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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7d3b1d | comb_count_permutations_fixed_v1_349078426_1778 | Let $m = 847$ and $n = 10$. Let $k$ be the largest prime number $p$ such that $2 \leq p \leq d$, where $d$ is the smallest divisor of $m$ that is at least 2. Compute $\binom{n}{k} \cdot !(n - k)$, where $!a$ denotes the number of derangements of $a$ elements. | 240 | graphs = [
Graph(
let={
"_m": Const(847),
"_n": Const(2),
"n": Const(10),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divi... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T13:55:31.285172Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T13:55:31.289199Z"
} | c7750f | 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": 619
},
"timestamp": "2026-02-15T22:02:30.480Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
716453 | nt_sum_totient_over_divisors_v1_1742523217_4561 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 20793600$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 9,120 | graphs = [
Graph(
let={
"n": 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(20793600)))), expr=Sum(Var("x"), Var("y")))),
"result": SumO... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T08:58:13.075617Z | {
"verified": true,
"answer": 9120,
"timestamp": "2026-02-08T08:58:13.081666Z"
} | 803ad1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1650
},
"timestamp": "2026-02-13T22:38:07.573Z",
"answer": 9120
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c76049 | modular_product_range_v1_1125832087_995 | Let $p$ be the product of the integers from $16$ to $96$, inclusive. Let $r$ be the remainder when $p$ is divided by $11503$. Let $q$ be the largest prime number less than or equal to $11$. Compute the Bell number $B_k$, where $k$ is the remainder when $|r|$ is divided by $q$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(16),
"prod": MathProduct(expr=Var("i"), var="i", start=Ref("_n"), end=Const(96)),
"result": Mod(value=Ref("prod"), modulus=Const(11503)),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(v... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | modular_product_range_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T03:24:54.170860Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:24:54.173700Z"
} | 5258f0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 13904
},
"timestamp": "2026-02-23T19:36:46.204Z",
"answer": 21147
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
a9a9ad | geo_count_lattice_rect_v1_548369836_244 | Compute the number of lattice points in the rectangle $[0, 378] \times [0, 171]$, including the boundary. Find the absolute value of this number. | 65,188 | graphs = [
Graph(
let={
"a": Const(378),
"b": Const(171),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T02:49:30.376021Z | {
"verified": true,
"answer": 65188,
"timestamp": "2026-02-08T02:49:30.377001Z"
} | 3d41aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 301
},
"timestamp": "2026-02-08T20:16:25.809Z",
"answer": 65188
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.93,
"hi": -0.95
} | ||||
979996 | antilemma_cartesian_v1_124444284_551 | Let $S$ be the set of all ordered pairs $(a, b)$ such that $a$ is an integer satisfying $1 \leq a \leq 39$ and $b$ is an integer satisfying $1 \leq b \leq 47$. Let $x$ be the number of elements in $S$. Compute the remainder when $44121 \times x$ is divided by $86378$. | 23,985 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(39)), right=IntegerRange(start=Const(1), end=Const(47)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(86378)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:21:21.968185Z | {
"verified": true,
"answer": 23985,
"timestamp": "2026-02-08T03:21:21.968866Z"
} | bc2560 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1231
},
"timestamp": "2026-02-09T19:01:44.995Z",
"answer": 23985
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
d8a3a8 | comb_count_permutations_fixed_v1_1116507919_509 | Let $x$ and $y$ be positive integers such that $xy = 25$. Let $n$ be the minimum value of $x + y$ over all such pairs. Define $k = 7$. Let $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute the remainder when $44121 \cdot r$ is divided by $66001$. | 28,880 | graphs = [
Graph(
let={
"n": 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(25)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(7),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T02:37:38.627603Z | {
"verified": true,
"answer": 28880,
"timestamp": "2026-02-08T02:37:38.629113Z"
} | eb2695 | 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": 933
},
"timestamp": "2026-02-08T19:38:49.559Z",
"answer": 28880
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -3.84,
"mid": -1.89,
"hi": 0.06
} | ||
bb524d | antilemma_coprime_grid_v1_677425708_164 | Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 49$ and $1 \leq j \leq 111$ such that $\gcd(i, j) = \phi(2)$. Find the value of $x$. | 3,379 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(2))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(49)), right=IntegerRange(start=Const(1), end=Const(111))))),
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 98ffdc | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 2 | 0.001 | 2026-02-08T03:06:49.803276Z | {
"verified": true,
