
},
"timestamp": "2026-02-12T16:37:45.610Z",
"answer": 32972
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
80b17f | antilemma_sum_equals_v1_1470522791_1886 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 69$, $1 \leq i \leq 68$, and $1 \leq j \leq 69$. Let $Q$ be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|x| + 2$. Find the value of $Q$. | 120 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(69)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(68)), right=IntegerRange(start=Const(1), end=Const(69))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.11 | 2026-02-08T14:03:40.603132Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T14:03:40.713467Z"
} | fabb65 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T19:47:17.460Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
f3b144 | antilemma_cartesian_v1_1978505735_3318 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 13$ and $1 \leq b \leq 16$. Compute $19044 - x$. | 18,836 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(16)))),
"_c": Const(19044),
"Q": Sub(Ref("_c"), Ref("x")),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T17:33:35.767364Z | {
"verified": true,
"answer": 18836,
"timestamp": "2026-02-08T17:33:35.768399Z"
} | a2e4fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 316
},
"timestamp": "2026-02-24T22:48:05.377Z",
"answer": 18836
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
181597 | antilemma_k3_v1_655260480_861 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $98796$. Let $c = 76197$. Compute the value of $Q = (c \cdot x) \bmod 88732$. | 24,664 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=98796), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(76197),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(88732)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:40:11.441973Z | {
"verified": true,
"answer": 24664,
"timestamp": "2026-02-08T15:40:11.443182Z"
} | 011acb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 985
},
"timestamp": "2026-02-16T12:48:28.674Z",
"answer": 24664
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2f5191 | comb_count_partitions_v1_349078426_1537 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 44$ and $n$ is divisible by 44. Let $s$ be the sum of all elements in $S$. Let $p(s)$ denote the number of integer partitions of $s$. Find the remainder when $44121 \cdot p(s)$ is divided by $69710$. | 64,085 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(44)), Eq(Mod(value=Var("n"), modulus=Const(44)), Const(0))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mo... | COMB | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_count_partitions_v1 | null | 2 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T13:42:01.951141Z | {
"verified": true,
"answer": 64085,
"timestamp": "2026-02-08T13:42:01.952349Z"
} | 93d4ac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 2503
},
"timestamp": "2026-02-24T18:57:36.464Z",
"answer": 64085
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8_SUM",... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
44bfb3 | nt_sum_totient_over_divisors_v1_238844314_169 | Let $n_0$ be the number of integers $t$ such that $8 \leq t \leq 4450$ and there exist integers $a$ and $b$ with $1 \leq a \leq 581$, $1 \leq b \leq 515$, and $t = 5a + 3b$. Let $n$ be the number of positive integers at most $n_0$ whose digit sum is even. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $... | 2,217 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=581)), Geq(left=Var... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/L3B"
] | db250f | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T13:09:07.981325Z | {
"verified": true,
"answer": 2217,
"timestamp": "2026-02-08T13:09:07.992520Z"
} | e0eea1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 6889
},
"timestamp": "2026-02-15T10:14:30.887Z",
"answer": 2217
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"le... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
230b7d | nt_sum_gcd_range_mod_v1_1520064083_7748 | Let $N$ be the number of positive integers $n \leq 15552$ such that $9$ divides the $n$-th Fibonacci number. Let $k = 96$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $M = 10691$, and let $\text{result}$ be the remainder when $\text{sum}$ is divided by $M$. Let $Q = 11111 - \text{result}$. Compute $Q$. | 3,575 | graphs = [
Graph(
let={
"_n": Const(15552),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(9), dividend=Fibonacci(arg=Var(name='n')))))),
"k": Const(96),
"M": Const(10691)... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.061 | 2026-02-08T09:17:20.086760Z | {
"verified": true,
"answer": 3575,
"timestamp": "2026-02-08T09:17:20.147481Z"
} | c32000 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 3021
},
"timestamp": "2026-02-14T02:14:38.552Z",
"answer": 3575
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a43333 | nt_count_divisible_and_v1_1431428450_17 | Let $n = 4$. Define
$$
S = \left\{ (k,j) \mid k \in \{1,2,3,4\},\ j \in \{1,2\} \right\}.
$$
Let $A$ be the sum of all values of $k$ as $(k,j)$ ranges over $S$. Define $d_1 = \frac{n \cdot A}{8}$.
Let $d_2$ be the number of integers $t$ such that $21 \leq t \leq 66$ and there exist integers $a$ and $b$ with $1 \leq a ... | 4,979 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(298740),
"d1": Div(Mul(Ref("_n"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), righ... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC",
"LIN_FORM"
] | 5650d8 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 12.002 | 2026-02-08T13:07:26.934994Z | {
"verified": true,
"answer": 4979,
"timestamp": "2026-02-08T13:07:38.937072Z"
} | ddc1c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1379
},
"timestamp": "2026-02-15T11:01:41.709Z",
"answer": 4979
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7afa71 | alg_qf_psd_min_v1_1218484723_16 | Let $S = \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 1053,\ 1 \leq b \leq 1152 \text{ such that } t = 3a + 5b,\ 8 \leq t \leq 8919 \}\right|$. Let $P = \min\{ x + y : x > 0, y > 0,\ xy = 13764100 \}$ and $D = \max \{ d_1 : d_1 \geq 1,\ d_1 \leq 8904,\ d_1 \mid 79539432 \}$. Find the minim... | 80,136 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_m")), Geq(Var("b"), Const(1)), Leq(Var("b... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"LIN_FORM",
"B3"
] | 644579 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"MAX_DIVISOR"
] | 3 | 0.283 | 2026-02-25T01:41:52.546483Z | {
"verified": true,
"answer": 80136,
"timestamp": "2026-02-25T01:41:52.829656Z"
} | 304c56 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 366,
"completion_tokens": 22113
},
"timestamp": "2026-03-28T21:34:56.206Z",
"answer": 80141
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
bc5b6c | modular_count_residue_v1_1520064083_7266 | Let $m$ be the number of integers $t$ such that $7 \leq t \leq 32$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 4a + 3b$. Let $r = 17$. Let $N = 80758$ and $U = 71824$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq U$ and $n \equiv r \pmod{m}$. C... | 50,881 | graphs = [
Graph(
let={
"_n": Const(80758),
"upper": Const(71824),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 6.103 | 2026-02-08T08:52:04.339566Z | {
"verified": true,
"answer": 50881,
"timestamp": "2026-02-08T08:52:10.442517Z"
} | 73e231 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 2022
},
"timestamp": "2026-02-13T22:49:49.725Z",
"answer": 50881
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
200f58 | nt_max_prime_below_v1_798873815_106 | Let $a=69$ and $b=71$. Let
$$u=\sum_{d\mid \gcd(a,b)} \mu(d),$$
where $\mu$ is the Möbius function.
Let $n=112$ and
$$s=\sum_{d\mid n} \mu(d).$$
Let $U=21316$. Consider all integers $N$ such that
\begin{itemize}
\item $N$ is prime,
\item $N\le U$, and
\item $N\ge M$, where $M$ is the number of integers $m$ with $1\le... | 58,161 | graphs = [
Graph(
let={
"a": Const(69),
"b": Const(71),
"u": SumOverDivisors(n=GCD(a=Ref(name='a'), b=Ref(name='b')), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Const(112),
"s": SumOverDivisors(n=Ref(name='n'), var='d', expr=MoebiusMu(n=Var(na... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MOBIUS_COPRIME",
"MOBIUS_SUM",
"L3C"
] | aef845 | nt_max_prime_below_v1 | two_moduli | 5 | 2 | [
"L3C",
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME",
"MOBIUS_SUM"
] | 4 | 2.403 | 2026-02-08T02:26:11.389662Z | {
"verified": true,
"answer": 58161,
"timestamp": "2026-02-08T02:26:13.792509Z"
} | 4e9076 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 431,
"completion_tokens": 4684
},
"timestamp": "2026-02-08T19:00:29.314Z",
"answer": 58161
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
89fa65 | comb_count_derangements_v1_784195855_7378 | Let $m = 14$. Let $k$ be the number of positive integers $n$ such that $1 \le n \le 31$ and $\gcd(n, m) = 1$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = k$. Compute the value of $!n$, the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(31)), Eq(GCD(a=Var("n"), b=Ref("_m")), Const(1))))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var... | NT | COMB | COUNT | sympy | C4 | [
"C4/COMB1"
] | 2d483a | comb_count_derangements_v1 | null | 5 | 0 | [
"C4",
"COMB1"
] | 2 | 0.001 | 2026-02-08T09:14:30.152584Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T09:14:30.154023Z"
} | 412c43 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1257
},
"timestamp": "2026-02-14T02:29:59.504Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dd2dab | nt_max_prime_below_v1_1742523217_5023 | Let $P$ be the set of all positive integers $p$ for which there exists an integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $P$. Let $T$ be the set of all prime numbers $n$ such that $n \geq L$ and $n \leq 38416$. Determine the value of the largest element in $T$. | 38,393 | graphs = [
Graph(
let={
"upper": Const(38416),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.997 | 2026-02-08T10:45:34.669339Z | {
"verified": true,
"answer": 38393,
"timestamp": "2026-02-08T10:45:35.665910Z"
} | a51773 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 4216
},
"timestamp": "2026-02-14T08:37:53.804Z",
"answer": 38393
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6778b8 | sequence_fibonacci_compute_v1_1520064083_7388 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq \sum_{i=1}^{23} i$ and $9$ divides the $k$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \geq 3$. Compute the $n$-th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": Const(9),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(23), expr=Var("k"))), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/COUNT_FIB_DIVISIBLE"
] | a53b1f | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T09:00:31.913397Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T09:00:31.915171Z"
} | fdfe77 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1728
},
"timestamp": "2026-02-13T23:31:30.472Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"stat... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
4d3a9c | diophantine_sum_product_min_v1_238844314_1158 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1382976$. Let $P$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the value of $x$ such that $1 \leq x \leq 96$ and $x(97 - x) = P$. | 48 | graphs = [
Graph(
let={
"_n": Const(96),
"S": Const(97),
"P": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1382976)))), ex... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.089 | 2026-02-08T14:00:24.136527Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T14:00:24.225223Z"
} | 86247f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 2109
},
"timestamp": "2026-02-15T22:53:16.405Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ae9767 | comb_count_partitions_v1_151522320_1991 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 97$ and $\gcd(k, 20) = 1$. Let $p(n)$ denote the number of integer partitions of $n$. Let $c$ be the number of integers $t$ with $11 \leq t \leq 2046$ that can be expressed as $t = 7a + 4b$ for some positive integers $a \leq 34$ and $b \leq 452$. C... | 37,872 | graphs = [
Graph(
let={
"_m": Const(97),
"_n": Const(67039),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"result": Partition(arg=Ref(name='n'))... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"C4"
] | 48f970 | comb_count_partitions_v1 | negation_mod | 7 | 0 | [
"C4",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T04:30:19.606039Z | {
"verified": true,
"answer": 37872,
"timestamp": "2026-02-08T04:30:19.609399Z"
} | 90c641 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 3908
},
"timestamp": "2026-02-12T00:51:01.853Z",
"answer": 37872
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
288cd2 | comb_count_derangements_v1_2051736721_4360 | Let $S$ be the set of all prime numbers $p$ such that $2 \leq p \leq 7$. Let $n$ be the largest prime number in $S$. Compute the number of derangements of a set with $n$ elements. Determine the value of this number. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(2)), Leq(Var("n2"), Const(7)), IsPrime(Var("n2")))))), IsPrime... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T17:55:34.018801Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:55:34.021783Z"
} | 59c0a9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 892
},
"timestamp": "2026-02-18T10:05:55.490Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
77fb8f | comb_count_permutations_fixed_v1_1218484723_713 | Let $D_n$ denote the number of derangements of $n$ elements. Let $k = \binom{12}{12} - \binom{10}{0}$ and $n = 7$. Define $M = \binom{n}{k} \cdot D_{n - k}$. Compute $41371 - M$. | 39,517 | graphs = [
Graph(
let={
"n": Const(7),
"k": Sub(Binom(n=Const(12), k=Const(12)), Binom(n=Const(10), k=Const(0))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"_c": Const(41371),
"Q":... | COMB | null | COUNT | sympy | ZERO_BINOM_N | [
"ZERO_BINOM_N",
"ONE_BINOM_0"
] | 1c72d2 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"ONE_BINOM_0",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-02-25T02:27:19.653627Z | {
"verified": true,
"answer": 39517,
"timestamp": "2026-02-25T02:27:19.655282Z"
} | c4a479 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 674
},
"timestamp": "2026-03-10T00:56:16.484Z",
"answer": 39517
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
dcf3e4 | geo_visible_lattice_v1_124444284_1231 | Let $n = 120$. Define a visible lattice point as an ordered pair $(x, y)$ of positive integers with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$.\\
Let $P$ be the number of visible lattice points for this $n$. Compute the remainder when $35960 \cdot P$ is divided by $72691$. | 71,602 | graphs = [
Graph(
let={
"n": Const(120),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(35960),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(72691)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.52 | 2026-02-08T03:45:54.653081Z | {
"verified": true,
"answer": 71602,
"timestamp": "2026-02-08T03:45:55.173118Z"
} | dcad91 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:55:19.723Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
cb653c | nt_sum_over_divisible_v1_1742523217_3189 | Let $S$ be the set of all nonnegative integers $j$ with $0 \leq j \leq 625$ such that $\binom{625}{j}$ is odd. Let $U$ be the sum of all elements in $S$. Let $d$ be a positive divisor of $100370000$ that is at most $U$. Define $\text{upper}$ to be the maximum such $d$. Compute the sum of all positive integers $n$ such ... | 53,052 | graphs = [
Graph(
let={
"_n": Const(90708),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(625)), Eq(Mod(value=Binom(n=Const(6... | NT | null | SUM | sympy | V8 | [
"V8/MAX_DIVISOR"
] | 0dd13c | nt_sum_over_divisible_v1 | null | 7 | 0 | [
"MAX_DIVISOR",
"V8"
] | 2 | 0.315 | 2026-02-08T05:42:47.359431Z | {
"verified": true,
"answer": 53052,
"timestamp": "2026-02-08T05:42:47.674728Z"
} | 3146ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 3935
},
"timestamp": "2026-02-12T12:41:12.717Z",
"answer": 53052
},
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
fbd01c | nt_num_divisors_compute_v1_124444284_1452 | Determine the number of positive integers $n$ such that $1 \leq n \leq 443$ and the sum of the (decimal) digits of $n$ is odd. Compute the number of positive divisors of this count. | 8 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(443)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"result": NumDivisors(n=Ref("n")),
},
... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"L3B"
] | cc148f | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"L3B"
] | 2 | 0.022 | 2026-02-08T03:53:01.291732Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T03:53:01.313514Z"
} | 5791a6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1480
},
"timestamp": "2026-02-10T16:15:15.338Z",
"answer": 8
},
{
"id":... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
bdbf5d | lin_form_endings_v1_1742523217_1217 | Let $ a = 27 $ and $ b = 36 $. Let $ \ell $ be the least common multiple of $ a $ and $ b $. Define $ s = \ell + a + b $. Let $ t = 11690 \cdot s $, and let $ x $ be the remainder when $ t $ is divided by 54276. Compute $ x $. | 45,054 | graphs = [
Graph(
let={
"a_coeff": Const(27),
"b_coeff": Const(36),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:32:16.193800Z | {
"verified": true,
"answer": 45054,
"timestamp": "2026-02-08T03:32:16.194808Z"
} | 44ab35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 675
},
"timestamp": "2026-02-10T05:12:03.624Z",
"answer": 45054
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
fd06ce | antilemma_sum_equals_v1_1439011603_1029 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 112$. Let $N$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 56$ and $1 \leq j \leq 56$ such that $i + j = N$. Let $x$ be the number of elements in $T$. Compute $2... | 24,281 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(112))))),
"x... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.009 | 2026-02-08T15:52:41.339796Z | {
"verified": true,
"answer": 24281,