"answer": 3379,
"timestamp": "2026-02-08T03:06:49.804345Z"
} | 8e0a60 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 4985
},
"timestamp": "2026-02-09T23:55:17.254Z",
"answer": 3379
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VA... | {
"lo": -6.5,
"mid": -0.15,
"hi": 5.67
} | ||
113d66 | nt_min_coprime_above_v1_784195855_651 | Let $a$ be the number of positive integers $n$ with $1 \leq n \leq 11559$ such that $\gcd(n, 10) = 1$. Let $b$ be the smallest integer greater than $a$ and at most $4816$ such that $\gcd(b, 182) = 1$. Compute the remainder when $44121 \cdot b$ is divided by $64007$. | 5,309 | graphs = [
Graph(
let={
"_n": Const(10),
"start": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11559)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"upper": Const(4816),
"modulus": Const(182),
... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | 08d162 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.034 | 2026-02-08T04:31:12.745530Z | {
"verified": true,
"answer": 5309,
"timestamp": "2026-02-08T04:31:12.779637Z"
} | e99e93 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1999
},
"timestamp": "2026-02-10T17:02:45.524Z",
"answer": 5309
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
237b6b | antilemma_sum_equals_v1_1978505735_234 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 93$, $1 \leq i \leq 91$, and $1 \leq j \leq 92$. Compute $6000 - x$. | 5,909 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(93)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(91)), right=IntegerRange(start=Const(1), end=Const(92))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.007 | 2026-02-08T15:14:09.113810Z | {
"verified": true,
"answer": 5909,
"timestamp": "2026-02-08T15:14:09.120355Z"
} | 5123ed | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 495
},
"timestamp": "2026-02-24T20:12:53.847Z",
"answer": 5909
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
c566b7 | comb_factorial_compute_v1_601307018_2136 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 25$ satisfying
$$
17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 63717632.
$$
Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(102),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Ref("_n"), Pow(Var("a"), Const(2)), Po... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.002 | 2026-03-10T02:50:17.856370Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-03-10T02:50:17.858606Z"
} | bd1387 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1398
},
"timestamp": "2026-03-29T04:24:07.297Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
473abd | geo_visible_lattice_v1_1526740231_81 | Let $n = 81$. A lattice point $(x, y)$ with $1 \leq x, y \leq n$ is said to be visible from the origin if $\gcd(x, y) = 1$. Let $R$ be the number of such visible lattice points. Compute the remainder when $65867 \cdot R$ is divided by $63556$. | 54,953 | graphs = [
Graph(
let={
"n": Const(81),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(65867), Ref("result")), modulus=Const(63556)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.46 | 2026-02-08T11:20:42.739872Z | {
"verified": true,
"answer": 54953,
"timestamp": "2026-02-08T11:20:43.199496Z"
} | 604360 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T13:27:48.709Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
e0d2ce | alg_sum_ap_v1_1218484723_7711 | Compute the remainder when $\sum_{k=0}^{1786} (12k + 62)$ is divided by the number of integers $t$ for which there exist integers $a, b$ with $1 \leq a \leq 711$, $1 \leq b \leq 2733$ such that $t = 5a + 2b$ and $7 \leq t \leq 9021$. | 3,779 | graphs = [
Graph(
let={
"_n": Const(1786),
"result": Mod(value=Summation(var="k", start=Const(0), end=Ref("_n"), expr=Sum(Mul(Const(12), Var("k")), Const(62))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'),... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sum_ap_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.037 | 2026-02-25T09:13:47.201119Z | {
"verified": true,
"answer": 3779,
"timestamp": "2026-02-25T09:13:47.238552Z"
} | 09c35d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T06:03:52.542Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
c58652 | sequence_lucas_compute_v1_655260480_415 | Let $n$ be the smallest divisor greater than or equal to 2 of 132673637. Let $m = 58277$ and let $d$ be the smallest divisor greater than or equal to 2 of 1859. Compute the remainder when the Bell number of $|L_n| \bmod d$ is divided by $m$, where $L_n$ denotes the $n$th Lucas number. | 57,698 | graphs = [
Graph(
let={
"_m": Const(58277),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1859))))),
"n": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(2)), D... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MIN_PRIME_FACTOR"
] | 6f8539 | sequence_lucas_compute_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T15:22:21.880499Z | {
"verified": true,
"answer": 57698,
"timestamp": "2026-02-08T15:22:21.884640Z"
} | 1414e7 | 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": 1596
},
"timestamp": "2026-02-16T04:51:22.894Z",
"answer": 57698
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aa3d40 | modular_sum_quadratic_residues_v1_124444284_942 | Let $m = 2$ and let $n$ be the sum of all real solutions $x$ to the equation
$$
x^2 - 1625x - 36234 = 0.
$$
Let $p$ be the number of positive integers $n'$ such that $1 \leq n' \leq n$ and
$$
n' \equiv \left\lfloor \frac{n'}{2} \right\rfloor \pmod{3}.
$$
Compute $\frac{p(p-1)}{4}$. | 73,035 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-1625), Var("x")), Const(-36234)), Const(0)))),
"p": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(... | NT | null | SUM | sympy | VIETA_SUM | [
"VIETA_SUM/L3C"
] | 217e6b | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"L3C",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T03:36:24.724995Z | {
"verified": true,
"answer": 73035,
"timestamp": "2026-02-08T03:36:24.726977Z"
} | 895022 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1585
},
"timestamp": "2026-02-10T00:19:06.437Z",
"answer": 73035
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VI... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
cc136e | geo_count_lattice_rect_v1_124444284_6750 | Compute the number of lattice points in the rectangle $[0, 361] \times [0, 155]$, including the boundary. | 56,472 | graphs = [
Graph(
let={
"a": Const(361),
"b": Const(155),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T08:37:22.074351Z | {
"verified": true,
"answer": 56472,
"timestamp": "2026-02-08T08:37:22.074973Z"
} | e52218 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 273
},
"timestamp": "2026-02-24T09:46:22.972Z",
"answer": 56472
},
{
"i... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
4ce39d_l | comb_sum_binomial_mod_v1_548369836_56 | Let $m = 29$ and $n = 114$. Define $s = \sum_{k=m}^{n} \binom{132}{k}$. Let $r$ be the remainder when $s$ is divided by $11821$. Let $p$ be the number of prime numbers $q$ such that $2 \leq q \leq 37$. Define $c$ to be the number of positive integers $k$ with $1 \leq k \leq 62856$ such that $p$ divides $F_k$, where $F_... | 0 | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/COUNT_FIB_DIVISIBLE"
] | c07044 | comb_sum_binomial_mod_v1 | affine_mod | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"COUNT_PRIMES"
] | 2 | 0.004 | 2026-02-08T02:44:43.167774Z | {
"verified": false,
"answer": 26798,
"timestamp": "2026-02-08T02:44:43.172188Z"
} | f69db7 | 4ce39d | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T16:01:50.542Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"sta... | {
"lo": 3.69,
"mid": 5.49,
"hi": 7.55
} | |
5575be | geo_count_lattice_triangle_v1_124444284_2042 | Let $A = (0,0)$, $B = (169,100)$, and $C = (289,111)$ be points in the coordinate plane. Define $\Delta$ to be the triangle with vertices $A$, $B$, and $C$.