"timestamp": "2026-02-08T15:52:41.348715Z"
} | 99cd05 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1040
},
"timestamp": "2026-02-24T18:53:50.325Z",
"answer": 24281
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
996bae | lin_form_endings_v1_1520064083_10078 | Let $a = 42$ and $b = 18$. Compute the remainder when $10797 \cdot \text{lcm}(a, b)$ is divided by $68903$. | 51,265 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(18),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(10797),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(68903),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T11:11:55.733325Z | {
"verified": true,
"answer": 51265,
"timestamp": "2026-02-08T11:11:55.733701Z"
} | f3f4df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 617
},
"timestamp": "2026-02-14T10:45:53.991Z",
"answer": 51265
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
61262e | comb_count_derangements_v1_1116507919_32 | Let $d_1$ be the smallest integer $d \geq 2$ that divides 900. Let $n$ be the smallest integer $d \geq d_1$ that divides 143143. Define $a_n = !n$, the number of derangements of $n$ elements. Let $c = 58549$ and $N = 99440$. Compute the remainder when $c \cdot a_n$ is divided by $N$. | 60,806 | graphs = [
Graph(
let={
"_n": Const(99440),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(900)))))), Divides(divisor=Var("d"), divide... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MIN_PRIME_FACTOR"
] | 16e0a1 | comb_count_derangements_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T02:23:51.383107Z | {
"verified": true,
"answer": 60806,
"timestamp": "2026-02-08T02:23:51.384751Z"
} | 4663ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1818
},
"timestamp": "2026-02-08T18:31:52.831Z",
"answer": 60806
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -0.18,
"mid": 1.41,
"hi": 2.79
} | ||
4dadc9 | lin_form_endings_v1_1918700295_2527 | Let $a = 105$ and $b = 60$. Let $g = \gcd(a, b)$. Compute the remainder when $15000 \cdot g$ is divided by $50267$. | 23,932 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(60),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(15000),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(50267),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T07:56:50.275031Z | {
"verified": true,
"answer": 23932,
"timestamp": "2026-02-08T07:56:50.275630Z"
} | 761a89 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 436
},
"timestamp": "2026-02-13T13:50:20.981Z",
"answer": 23932
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
bb8eb4 | algebra_quadratic_discriminant_v1_1915831931_2033 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 88045650$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $S$. Now let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq N$ and $3$ divides the $n$th Fibonacci num... | 1 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"COPRIME_PAIRS/COUNT_FIB_DIVISIBLE/COPRIME_PAIRS"
] | 02cb16 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 3 | 0.058 | 2026-02-08T16:35:43.019274Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:35:43.076824Z"
} | d0c8d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 1867
},
"timestamp": "2026-02-17T07:35:29.674Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fa0edf | nt_count_coprime_and_v1_655260480_3070 | Let $n = 44121$. Define $U$ to be the number of positive integers $k$ such that $1 \leq k \leq 14571$ and $\gcd(k, 20) = 1$. Let $R$ be the number of positive integers $m$ such that $1 \leq m \leq U$, $\gcd(m, 3) = 1$, and $\gcd(m, 7) = 1$. Compute the remainder when $n \cdot R$ is divided by $91232$. | 83,531 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(14571)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"k1": Const(3),
"k2": Const(7),
"res... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.609 | 2026-02-08T17:09:33.793585Z | {
"verified": true,
"answer": 83531,
"timestamp": "2026-02-08T17:09:34.403007Z"
} | c1bb5a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1590
},
"timestamp": "2026-02-17T21:02:40.445Z",
"answer": 83531
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c3d22c | modular_count_residue_v1_397696148_1155 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Define $r$ to be the minimum value of $x + y$ over all pairs in $S$. Let $N$ be the number of positive integers $n$, with $1 \le n \le 90000$, such that $n \equiv r \pmod{20}$. Compute $38809 - N$. | 34,309 | graphs = [
Graph(
let={
"upper": Const(90000),
"m": Const(20),
"r": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(49)))), e... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 4 | 0 | [
"B3"
] | 1 | 5.553 | 2026-02-08T12:23:35.162144Z | {
"verified": true,
"answer": 34309,
"timestamp": "2026-02-08T12:23:40.714686Z"
} | 4c37da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 552
},
"timestamp": "2026-02-15T00:33:00.892Z",
"answer": 34309
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
89078e | diophantine_sum_product_min_v1_865884756_1094 | Let $ m = 66 $. Let $ S $ be the largest prime number $ n $ such that $ 2 \leq n \leq 68 $. Define $ P $ to be the number of integers $ t $ such that $ 38 \leq t \leq 3419 $ and there exist positive integers $ a $, $ b $ with $ 1 \leq a \leq 148 $, $ 1 \leq b \leq 50 $, and $ t = 21a + 6b + 11 $. Let $ \text{result} $ ... | 1,336 | graphs = [
Graph(
let={
"_m": Const(66),
"_n": Const(2),
"S": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(68)), IsPrime(Var("n"))))),
"P": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"B1",
"MAX_PRIME_BELOW",
"LIN_FORM"
] | db7bcb | diophantine_sum_product_min_v1 | quadratic_mod | 7 | 0 | [
"B1",
"LIN_FORM",
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 4 | 0.07 | 2026-02-08T15:47:16.812153Z | {
"verified": true,
"answer": 1336,
"timestamp": "2026-02-08T15:47:16.882369Z"
} | 505cea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 4273
},
"timestamp": "2026-02-16T13:34:52.725Z",
"answer": 1336
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_P... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6e031 | comb_bell_compute_v1_717093673_1953 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, $5 \leq t \leq 15$, and $t = 3a + 2b$. Let $n$ be the number of elements in $S$. Let $B_n$ denote the Bell number, which counts the number of partitions of a set of $n$ elements. Compute the rema... | 60,193 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:24:53.257421Z | {
"verified": true,
"answer": 60193,
"timestamp": "2026-02-08T16:24:53.260023Z"
} | 7d162b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1868
},
"timestamp": "2026-02-24T20:56:41.556Z",
"answer": 60193
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
e1f368 | modular_mod_compute_v1_677425708_1757 | Let $a = 47$ and $m = 2028$. Let $r = a \bmod m$. Let $p$ be the largest prime number at most $3008$, and let $q$ be the largest prime number at most $313$. Compute the value of
$$
(r \bmod 317) + p \cdot (r \bmod q),
$$
and then find the remainder when this result is divided by $83194$. | 57,900 | graphs = [
Graph(
let={
"_m": Const(83194),
"_n": Const(2),
"a": Const(47),
"m": Const(2028),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Va... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | modular_mod_compute_v1 | two_moduli | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T04:26:15.260427Z | {
"verified": true,
"answer": 57900,
"timestamp": "2026-02-08T04:26:15.263273Z"
} | afe759 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1923
},
"timestamp": "2026-02-10T00:29:01.974Z",
"answer": 57900
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
87fe02 | modular_mod_compute_v1_601307018_6483 | Let $m$ be the number of ordered pairs $(a1, b)$ of positive integers with $1 \leq a1, b \leq 40$ such that $25b^2 + 10a1^2 - 18a1b \leq 18080$. Let $M = 28900 \bmod m$. Find the remainder when $44121M$ is divided by $76477$. | 20,339 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(28900),
"m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Sum(Mul(Const... | NT | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | modular_mod_compute_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.003 | 2026-03-10T07:07:50.121171Z | {
"verified": true,
"answer": 20339,
"timestamp": "2026-03-10T07:07:50.124560Z"
} | 1fba3b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 7124
},
"timestamp": "2026-04-19T04:32:09.665Z",
"answer": 20339
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
deebd3 | nt_count_coprime_v1_1742523217_4832 | Let $k$ be the sum of all real solutions $x$ to the equation
$$
x^2 - 4x - 7052 = \sum_{d \mid \gcd(12,12)} \mu(d),
$$
where $\mu$ denotes the M\"obius function. Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 20164$ such that $\gcd(n,k) = \phi(1)$, where $\phi$ is Euler's totient function. Compute $... | 10,082 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(20164),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-4), Var("x")), Const(-7052)), SumOverDivisors(n=GCD(a=Const(value=12), b=Const(value=12)), var='d', expr=Moe... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"VIETA_SUM",
"ONE_PHI_1"
] | c2c872 | nt_count_coprime_v1 | null | 6 | 0 | [
"MOBIUS_COPRIME",
"ONE_PHI_1",
"VIETA_SUM"
] | 3 | 9.076 | 2026-02-08T09:18:45.298280Z | {
"verified": true,
"answer": 10082,
"timestamp": "2026-02-08T09:18:54.374436Z"
} | 0075a5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 798
},
"timestamp": "2026-02-21T03:46:49.185Z",
"answer": 10082
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
294d8f | sequence_lucas_compute_v1_48377204_485 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 570$ and $F_{n_1}$, the $n_1$th Fibonacci number, is divisible by 20. Compute $L_n$, the $n$th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_n": Const(570),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Divides(divisor=Const(20), dividend=Fibonacci(arg=Var(name='n1')))))),
"result": Lucas(arg=Ref(name='n')),
... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_lucas_compute_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T15:30:52.749560Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T15:30:52.751297Z"
} | da98f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1161
},
"timestamp": "2026-02-16T07:32:33.065Z",
"answer": 9349
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3f1f4d | sequence_count_fib_divisible_v1_971394319_535 | Let $n$ be a positive integer such that $1 \leq n \leq 627$ and $9$ divides the $n$th Fibonacci number. Compute the number of such integers $n$. | 52 | graphs = [