Let $A_2$ be twice the area of $\Delta$. Compute $A_2$ using the formula
$$
A_2 = \left| 169 \sum_{d \mid 111} \phi(d) + 289 \cdot (-100) \right|,
$$
where $\phi$... | 20,851 | graphs = [
Graph(
let={
"_n": Const(289),
"area_2x": Abs(arg=Sum(Mul(Const(value=169), SumOverDivisors(n=Const(value=111), var='d', expr=EulerPhi(n=Var(name='d')))), Mul(Const(value=289), Sub(left=Const(value=0), right=Const(value=100))))),
"boundary": Sum(GCD(a=Abs(arg=C... | NT | null | COUNT | sympy | B3 | [
"B3",
"K3"
] | b88822 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"K3"
] | 2 | 0.008 | 2026-02-08T04:16:52.795426Z | {
"verified": true,
"answer": 20851,
"timestamp": "2026-02-08T04:16:52.803426Z"
} | 09e36f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 344,
"completion_tokens": 1809
},
"timestamp": "2026-02-10T15:59:23.439Z",
"answer": 20851
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
070b5f | comb_count_permutations_fixed_v1_48377204_224 | Let $n = 8$ and $k = 6$. Define $r$ to be the number of ways to choose a subset of $k$ elements from an $n$-element set and then permute the remaining $n-k$ elements such that no element remains in its original position. Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 21233664$. For... | 9,188 | graphs = [
Graph(
let={
"n": Const(8),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | comb_count_permutations_fixed_v1 | negation_mod | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T15:18:26.528800Z | {
"verified": true,
"answer": 9188,
"timestamp": "2026-02-08T15:18:26.531137Z"
} | 457ec5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1977
},
"timestamp": "2026-02-24T20:23:30.426Z",
"answer": 9188
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
5a84b8 | nt_count_coprime_v1_1742523217_3370 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25000000$. Let $m$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 10$. Let $p$ be the maximum value of $xy$ over all such pairs. Let $k$ be... | 9,566 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": Const(2),
"upper": 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(25000000)))... | NT | null | COUNT | sympy | B1 | [
"B1/MAX_PRIME_BELOW",
"B3"
] | b81747 | nt_count_coprime_v1 | null | 6 | 0 | [
"B1",
"B3",
"MAX_PRIME_BELOW"
] | 3 | 0.764 | 2026-02-08T05:49:08.410422Z | {
"verified": true,
"answer": 9566,
"timestamp": "2026-02-08T05:49:09.174792Z"
} | 4231ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1625
},
"timestamp": "2026-02-12T14:52:49.290Z",
"answer": 9566
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ce3825 | comb_count_permutations_fixed_v1_2051736721_5786 | Let $n$ be the number of positive integers $m$ such that $1 \leq m \leq 23$ and the sum of the digits of $m$ is divisible by 2. Compute the value of $\binom{n}{7} \cdot !(n - 7)$, where $!k$ denotes the number of derangements of $k$ elements. | 2,970 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(23)), Eq(Mod(value=DigitSum(Var("n1")), modulus=Ref("_n")), Const(0))))),
"k": Const(7),
"result": Mul(Binom(... | COMB | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.003 | 2026-02-08T18:47:57.644890Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T18:47:57.647774Z"
} | d6783a | 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": 1254
},
"timestamp": "2026-02-18T19:37:20.721Z",
"answer": 2970
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V7",
"status"... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
f6c6a3 | nt_min_with_divisor_count_v1_1742523217_3854 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1587600$. Define $T$ to be the set of all values $x + y$ where $(x,y) \in S$. Let $m$ be the minimum element of $T$. Let $n = 172$. Define $U$ to be the set of all positive integers $k$ such that $1 \le k \le m$ and $k$ has exactly thr... | 7,392 | graphs = [
Graph(
let={
"_n": Const(172),
"upper": 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(1587600)))), expr=Sum(Var("x"), Var("y... | NT | null | EXTREMUM | sympy | B1 | [
"B1",
"B3"
] | 2cc80e | nt_min_with_divisor_count_v1 | negation_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.104 | 2026-02-08T06:07:02.283404Z | {
"verified": true,
"answer": 7392,
"timestamp": "2026-02-08T06:07:02.387343Z"
} | 03324f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1836
},
"timestamp": "2026-02-12T19:56:24.727Z",
"answer": 7392
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
80feee | nt_lcm_compute_v1_124444284_187 | Let $a$ be the number of positive integers $n$ with $1 \leq n \leq 5248$ such that the $n$th Fibonacci number is divisible by 7. Let $b = 820$. Compute the least common multiple of $a$ and $b$. | 3,280 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(5248)), Divides(divisor=Const(7), dividend=Fibonacci(arg=Var(name='n')))))),
"b": Const(820),
"result": LCM(a=Ref("a"), b=Ref("b")),
... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_lcm_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"COUNT_PRIMES"
] | 2 | 0.008 | 2026-02-08T03:03:36.005903Z | {
"verified": true,
"answer": 3280,
"timestamp": "2026-02-08T03:03:36.013928Z"
} | 462319 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1172
},
"timestamp": "2026-02-09T14:29:23.486Z",
"answer": 3280
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"s... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
1f54c1 | nt_sum_divisors_compute_v1_2080023795_182 | Let $n = 51529$. Compute the sum of all positive divisors of $n$. | 51,757 | graphs = [
Graph(
let={
"n": Const(51529),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/DIVISOR_PARITY",
"BIG_OMEGA_ZERO"
] | 7b74ca | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"BIG_OMEGA_ZERO",
"DIVISOR_PARITY",
"MIN_PRIME_FACTOR"
] | 3 | 0.007 | 2026-02-08T11:35:16.944499Z | {
"verified": true,
"answer": 51757,
"timestamp": "2026-02-08T11:35:16.951797Z"
} | ff18a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1913
},
"timestamp": "2026-02-08T20:50:23.613Z",
"answer": 51757
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF... | {
"lo": -2.04,
"mid": 1.68,
"hi": 4.67
} | ||
36d4f6 | comb_count_partitions_v1_48377204_555 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 55$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 9$, and $t = 4a + 3b$. Compute the number of integer partitions of $n$. | 63,261 | graphs = [
Graph(
let={
"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(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T15:32:27.958316Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T15:32:27.960284Z"
} | a05dd5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4520
},
"timestamp": "2026-02-24T18:05:34.902Z",
"answer": 63261
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
9b5b44 | nt_count_intersection_v1_153355830_2412 | Let $m = 625$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $s$ be the minimum value of $x + y$ over all such pairs. Now, consider the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s$. Let $p$ be the number of such pairs. Now, let $a... | 78,874 | graphs = [
Graph(
let={
"_m": Const(625),
"_n": Const(44121),
"N": Const(100000),
"a": Const(3),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=V... | NT | null | COUNT | sympy | B3 | [
"B3/COMB1/B3"
] | 97ebcf | nt_count_intersection_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 8.059 | 2026-02-08T07:06:52.861132Z | {
"verified": true,
"answer": 78874,
"timestamp": "2026-02-08T07:07:00.919766Z"
} | 4de60e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 2514
},
"timestamp": "2026-02-13T07:51:23.786Z",
"answer": 78874
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c9ba85 | nt_max_prime_below_v1_784195855_6512 | Let $S$ 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 $m$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $m \leq n \leq 56644$. | 56,633 | graphs = [
Graph(
let={
"upper": Const(56644),
"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 | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.325 | 2026-02-08T08:42:32.337705Z | {
"verified": true,
"answer": 56633,
"timestamp": "2026-02-08T08:42:33.662612Z"
} | 7080c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 2243
},
"timestamp": "2026-02-13T20:38:29.174Z",
"answer": 56633
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
0306a5 | diophantine_product_count_v1_1978505735_5524 | Let $k$ be the number of positive integers $n$ at most $1440$ such that $21$ divides the $n$-th Fibonacci number. Let $u$ be the largest prime number at least $2$ and at most $72$. Compute the number of positive integers $x$ at most $u$ such that $x$ divides $k$ and $\frac{k}{x} \leq u$. | 14 | graphs = [