Graph(
let={
"upper": Const(627),
"d": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM",
"B3"
] | 688dbe | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.205 | 2026-02-08T13:09:49.199457Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T13:09:49.404013Z"
} | 3eddd1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1704
},
"timestamp": "2026-02-15T09:53:31.213Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e240a8 | antilemma_sum_equals_v1_655260480_3012 | Let $n = 69$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 68$, $1 \leq j \leq 69$, and $i + j = n$. | 68 | graphs = [
Graph(
let={
"_n": Const(69),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(68)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.141 | 2026-02-08T17:08:36.691855Z | {
"verified": true,
"answer": 68,
"timestamp": "2026-02-08T17:08:36.833189Z"
} | 7b38a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 860
},
"timestamp": "2026-02-24T22:20:03.719Z",
"answer": 68
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
9541d2 | diophantine_product_count_v1_1915831931_4127 | Let $k$ be the sum of all real solutions $x$ to the equation $x^2 - 180x + 8096 = 0$. Let $\text{upper} = \sum_{k_1=1}^{12} k_1$. Compute the number of positive integers $x_1$ such that $1 \le x_1 \le \text{upper}$, $x_1$ divides $k$, and $\frac{k}{x_1} \le \text{upper}$. | 14 | graphs = [
Graph(
let={
"_n": Const(12),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-180), Var("x")), Const(8096)), Const(0)))),
"upper": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Var("k1")),
... | NT | null | COUNT | sympy | VIETA_SUM | [
"SUM_ARITHMETIC",
"VIETA_SUM"
] | 7e2fc0 | diophantine_product_count_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC",
"VIETA_SUM"
] | 2 | 0.069 | 2026-02-08T18:07:26.824467Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T18:07:26.893714Z"
} | d80e57 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 2120
},
"timestamp": "2026-02-18T14:24:19.386Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bba262 | modular_sum_quadratic_residues_v1_601307018_4397 | Let $F_n$ denote the $n$-th Fibonacci number, and let $p$ be the number of positive integers $n$ with $1 \leq n \leq 12984$ such that $14 \mid F_n$. Compute $\frac{p(p - 1)}{4}$. | 73,035 | graphs = [
Graph(
let={
"_n": Const(14),
"p": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(12984)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Co... | NT | null | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-03-10T04:57:28.847174Z | {
"verified": true,
"answer": 73035,
"timestamp": "2026-03-10T04:57:28.850116Z"
} | cab1a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 2054
},
"timestamp": "2026-03-29T12:06:51.329Z",
"answer": 129780
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
311dc1 | diophantine_fbi2_min_v1_1820931509_458 | Let $k = 60$. Let $d$ be the smallest integer such that $5 \leq d \leq 70$, $d$ divides $k$, and $\frac{k}{d} \geq \sum_{i=1}^{2} i$. Compute the remainder when $54353 \cdot d$ is divided by $55841$. | 48,401 | graphs = [
Graph(
let={
"k": Const(60),
"upper": Const(70),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Summation(var="k"... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.006 | 2026-02-08T11:38:18.327304Z | {
"verified": true,
"answer": 48401,
"timestamp": "2026-02-08T11:38:18.333062Z"
} | 124c2a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 703
},
"timestamp": "2026-02-14T17:53:35.588Z",
"answer": 48401
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b7447b | nt_euler_phi_compute_v1_898971024_2807 | Let $n = 38416$. Define $\varphi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $r$ be the remainder when $|\varphi(n)|$ is divided by $11$. Let $Q$ be the $r$-th Bell number, which counts the number of partitions of a set of $r$ elements. Compute $Q$. | 4,140 | graphs = [
Graph(
let={
"n": Const(38416),
"result": EulerPhi(n=Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_euler_phi_compute_v1 | bell_mod | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.011 | 2026-02-08T16:59:21.572076Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:59:21.583291Z"
} | 3ff840 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 697
},
"timestamp": "2026-02-17T17:30:19.928Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c5e12e | nt_sum_divisors_compute_v1_458359167_3374 | Let $n = 31684$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Compute $\sigma(n)$. | 56,077 | graphs = [
Graph(
let={
"n": Const(31684),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3/DIVISOR_PARITY",
"OMEGA_ZERO"
] | 4839d8 | nt_sum_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"DIVISOR_PARITY",
"OMEGA_ZERO"
] | 3 | 0.004 | 2026-02-08T08:19:28.317170Z | {
"verified": true,
"answer": 56077,
"timestamp": "2026-02-08T08:19:28.320881Z"
} | 44fe87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 1128
},
"timestamp": "2026-02-13T17:07:38.823Z",
"answer": 56077
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
9ca494 | sequence_count_fib_divisible_v1_397696148_1221 | Let $r$ be the number of positive integers $n \leq 586$ such that $15$ divides the $n$-th Fibonacci number. Let $s$ be the number of positive integers $n \leq 5047$ that are relatively prime to $10$. Compute $r^2 + 4r + s$. | 2,976 | graphs = [
Graph(
let={
"_n": Const(5047),
"upper": Const(586),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name=... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 40da2d | sequence_count_fib_divisible_v1 | quadratic_mod | 6 | 0 | [
"C4"
] | 1 | 0.027 | 2026-02-08T12:25:19.274029Z | {
"verified": true,
"answer": 2976,
"timestamp": "2026-02-08T12:25:19.301065Z"
} | 6c220d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1539
},
"timestamp": "2026-02-15T01:04:28.095Z",
"answer": 2976
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
221ebf | nt_sum_gcd_range_mod_v1_124444284_9370 | Let $N$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 182$. Let $k = \sum_{i=1}^{15} i$. Define $S = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remainder when $S$ is divided by $10133$. | 1,303 | graphs = [
Graph(
let={
"_n": Const(15),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(182)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B1"
] | c1222e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.39 | 2026-02-08T12:25:55.221068Z | {
"verified": true,
"answer": 1303,
"timestamp": "2026-02-08T12:25:55.610740Z"
} | e31f48 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 2391
},
"timestamp": "2026-02-15T00:50:34.558Z",
"answer": 1303
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e6c708 | geo_count_lattice_triangle_v1_898971024_74 | Let $A$ be the value of $|100 \cdot 100 + 50 \cdot (0 - 25)|$. Let $B$ be the sum
$$
\gcd(|100|, |25|) + \gcd(|50 - 100|, |100 - 25|) + \gcd(|0 - 50|, |0 - 100|).
$$
Define $C = \frac{A + 2 - B}{2}$. Let $Q$ be the remainder when $10885 \cdot C$ is divided by $54086$.
Compute $Q$. | 33,690 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=100)), Mul(Const(value=50), Sub(left=Const(value=0), right=Const(value=25))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=25))), GCD(a=Abs(arg=Sub(left=Const(value=50), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.005 | 2026-02-08T15:10:46.644247Z | {
"verified": true,
"answer": 33690,
"timestamp": "2026-02-08T15:10:46.649658Z"
} | 58f43d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 816
},
"timestamp": "2026-02-16T00:58:00.884Z",
"answer": 33690
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
0f42af | antilemma_k2_v1_1470522791_1339 | Let $n = 319$. Define
$$
x = \sum_{k=1}^{319} \phi(k) \left\lfloor \frac{319}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $c = 25313$. Compute the remainder when $c \cdot x$ is divided by $86375$. | 64,645 | graphs = [
Graph(
let={
"_n": Const(319),
"x": Summation(var="k", start=Const(1), end=Const(319), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(25313),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(86375)),
},
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:35:37.160499Z | {
"verified": true,
"answer": 64645,
"timestamp": "2026-02-08T13:35:37.161225Z"
} | a0e69b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 6762
},
"timestamp": "2026-02-15T18:21:17.773Z",
"answer": 64645
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
15ebc7 | modular_mod_compute_v1_717093673_1838 | Let $d$ be a positive integer such that $1 \leq d \leq 186$ and $d$ divides $35526$. Let $s$ be the maximum value of $d$ over all such $d$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Let $a$ be the maximum value of $xy$ over all such pairs. Let $Q$ be the remainder when $... | 21,915 | graphs = [
Graph(
let={
"_n": Const(60723),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), MaxOverSet(set=SolutionsSet(var=Var("d"), cond... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/B1"
] | 137cb2 | modular_mod_compute_v1 | null | 6 | 0 | [
"B1",
"MAX_DIVISOR"
] | 2 | 0.005 | 2026-02-08T16:22:20.731086Z | {
"verified": true,
"answer": 21915,
"timestamp": "2026-02-08T16:22:20.736208Z"
} | c8bdd8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 7778
},
"timestamp": "2026-02-17T01:35:44.740Z",
"answer": 21915
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
30c459 | modular_inverse_v1_865884756_5347 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 20449$. Let $m = 461$ and let $u$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 20$ and $1 \le j \le 23$. Find the smallest positive integer $x_1$ such that $1 \le x_1 \le u$ and $a x_1 \equiv 1 \pmod{m}$. | 108 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(20449)))), expr=Sum(Var("x"), Var("y")))),
"m": Const(461),
... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"B3"
] | 0ad34f | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 0.022 | 2026-02-08T18:34:09.482849Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T18:34:09.504728Z"
} | ce6baa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1813
},
"timestamp": "2026-02-18T17:49:42.442Z",
"answer": 108
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
00743c | nt_min_coprime_above_v1_124444284_8396 | Let $a = 56169$ and $b = 56299$. Let $m$ be the sum
$$
\sum_{k=1}^{s} k,
$$
where $s = \sum_{k=1}^{t} k$ and $t$ is the largest prime number satisfying $2 \leq t \leq 5$.