Graph(
let={
"_m": Const(1440),
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Divides(divisor=Const(21), dividend=Fibonacci(arg=Var(name='n')))))),
"upper": MaxOverS... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2b3346 | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.007 | 2026-02-08T19:02:40.214301Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T19:02:40.221629Z"
} | afc5e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2028
},
"timestamp": "2026-02-18T21:12:25.809Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
026857 | nt_count_intersection_v1_1820931509_270 | Let $N$ be the sum of all real solutions $x$ to the equation $x^2 - 5000x - 176225 = 0$. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $\gcd(n, 6) = 1$. Compute the remainder when $19993 \cdot r$ is divided by 82199. | 59,779 | graphs = [
Graph(
let={
"N": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-5000), Var("x")), Const(-176225)), Const(0)))),
"a": Const(11),
"b": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), con... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_intersection_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.168 | 2026-02-08T11:27:51.340143Z | {
"verified": true,
"answer": 59779,
"timestamp": "2026-02-08T11:27:51.508640Z"
} | c2b628 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 976
},
"timestamp": "2026-02-14T14:38:33.385Z",
"answer": 59779
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b3f80e | antilemma_k3_v1_1978505735_7879 | Let $n = 97676$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 97,676 | graphs = [
Graph(
let={
"_n": Const(97676),
"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 | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T20:34:08.909701Z | {
"verified": true,
"answer": 97676,
"timestamp": "2026-02-08T20:34:08.910434Z"
} | f9e6fc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 272
},
"timestamp": "2026-02-19T00:40:28.909Z",
"answer": 97676
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d45ff2 | nt_min_crt_v1_458359167_4396 | Let $m = 7$ and $k = 11$. Let $a = 0$ and define
$$
b = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $\text{upper} = 77$. Consider the set of all integers $n$ such that $1 \leq n \leq 77$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. Compute t... | 21 | graphs = [
Graph(
let={
"m": Const(7),
"k": Const(11),
"a": Const(0),
"b": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"upper": Const(77),
"result": MinOverSet(set=So... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"K2"
] | 6897ab | nt_min_crt_v1 | null | 6 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.051 | 2026-02-08T11:44:57.589127Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T11:44:57.640140Z"
} | 948fbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 945
},
"timestamp": "2026-02-14T18:36:56.382Z",
"answer": 21
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d4720f | sequence_fibonacci_compute_v1_1520064083_9511 | Let $n = \sum_{d \mid 24} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \ge 3$. Find the value of $F_n$. | 46,368 | graphs = [
Graph(
let={
"_n": Const(24),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T10:49:12.347133Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T10:49:12.348269Z"
} | 298914 | 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": 638
},
"timestamp": "2026-02-14T08:55:18.468Z",
"answer": 46368
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
709143 | alg_linear_system_2x2_v1_1218484723_152 | Let $\det = (-1)(-10) - (-17)(16)$. Let $M = (-41800)(-10) - (-845114) \cdot N$, where $N$ is the number of integers $a$ with $0 \leq a \leq 3720$ such that $((a^3 \bmod 3721)^3 \bmod 3721)^3 \bmod 3721)^3 \bmod 3721 = a$, but $a^3 \not\equiv a \pmod{3721}$, $(a^3)^3 \not\equiv a \pmod{3721}$, and $((a^3)^3)^3 \not\equ... | 49,909 | graphs = [
Graph(
let={
"_n": Const(3721),
"num_x": Sub(Mul(Const(-41800), Const(-10)), Mul(Const(-845114), CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(3720)), Eq(Mod(value=Pow(Mod(value=Pow(Mod(value=Pow(Mod(value=Pow(Var("a... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | alg_linear_system_2x2_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.004 | 2026-02-25T01:51:11.716313Z | {
"verified": true,