Consider the set of all integers $n$ such that $n > a$, $n \leq b$, and $\gcd(n, m) = 1$. Determine the value of the smallest element of this set. | 56,171 | graphs = [
Graph(
let={
"start": Const(56169),
"upper": Const(56299),
"modulus": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/SUM_ARITHMETIC",
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 815897 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.015 | 2026-02-08T09:40:55.595858Z | {
"verified": true,
"answer": 56171,
"timestamp": "2026-02-08T09:40:55.610951Z"
} | 9c701c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 737
},
"timestamp": "2026-02-14T05:37:21.715Z",
"answer": 56171
},
{... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
26156e | sequence_fibonacci_compute_v1_971394319_1073 | Let $m = 2$. Let $p$ be the number of prime numbers $n$ such that $m \leq n \leq 13$. Let $n = \sum_{k=1}^{p} k$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute $F_n$. | 10,946 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(13)), IsPrime(Var("n"))))),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": F... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/SUM_ARITHMETIC"
] | e7107b | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T13:29:15.738258Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T13:29:15.740109Z"
} | c65edf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 519
},
"timestamp": "2026-02-15T16:29:07.443Z",
"answer": 10946
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
aa24cc | diophantine_fbi2_min_v1_971394319_1592 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 1296$. Let $d$ be the smallest integer $d$ satisfying $d \geq 1 + 2 + 3$, $d \leq 82$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. Let $c$ be the maximum value of $xy$ over all ordered pairs of positive integers ... | 6,555 | graphs = [
Graph(
let={
"_m": Const(162),
"_n": Const(3),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1296)))), expr... | NT | null | EXTREMUM | sympy | B1 | [
"B1",
"SUM_ARITHMETIC",
"B3"
] | 0e463f | diophantine_fbi2_min_v1 | negation_mod | 6 | 0 | [
"B1",
"B3",
"SUM_ARITHMETIC"
] | 3 | 0.009 | 2026-02-08T13:46:41.095102Z | {
"verified": true,
"answer": 6555,
"timestamp": "2026-02-08T13:46:41.103919Z"
} | 97b8d7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 971
},
"timestamp": "2026-02-15T20:24:46.134Z",
"answer": 6555
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
8eefe6 | nt_gcd_compute_v1_168721529_1202 | Let $a = 33150$ and $b = 77350$. Let $d = \gcd(a, b)$. Let $p_{\text{max}}$ be the largest prime number $n$ such that $2 \leq n \leq 12$. Compute the Bell number $B_r$, where $r$ is the remainder when $|d|$ is divided by $p_{\text{max}}$. | 203 | graphs = [
Graph(
let={
"a": Const(33150),
"b": Const(77350),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_gcd_compute_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T13:31:38.957779Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T13:31:38.959003Z"
} | a76581 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1040
},
"timestamp": "2026-02-09T14:35:13.393Z",
"answer": 203
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
e01e8d | antilemma_sum_equals_v1_784195855_1959 | Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 77$ and $1 \leq j \leq 77$ such that $i + j = 77$. Let $Q = 10946 - x$. Find the value of $Q$. | 10,870 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(77)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(77)), right=IntegerRange(start=Const(1), end=Const(77))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T05:24:50.188763Z | {
"verified": true,
"answer": 10870,
"timestamp": "2026-02-08T05:24:50.192685Z"
} | bc88f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 634
},
"timestamp": "2026-02-24T03:28:28.038Z",
"answer": 10870
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
8f2350 | antilemma_k3_v1_548369836_206 | Let $n = 99537$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function. Compute $x$. | 99,537 | graphs = [
Graph(
let={
"_n": Const(99537),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T02:49:15.239238Z | {
"verified": true,
"answer": 99537,
"timestamp": "2026-02-08T02:49:15.239495Z"
} | 8ae0ca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 249
},
"timestamp": "2026-02-08T20:11:59.371Z",
"answer": 99537
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.98
} | ||
26bf62 | diophantine_product_count_v1_1125832087_717 | Let $\text{upper}$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 590$. Let $k = 420$. Determine the number of positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$. Compute this number. | 22 | graphs = [
Graph(
let={
"_n": Const(590),
"k": Const(420),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2'))... | NT | null | COUNT | sympy | LIN_FORM | [
"COMB1"
] | 567f58 | diophantine_product_count_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.1 | 2026-02-08T03:13:52.988973Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T03:13:53.089078Z"
} | a76566 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2074
},
"timestamp": "2026-02-10T13:32:43.512Z",
"answer": 22
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
38c7cd | modular_count_residue_v1_655260480_5771 | Let $r = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$. Compute the number of integers $n$ with $1 \leq n \leq 39204$ such that $n \equiv r \pmod{5}$. | 7,841 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(39204),
"m": Const(5),
"r": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 3 | 0 | [
"K2"
] | 1 | 1.296 | 2026-02-08T18:39:32.181208Z | {
"verified": true,
"answer": 7841,
"timestamp": "2026-02-08T18:39:33.477175Z"
} | 5cc676 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 707
},
"timestamp": "2026-02-18T18:29:12.624Z",
"answer": 7841
},
{
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d3c05b | comb_binomial_compute_v1_2080023795_26 | Let $m=2$. Let $n_0$ be the smallest integer $d$ such that $d \ge m$ and $d$ divides $875$.
Consider all integers $t$ for which there exist integers $a$ and $b$ satisfying
\[1 \le a \le 21, \quad 1 \le b \le 135, \quad 36 \le t \le 1944, \quad t = 15a + 12b + 9.\]
Let $C$ be the number of such integers $t$.
Consider ... | 792 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(875))))),
"n": MaxKDivides(target=Factorial(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elemen... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3/V1",
"MIN_PRIME_FACTOR/V1"
] | 6848a6 | comb_binomial_compute_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"MIN_PRIME_FACTOR",
"V1"
] | 4 | 0.005 | 2026-02-08T11:30:15.835604Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T11:30:15.840510Z"
} | 57e193 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 4679
},
"timestamp": "2026-02-10T04:02:36.857Z",
"answer": 745395651
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status":... | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
93167a | modular_sum_quadratic_residues_v1_865884756_824 | Let $n = 67591$. Let $p$ be the smallest prime divisor of $n$. Compute $\frac{p(p-1)}{4}$. | 16,448 | graphs = [
Graph(
let={
"_n": Const(67591),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T15:37:15.441208Z | {
"verified": true,
"answer": 16448,
"timestamp": "2026-02-08T15:37:15.443426Z"
} | 138f9b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 2303
},
"timestamp": "2026-02-16T09:31:54.423Z",
"answer": 16448
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e4de92_n | alg_sym_quad_system_v1_1218484723_6469 | A physicist studies triples of positive integer energy levels $(a, b, c)$ in a system where the balance condition $a^{2} + b^{2} + c^{2} = ab + bc + ca$ must hold. The total "weighted energy" of such a triple is $a^{4} + b^{4} + c^{4}$. The system is further constrained so that $1a + 8b + 3c$ equals the number of disti... | 3,051 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"C2"
] | c556ae | alg_sym_quad_system_v1 | null | 7 | null | [
"C2",
"LIN_FORM"
] | 2 | 0.017 | 2026-02-25T08:01:44.643853Z | null | 5cb280 | e4de92 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 357,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T01:27:48.812Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
8bd72d | diophantine_fbi2_min_v1_784195855_8988 | Let $n = 2$ and $k = 33$. Let $A$ be the set of all prime numbers $p$ such that $2 \leq p \leq 7$. Let $m$ be the maximum element of $A$. Define $D$ to be the set of all positive integers $d$ such that $d \geq m$, $d \leq 43$, $d$ divides $k$, and $\frac{k}{d} \geq \sum_{i=1}^{2} i$. Compute the minimum value of $d$ in... | 11 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(33),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(7)... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 15f63b | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.015 | 2026-02-08T16:26:41.794122Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T16:26:41.809217Z"
} | a7ed61 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 374
},
"timestamp": "2026-02-16T07:25:03.504Z",
"answer": 7
},
{
"id": 11,
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"statu... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
5ceac4 | algebra_poly_eval_v1_1978505735_8395 | Let $b = 6$. Define
$$
S = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor
$$
and let $e$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 360$, and $\gcd(p, q) = 1$. Let $f$ be the value of
$$
S \cdot 6^e - 8 \cdot 6^{\sum_{k_1=1}^{2} \phi(k_1) \lef... | 11,010 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(2),
"b": Const(6),
"result": Sum(Mul(Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))), Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"K2"
] | 5d07bf | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 0.011 | 2026-02-08T20:48:50.388137Z | {
"verified": true,
"answer": 11010,
"timestamp": "2026-02-08T20:48:50.399126Z"
} | 1eaf38 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 2486
},
"timestamp": "2026-02-19T01:12:25.554Z",
"answer": 11010
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e2aa82 | nt_count_divisors_in_range_v1_655260480_786 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 13719616$. Let $s$ be the minimum value of $x + y$ over all $(x, y) \in S$. Let $b$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s$. Let $n = 221760$, $a = 41$, and let $d$ be a positive ... | 108 | graphs = [
Graph(
let={
"n": Const(221760),
"a": Const(41),
"b": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), E... | NT | null | COUNT | sympy | B3 | [
"B3/COMB1"
] | e26f7e | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.142 | 2026-02-08T15:36:42.682807Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T15:36:42.824806Z"
} | a5846c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 4416
},
"timestamp": "2026-02-16T10:29:54.794Z",
"answer": 108
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d5560c | alg_poly4_sum_v1_601307018_3947 | Let $A = \left|\left\{ n : 1 \le n \le 107777,\ n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11} \right\}\right|$, and let $D = \min\{ |x - y| : x, y > 0,\ xy = 192138800 \}$. Define $r$ to be the largest positive integer $d$ such that $d \mid A$ and $d^2 \le D$. Compute the remainder when
$$
\sum_{\substack{1... | 8,481 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(4),
"_n": Const(257),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(454)), Geq(Var("b"), C... | NT | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF/B3_CLOSEST",
"L3C/B3_CLOSEST"
] | e83b36 | alg_poly4_sum_v1 | null | 7 | 0 | [
"B3_CLOSEST",
"B3_DIFF",
"L3C"
] | 3 | 1.319 | 2026-03-10T04:33:18.505303Z | {
"verified": true,
"answer": 8481,
"timestamp": "2026-03-10T04:33:19.824792Z"
} | 02c44f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 310,
"completion_tokens": 27698
},
"timestamp": "2026-03-29T10:31:44.543Z",
"answer": 46405
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok_later"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
9c2534 | modular_inverse_v1_124444284_5654 | Let $a = 12$. Let $S$ be the set of all positive integers $d$ such that $d \leq 601$ and $d$ divides $370817$. Define
$$
m = \sum_{d \in S} \phi(d),
$$
where $\phi$ denotes Euler's totient function. Let $T$ be the set of all positive integers $x$ such that $x \leq 600$ and
$$
12x \equiv 1 \pmod{m}.
$$
Determine the va... | 551 | graphs = [
Graph(
let={
"a": Const(12),
"m": SumOverDivisors(n=MaxOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(left=Var(name='d'), right=Const(value=1)), Leq(left=Var(name='d'), right=Const(value=601)), Divides(divisor=Var(name='d'), dividend=Const(value=370817))))),... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/K3"
] | 97a225 | modular_inverse_v1 | null | 6 | 0 | [
"K3",
"MAX_DIVISOR"
] | 2 | 0.028 | 2026-02-08T06:45:48.481176Z | {
"verified": true,
"answer": 551,
"timestamp": "2026-02-08T06:45:48.509284Z"
} | d2daa5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 3784
},
"timestamp": "2026-02-13T04:21:07.690Z",
"answer": 551
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MA... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
0e4aab | modular_modexp_compute_v1_458359167_4997 | Let $e$ be the number of nonnegative integers $j$ not exceeding 89854 such that $\binom{89854}{j}$ is odd. Compute the remainder when $5^e$ is divided by 16900. | 8,425 | graphs = [
Graph(
let={
"a": Const(5),
"e": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(89854)), Eq(Mod(value=Binom(n=Const(89854), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"m":... | NT | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_modexp_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T12:11:22.056699Z | {
"verified": true,
"answer": 8425,
"timestamp": "2026-02-08T12:11:22.057837Z"
} | e44ad4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 3387
},
"timestamp": "2026-02-14T23:09:58.199Z",
"answer": 8425
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
4dc345 | diophantine_product_count_v1_677425708_4304 | Let $A$ be the set of positive integers $x$ such that $1 \leq x \leq 441$, $x$ divides $720$, and $\frac{720}{x} \leq 441$. Let $a$ be the number of elements in $A$. Let $B$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $b$ ... | 4,124 | graphs = [
Graph(
let={
"_n": Const(52332),
"k": Const(720),
"upper": Const(441),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Re... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | diophantine_product_count_v1 | mod_exp | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.035 | 2026-02-08T06:32:11.984016Z | {
"verified": true,
"answer": 4124,
"timestamp": "2026-02-08T06:32:12.018544Z"
} | 16799d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1614
},
"timestamp": "2026-02-13T01:34:17.749Z",
"answer": 4124
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d99e0e | nt_count_divisible_and_v1_458359167_5159 | Let $n = 4$ and $N = 100560$. For each integer $k$ from $1$ to $n$, define $\phi(k)$ to be the number of positive integers at most $k$ that are relatively prime to $k$. Let $S_k$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 90$, and $\gcd(p, q) = 1$. Define $... | 1,676 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(100560),
"d1": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2"
] | 846647 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 4.445 | 2026-02-08T12:18:42.135266Z | {
"verified": true,
"answer": 1676,
"timestamp": "2026-02-08T12:18:46.580015Z"
} | 3b4151 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1610
},
"timestamp": "2026-02-15T00:03:00.661Z",
"answer": 1676
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
97389d | antilemma_sum_equals_v1_1520064083_7851 | Let $m = 73$. Define $n$ to be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 73$, $1 \leq j \leq 73$, and $i + j = m$. Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 71$, $1 \leq j \leq 71$, and $i + j = n$. | 71 | graphs = [
Graph(
let={
"_m": Const(73),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(73)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.059 | 2026-02-08T09:20:41.935812Z | {
"verified": true,
"answer": 71,
"timestamp": "2026-02-08T09:20:41.994759Z"
} | 588314 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 7357
},
"timestamp": "2026-02-24T11:08:06.584Z",
"answer": 71
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
f5162f | sequence_count_fib_divisible_v1_655260480_23 | Let $d = 8$ and $N = 611$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq N$ and $d$ divides the $n$-th Fibonacci number. | 101 | graphs = [
Graph(
let={
"upper": Const(611),
"d": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"L3C/MAX_PRIME_BELOW"
] | 8ff24e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"L3C",
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 3 | 0.175 | 2026-02-08T15:08:13.900984Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T15:08:14.076023Z"
} | d74510 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 622
},
"timestamp": "2026-02-16T05:15:34.414Z",
"answer": 50
},
{
"id": 11,
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
52ad00 | antilemma_k3_v1_1431428450_414 | Compute $$\sum_{d \mid 25094} \phi(d),$$ where $\phi$ denotes Euler's totient function. | 25,094 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=25094), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T13:27:02.009105Z | {
"verified": true,
"answer": 25094,
"timestamp": "2026-02-08T13:27:02.009414Z"
} | eda4b9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 4277
},
"timestamp": "2026-02-15T15:11:05.865Z",
"answer": 25094
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a04c51 | comb_count_derangements_v1_1978505735_1975 | Let $T$ be the set of all integers $t$ such that $7 \le t \le 89$ and $t = 3a + 4b$ for some positive integers $a \le 11$ and $b \le 14$. Let $d$ be the smallest integer $d \ge 2$ that divides the number of elements in $T$. Compute the subfactorial of $d$. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condit... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | comb_count_derangements_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T16:35:09.429402Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T16:35:09.432639Z"
} | 1054a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 5682
},
"timestamp": "2026-02-17T07:17:07.255Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a59291 | comb_count_permutations_fixed_v1_601307018_10262 | Let $D_n$ denote the number of derangements of $n$ elements. For an integer $a$, define
\[R \equiv 3a^{4} + 2a^{3} - a - 3 \pmod{6889},\]
and then define
\[S \equiv 3R^{4} + 2R^{3} - R - 3 \pmod{6889}.