"answer": 49909,
"timestamp": "2026-02-25T01:51:11.720438Z"
} | 6497aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 316,
"completion_tokens": 3732
},
"timestamp": "2026-03-28T21:49:33.288Z",
"answer": 49909
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
056ad7 | comb_count_derangements_v1_717093673_3667 | Let $m = 2$. Define $n'$ to be the sum of all positive integers $n_1$ such that $1 \leq n_1 \leq m$ and $n_1$ is even. Let $n$ be the smallest positive integer $d$ such that $d \geq n'$ and $d$ divides $143143$. Define $r = !n$, the subfactorial of $n$. Determine the value of $k$, the smallest positive integer such tha... | 336 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_m")), Eq(Mod(value=Var("n1"), modulus=Const(2)), Const(0))))),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=An... | NT | COMB | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MIN_PRIME_FACTOR"
] | 57d6d0 | comb_count_derangements_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T17:45:42.796604Z | {
"verified": true,
"answer": 336,
"timestamp": "2026-02-08T17:45:42.799386Z"
} | 4a2bbb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 3097
},
"timestamp": "2026-02-18T07:13:41.711Z",
"answer": 336
},
{
... | 1 | [
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0baf35 | nt_sum_over_divisible_v1_865884756_191 | Let $R$ be the sum of all positive integers $n$ such that $1 \leq n \leq 48841$ and $n$ is divisible by $197$. Let $C$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 21$, $1 \leq j \leq 24$, and $\gcd(i, j) = 1$. Compute the remainder when
$$
\left(R \bmod 307\right) + 7001 \cdot \lef... | 15,677 | graphs = [
Graph(
let={
"_n": Const(53631),
"upper": Const(48841),
"divisor": Const(197),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Co... | NT | null | SUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 283923 | nt_sum_over_divisible_v1 | two_moduli | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 1.914 | 2026-02-08T15:15:21.220600Z | {
"verified": true,
"answer": 15677,
"timestamp": "2026-02-08T15:15:23.134772Z"
} | 3c4e86 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 4240
},
"timestamp": "2026-02-10T05:22:38.444Z",
"answer": 15365
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
8c1bbd | diophantine_product_count_v1_1116507919_121 | Let $n = 5$ and $k = 360$. For each ordered pair $(x, y)$ of positive integers such that $xy = 15376$, compute the sum $x + y$. Let $S$ be the set of all such sums. Define $\text{upper}$ to be the number of positive integers $j$ such that $j \leq \min(S)$ and $j^n \leq 938120019968$. Compute the number of positive inte... | 22 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(360),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive... | NT | null | COUNT | sympy | B3 | [
"B3/C3"
] | 3e4f89 | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"C3"
] | 2 | 0.042 | 2026-02-08T02:26:20.020854Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T02:26:20.063128Z"
} | 372c05 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 7477
},
"timestamp": "2026-02-08T19:05:43.246Z",
"answer": 22
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"le... | {
"lo": -0.14,
"mid": 1.48,
"hi": 2.91
} | ||
3ef149 | antilemma_k2_v1_1978505735_4624 | Let $n = 134$. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{134}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute $x$. | 9,045 | graphs = [
Graph(
let={
"_n": Const(134),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(134), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/IDENTITY_POW_ZERO/K2",
"K2"
] | cf129a | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_POW_ZERO",
"K13",
"K2",
"K3"
] | 4 | 0.004 | 2026-02-08T18:24:38.717265Z | {
"verified": true,
"answer": 9045,
"timestamp": "2026-02-08T18:24:38.721720Z"
} | b8b603 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1061
},
"timestamp": "2026-02-18T16:54:44.919Z",
"answer": 9045
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
52bc7f | nt_min_phi_inverse_v1_458359167_2932 | Let $m=58564$. Consider all ordered pairs $(x,y)$ of positive integers such that $xy=m$. For each such pair, compute $x+y$. Let $d$ be the minimum of these values of $x+y$.
Let $N$ be the number of positive integers $k$ with $1\le k\le 69696$ such that $d$ divides $k$.