\]
Let
\[k = \sum_{k_1 = \binom{14}{0}}^{\left|\{ a : a \ge 0,\ a \le \left|\{ t : \text{there exist integers } a, b \... | 55,856 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Const(8),
"k": Summation(var="k1", start=Binom(n=Const(14), k=Const(0)), end=CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("t"), condition... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/POLY_ORBIT_HENSEL/SUM_ARITHMETIC",
"ONE_BINOM_0"
] | dc6016 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"LIN_FORM",
"ONE_BINOM_0",
"POLY_ORBIT_HENSEL",
"SUM_ARITHMETIC"
] | 4 | 0.005 | 2026-03-10T10:46:50.540056Z | {
"verified": true,
"answer": 55856,
"timestamp": "2026-03-10T10:46:50.545393Z"
} | 432c8b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 378,
"completion_tokens": 6868
},
"timestamp": "2026-04-19T13:22:57.370Z",
"answer": 55856
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
6c4822 | nt_sum_divisors_range_v1_1125832087_797 | Let $U$ be the number of positive integers $n$ such that $1 \leq n \leq 17221$ and $\gcd(n, 20) = 1$. Let $D$ be the sum of the number of positive divisors of each integer from $1$ to $U$. Let $R = 89506 \cdot D$. Compute the remainder when $R$ is divided by $54873$. | 17,382 | graphs = [
Graph(
let={
"_n": Const(89506),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(17221)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var... | NT | null | SUM | sympy | C4 | [
"C4"
] | 08d162 | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.296 | 2026-02-08T03:19:15.810844Z | {
"verified": true,
"answer": 17382,
"timestamp": "2026-02-08T03:19:16.107094Z"
} | 458ad6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 6292
},
"timestamp": "2026-02-10T13:12:27.537Z",
"answer": 17382
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ada9b8 | nt_num_divisors_compute_v1_397696148_256 | Let $n = 12321$. Let $\text{result}$ be the number of positive divisors of $n$. Let $Q$ be the remainder when $|\text{result}|$ is divided by $62640$. Find the value of $Q$. | 9 | graphs = [
Graph(
let={
"n": Const(12321),
"result": NumDivisors(n=Ref("n")),
"Q": Mod(value=Abs(arg=Ref(name='result')), modulus=Const(62640)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"LIN_FORM"
] | 1 | 0.186 | 2026-02-08T11:23:54.081457Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T11:23:54.267752Z"
} | 970e34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1476
},
"timestamp": "2026-02-14T13:34:21.631Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
151756 | geo_visible_lattice_v1_1918700295_1162 | Let $n = 121$. Define a visible lattice point as a point $(x, y)$ in the coordinate grid with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points for this $n$. Compute the remainder when $44121 \cdot R$ is divided by $58853$. | 22,691 | graphs = [
Graph(
let={
"n": Const(121),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(58853)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.664 | 2026-02-08T05:36:37.225177Z | {
"verified": true,
"answer": 22691,
"timestamp": "2026-02-08T05:36:37.889521Z"
} | c97bd9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T04:05:09.952Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
4f3c2d | geo_count_lattice_triangle_v1_601307018_4634 | Let $R = |120 \cdot 169 + 169 \cdot (-4)|$ and let $S = \gcd(120, 4) + \gcd(|169 - 120|, |169 - 4|) + \gcd(169, \min\{ 48a b^2 + 37a^3 + 84a^2b : 1 \le a, b \le 17 \})$. Compute $\frac{R + 2 - S}{2}$. | 9,716 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Const(3),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=169)), Mul(Const(value=169), Sub(left=Const(value=0), right=Const(value=4))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(v... | GEOM | NT | COUNT | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"POLY3_MIN"
] | 1 | 0.025 | 2026-03-10T05:16:54.706182Z | {
"verified": true,
"answer": 9716,
"timestamp": "2026-03-10T05:16:54.731531Z"
} | 507216 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1039
},
"timestamp": "2026-03-29T12:55:45.982Z",
"answer": 9716
},
{
"i... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
1a37ff | sequence_fibonacci_compute_v1_1520064083_7931 | Let $N$ be the number of integers $t$ with $7 \leq t \leq 34$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 7$ and $1 \leq b \leq 4$, such that $t = 2a + 5b$. Let $F_N$ denote the $N$-th Fibonacci number, defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $r$ b... | 5 | graphs = [
Graph(
let={
"_n": Const(11),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Var(n... | COMB | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.015 | 2026-02-08T09:22:48.575560Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T09:22:48.590823Z"
} | 7d9b4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 822
},
"timestamp": "2026-02-24T11:17:24.895Z",
"answer": 5
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
8f0478 | modular_count_residue_v1_809748730_1228 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 225$. Let $r = 29$ and let $\text{upper} = 87616$.
Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n \equiv r \pmod{m}$.
Let $Q$ be the number of po... | 1,176 | graphs = [
Graph(
let={
"_n": Const(12288),
"upper": Const(87616),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(225))... | NT | null | COUNT | sympy | L3C | [
"L3C",
"B3"
] | 2b12be | modular_count_residue_v1 | negation_mod | 6 | 0 | [
"B3",
"L3C"
] | 2 | 6.273 | 2026-02-08T12:16:31.101144Z | {
"verified": true,
"answer": 1176,
"timestamp": "2026-02-08T12:16:37.374507Z"
} | 39a67e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1171
},
"timestamp": "2026-02-14T23:38:02.404Z",
"answer": 1176
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c35e3a | comb_binomial_compute_v1_1116507919_26 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 13$. Compute $\binom{n}{5}$. | 1,287 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(13)), IsPrime(Var("n"))))),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T02:23:43.475058Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T02:23:43.477096Z"
} | e2a9f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 300
},
"timestamp": "2026-02-08T18:29:39.593Z",
"answer": 1287
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
... | {
"lo": -7.1,
"mid": -5.34,
"hi": -3.62
} | ||
f2aef6 | nt_gcd_compute_v1_48377204_712 | Let $a = 41885$ and $b = 92147$. Define $\text{result} = \gcd(a, b)$. Let $c$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 110889$. Compute the sum of $d_i \cdot (i+1)^2$ over all digits $d_i$ of $\text{result}$ (in base 10, starting from the units digit as $i=0$), and ad... | 856 | graphs = [
Graph(
let={
"a": Const(41885),
"b": Const(92147),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 8e300c | nt_gcd_compute_v1 | digits_weighted_mod | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T15:39:34.283345Z | {
"verified": true,
"answer": 856,
"timestamp": "2026-02-08T15:39:34.287168Z"
} | a1afeb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 787
},
"timestamp": "2026-02-16T10:44:15.777Z",
"answer": 856
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
85428c | modular_modexp_compute_v1_1742523217_5052 | Let $a$ be the smallest divisor of $141151$ that is at least $2$. Let $e$ be the number of integers $n$ with $1 \leq n \leq 60549$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $m = 60025$ and let $r = a^e \bmod m$. Compute the remainder when $88541r$ is divided by $78582$. | 65,102 | graphs = [
Graph(
let={
"_n": Const(78582),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(141151))))),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"L3C"
] | 156825 | modular_modexp_compute_v1 | null | 7 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T10:45:48.762325Z | {
"verified": true,
"answer": 65102,
"timestamp": "2026-02-08T10:45:48.764127Z"
} | e5bf8d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 2760
},
"timestamp": "2026-02-14T08:40:38.128Z",
"answer": 65102
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7addf2 | lin_form_endings_v1_151522320_1532 | Let $a = 32$ and $b = 56$. Compute $\gcd(a, b)$, and let $d = \gcd(65, \gcd(a, b))$. Define $s = \left\lfloor \frac{65}{d} \right\rfloor$. Multiply $s$ by $11603$, and let the result be $t$. Find the remainder when $t$ is divided by $74388$. | 10,315 | graphs = [
Graph(
let={
"a_coeff": Const(32),
"b_coeff": Const(56),
"k_val": Const(65),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(11... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:05:01.136884Z | {
"verified": true,
"answer": 10315,
"timestamp": "2026-02-08T04:05:01.137902Z"
} | f5c0af | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 573
},
"timestamp": "2026-02-10T15:19:36.312Z",
"answer": 10315
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
808e17 | diophantine_product_count_v1_1520064083_5384 | Let $n = 900$. Define $k$ to be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = n$. Let $\text{upper} = 19$. Define $\text{result}$ to be the number of positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{uppe... | 6 | graphs = [
Graph(
let={
"_n": Const(900),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | K14 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"K14"
] | 2 | 0.125 | 2026-02-08T06:46:23.156201Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T06:46:23.281503Z"
} | cbe1e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1223
},
"timestamp": "2026-02-13T04:13:43.115Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1459a3 | comb_sum_binomial_row_v1_865884756_5576 | Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 4$ and $1 \leq j \leq 6$ such that $\gcd(i, j) = 1$. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Co... | NT | null | SUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T18:42:15.542035Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T18:42:15.542946Z"
} | da4537 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 825
},
"timestamp": "2026-02-18T18:46:53.093Z",
"answer": 65536
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8292f3 | alg_sym_quad_system_v1_1218484723_1488 | Let $S$ be the set of positive integers $n \le 18875$ with odd digit sum. Let $k = |S|$. Let $T$ be the set of integer pairs $(a_1, b_1)$ with $1 \le a_1, b_1 \le 25$ satisfying $$17a_1^4 + 68a_1^3b_1 + 102a_1^2b_1^2 + 68a_1b_1^3 + 17b_1^4 = 170000,$$ and let $m = |T|$. Let $D$ be the set of positive integer triples $(... | 5,577 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": Const(5),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Ref("_m")), P... | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"POLY4_COUNT",
"LIN_FORM",
"L3B"
] | ece2ab | alg_sym_quad_system_v1 | null | 7 | 0 | [
"L3B",
"LIN_FORM",
"POLY4_COUNT",
"SUM_GEOM"
] | 4 | 0.378 | 2026-02-25T03:11:58.009810Z | {
"verified": true,
"answer": 5577,
"timestamp": "2026-02-25T03:11:58.387345Z"
} | 50a52e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 390,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T04:09:17.820Z",
"answer": 447
},
{
... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
efd994 | algebra_poly_eval_v1_153355830_226 | Let $y = \sum_{k=1}^{6} \varphi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\varphi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot (3y^2 + 3y + 9)$ is divided by $60730$. | 29,305 | graphs = [
Graph(
let={
"_n": Const(9),
"y": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Sum(Mul(Const(3), Pow(Ref("y"), Const(2))), Mul(Const(3), Ref("y")), Ref("_n")),
"Q": Mod(v... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T02:58:24.362322Z | {
"verified": true,
"answer": 29305,
"timestamp": "2026-02-08T02:58:24.363474Z"
} | 6e004d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1230
},
"timestamp": "2026-02-10T12:25:03.201Z",
"answer": 29305
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
5afe0c | diophantine_fbi2_count_v1_809748730_839 | Let $k$ be the largest positive integer $d$ such that $1 \leq d \leq 720$ and $d$ divides $527760$. Compute the number of positive integers $d$ such that $4 \leq d \leq 81$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 79$. | 15 | graphs = [
Graph(
let={
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(720)), Divides(divisor=Var("d"), dividend=Const(527760))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), ... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.011 | 2026-02-08T11:47:08.716420Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T11:47:08.727218Z"
} | caa241 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1810
},
"timestamp": "2026-02-14T18:33:06.698Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d6522e | comb_count_derangements_v1_1978505735_583 | Let $n = 21$. Define $N$ to be the number of positive integers $n_1 \leq 130$ such that $\gcd(n_1, n) = 1$ and $n_1$ is divisible by
$$
\sum_{k=1}^4 \varphi(k) \left\lfloor \frac{4}{k} \right\rfloor.
$$
The subfactorial $!k$ is the number of derangements of $k$ elements. Compute $!N$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(21),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(130)), Divides(divisor=Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))... | NT | COMB | COUNT | sympy | K2 | [
"K2/C5"
] | 26a204 | comb_count_derangements_v1 | null | 5 | 0 | [
"C5",
"K2"
] | 2 | 0.003 | 2026-02-08T15:28:04.877577Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T15:28:04.880452Z"
} | 304086 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1246
},
"timestamp": "2026-02-16T06:46:37.259Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a85d63 | comb_count_permutations_fixed_v1_1520064083_10191 | Let $n$ be the largest prime number such that $2 \leq n \leq 11$. Let $k = 7$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 2,970 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"k": Const(7),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T11:16:00.477290Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T11:16:00.479126Z"
} | e1eca0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 884
},
"timestamp": "2026-02-15T21:10:59.266Z",
"answer": 2970
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
896f4d | modular_mod_compute_v1_397696148_66 | Let $m$ be the maximum value of $xy$ over all positive integers $x$ and $y$ such that $x + y = 102$. Compute the remainder when $-26896$ is divided by $m$. | 1,715 | graphs = [
Graph(
let={
"_n": Const(102),
"a": Const(-26896),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), ex... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T11:16:54.936686Z | {
"verified": true,
"answer": 1715,
"timestamp": "2026-02-08T11:16:54.939220Z"
} | d84228 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 970
},
"timestamp": "2026-02-14T11:01:05.146Z",
"answer": 1715
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3e0fbf | nt_count_coprime_v1_124444284_8265 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 20374200$, $\gcd(p, q) = 1$, and $p < q$. Determine the number of positive integers $n \leq 55696$ such that $\gcd(n, k) = 1$. | 27,848 | graphs = [
Graph(
let={
"upper": Const(55696),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=20374200)), Eq(left=GCD(a=Var(name='p'), b... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_coprime_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.427 | 2026-02-08T09:37:19.363366Z | {
"verified": true,
"answer": 27848,
"timestamp": "2026-02-08T09:37:23.790086Z"
} | a5e150 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1579
},
"timestamp": "2026-02-14T05:15:06.627Z",
"answer": 27848
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7396a9 | nt_count_coprime_and_v1_153355830_15 | Let $k_1 = 8$. Let $k_2$ be the number of integers $t$ such that $15 \leq t \leq 45$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 6a + 9b$. Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 32145$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Compute the remainde... | 87,904 | graphs = [
Graph(
let={
"_n": Const(55555),
"upper": Const(32145),
"k1": Const(8),
"k2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 2.931 | 2026-02-08T02:51:05.051653Z | {
"verified": true,
"answer": 87904,
"timestamp": "2026-02-08T02:51:07.983036Z"
} | 08ac8f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:26:20.175Z",
"answer": 5938
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 3.04,
"mid": 4.77,
"hi": 6.54
} | ||
9a3975 | nt_sum_divisors_mod_v1_717093673_964 | Let $n$ be the number of positive integers $k$ at most $458640$ that are divisible by $91$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10859$. | 8,485 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(458640)), Divides(divisor=Const(91), dividend=Var("k"))), domain='positive_integers')),
"M": Const(10859),
"sigma": SumDivisors(n=Ref("n")),... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T15:46:08.514495Z | {
"verified": true,
"answer": 8485,
"timestamp": "2026-02-08T15:46:08.516628Z"
} | a58768 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 1057
},
"timestamp": "2026-02-16T13:53:58.189Z",
"answer": 8485
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e7248f | lin_form_endings_v1_784195855_7037 | Let $a = 70$ and $b = 42$. Define $\ell$ to be the least common multiple of $a$ and $b$. Let $s = 3\ell + a + b$. Compute the remainder when $10141 \cdot s$ is divided by $80469$. | 41,005 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(42),
"k_val": Const(3),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:03:46.085211Z | {
"verified": true,
"answer": 41005,
"timestamp": "2026-02-08T09:03:46.085735Z"
} | b4329b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 847
},
"timestamp": "2026-02-13T23:54:29.054Z",
"answer": 41005
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8db371 | diophantine_product_count_v1_1918700295_4524 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 44100$.
Let $r$ be the number of positive integers $n$ not exceeding $577$ such that $\gcd(n, 14) = 1$.
Let $s$ be the number of positive integers $x$ not exceeding $r$ such that $x$ divides $k$ and $\frac{k}{x} \leq ... | 61,304 | graphs = [
Graph(
let={
"_n": Const(577),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(44100)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"C4",
"B3"
] | 8d18b3 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"C4",
"COUNT_SUM_EQUALS"
] | 3 | 0.061 | 2026-02-08T09:25:23.037929Z | {
"verified": true,
"answer": 61304,
"timestamp": "2026-02-08T09:25:23.099255Z"
} | bb2d47 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2029
},
"timestamp": "2026-02-14T04:07:33.318Z",
"answer": 61304
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9cf3d | nt_count_primes_v1_865884756_1491 | Let $S$ be the set of positive integers $n_1$ with $1 \leq n_1 \leq 5$ and $\gcd(n_1, 6) = 1$. Let $T$ be the set of prime numbers $n$ such that $n \geq |S|$ and $n \leq 20160$. Compute the number of elements in $T$. | 2,280 | graphs = [
Graph(
let={
"upper": Const(20160),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(5)), Eq(GCD(a=Var("n1"), b=Const(6)), Const(1))))... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_primes_v1 | null | 4 | 0 | [
"C4"
] | 1 | 1.577 | 2026-02-08T16:04:48.286306Z | {
"verified": true,
"answer": 2280,
"timestamp": "2026-02-08T16:04:49.863150Z"
} | 7eb75e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1238
},
"timestamp": "2026-02-16T20:08:18.995Z",
"answer": 2280
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b9c786 | nt_count_divisors_in_range_v1_153355830_3023 | Let $a$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 5929$. Compute the number of positive divisors $d$ of $720$ such that $a \leq d \leq b$. | 19 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(720),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mu... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"B1",
"B3"
] | 655d51 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B1",
"B3",
"COUNT_COPRIME_GRID"
] | 3 | 0.073 | 2026-02-08T07:32:50.163730Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T07:32:50.237192Z"
} | 3f686c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1257
},
"timestamp": "2026-02-13T11:00:35.924Z",
"answer": 19
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
94b021 | antilemma_sum_factor_cartesian_v1_677425708_215 | Let $B$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. For each ordered pair $(i, j)$ of integers with $1 \leq i \leq 22$ and $1 \leq j \leq 15$, compute $\phi(|B|)$, where $\phi$ is Euler's totient function. Let $S$ be th... | 34,156 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | 0bec54 | antilemma_sum_factor_cartesian_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.002 | 2026-02-08T03:09:31.682001Z | {
"verified": true,
"answer": 34156,
"timestamp": "2026-02-08T03:09:31.683723Z"
} | 33e1d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 1404
},
"timestamp": "2026-02-08T20:25:11.491Z",
"answer": 34156
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
},
{
"lemma": "SUM_FACTOR_CARTES... | {
"lo": 1.03,
"mid": 4.13,
"hi": 6.46
} | ||
816dc9 | diophantine_product_count_v1_784195855_7044 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 57600$. Let $u$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 10201$. Determine the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac... | 20 | graphs = [
Graph(
let={
"_m": Const(10201),
"_n": Const(57600),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-08T09:03:52.295324Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T09:03:52.309650Z"
} | 94e2dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2623
},
"timestamp": "2026-02-13T23:56:03.851Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
676c15 | alg_telescope_v1_1218484723_1454 | Let $T$ be the set of integers $t$ such that $t = 7a + 4b$ for some integers $a, b$ with $1 \le a \le 241$, $1 \le b \le 51$, and $11 \le t \le 1891$. Let $L = |T|$. Let $B = |\{ n : 1 \le n \le 17140,\ S(n) \bmod 2 = 1 \}|$, where $S(n)$ denotes the sum of the digits of $n$. Compute $R = \left( \sum_{k=0}^{L} \left((k... | 75,001 | graphs = [
Graph(
let={
"_m": Const(57973),
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'),... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"L3B"
] | f85b0e | alg_telescope_v1 | null | 6 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.085 | 2026-02-25T03:10:03.511677Z | {
"verified": true,
"answer": 75001,
"timestamp": "2026-02-25T03:10:03.596734Z"
} | 7a9920 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 291,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T03:50:49.057Z",
"answer": 41534
},
{
... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.43,
"mid": 6.62,
"hi": 9.7
} |
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