Now consider all ordered pairs $(x,y)$ of positi... | 2 | graphs = [
Graph(
let={
"_m": Const(58564),
"_n": Const(11),
"upper": Const(100),
"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("... | NT | COMB | EXTREMUM | sympy | B3 | [
"B3/C2/B3"
] | ce6951 | nt_min_phi_inverse_v1 | null | 8 | 0 | [
"B3",
"C2"
] | 2 | 0.012 | 2026-02-08T06:50:32.986808Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T06:50:32.999202Z"
} | b786ea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 2133
},
"timestamp": "2026-02-13T05:24:18.107Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
7fa421 | comb_count_partitions_v1_677425708_1069 | Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x \cdot y = 361$. Let $m$ be the minimum value of $x + y$ over all pairs in $T$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 38$ and $n$ is divisible by $m$. Let $N$ be the sum of all elements in $S$. Find the n... | 26,015 | graphs = [
Graph(
let={
"_m": Const(38),
"_n": 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(361)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 138b1a | comb_count_partitions_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.149 | 2026-02-08T03:59:46.662025Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T03:59:46.810905Z"
} | 805355 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 936
},
"timestamp": "2026-02-09T15:23:11.565Z",
"answer": 26015
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
c4c2e1 | nt_count_divisible_and_v1_153355830_949 | Let $d_2$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 16$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 30912$, $n$ is divisible by 6, and $n$ is divisible by $d_2$. Compute the remainder when $28540 \cdot N$ is divided by $74481$. | 40,387 | graphs = [
Graph(
let={
"upper": Const(30912),
"d1": Const(6),
"d2": 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(16)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 13.757 | 2026-02-08T04:18:25.941790Z | {
"verified": true,
"answer": 40387,
"timestamp": "2026-02-08T04:18:39.698908Z"
} | 1cfa6e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1034
},
"timestamp": "2026-02-10T16:08:33.952Z",
"answer": 40387
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
7b7094 | diophantine_fbi2_count_v1_1353956133_826 | Let $d = 82$. Define $S_1$ as the set of all ordered pairs of positive odd integers $(x, y)$ such that $x + y = 162$. Let $m$ be the number of elements in $S_1$. Let $k = 120$ and $n = 2$. Define $S_2$ as the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = d$. Let $P$ be the set of all values ... | 7,035 | graphs = [
Graph(
let={
"_d": Const(82),
"_m": 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")), C... | NT | null | COUNT | sympy | COMB1 | [
"COMB1/B1",
"B1/B3"
] | c05788 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B1",
"B3",
"COMB1"
] | 3 | 0.014 | 2026-02-08T11:52:52.535426Z | {
"verified": true,
"answer": 7035,
"timestamp": "2026-02-08T11:52:52.549450Z"
} | e6db69 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 1695
},
"timestamp": "2026-02-14T19:57:05.046Z",
"answer": 7035
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
273631 | comb_count_permutations_fixed_v1_124444284_5460 | Let $n = 7$ and $k = 5$. Define $r = \binom{n}{k} \cdot !(n-k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 777924$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $s - r$. | 1,743 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(5),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | comb_count_permutations_fixed_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T06:36:51.096964Z | {
"verified": true,
"answer": 1743,
"timestamp": "2026-02-08T06:36:51.098856Z"
} | 60f4b0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 1034
},
"timestamp": "2026-02-24T06:35:54.526Z",
"answer": 1743
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
43209e | nt_count_divisible_v1_124444284_5102 | Let $d$ be the number of ordered pairs $(i,j)$ of integers such that $1 \le i \le 18$, $1 \le j \le 18$, and $i + j = 18$. Let $r = \sum_{k=0}^{3} (-1)^k \binom{3}{k}$. Compute the number of integers $n$ such that $0! \le n \le 53824$ and $n \equiv r \pmod{d}$. | 3,166 | graphs = [
Graph(
let={
"_n": Const(18),
"upper": Const(53824),
"divisor": 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(18)), r... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 633ce8 | nt_count_divisible_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 3 | 1.797 | 2026-02-08T06:23:34.282866Z | {
"verified": true,
"answer": 3166,
"timestamp": "2026-02-08T06:23:36.079945Z"
} | b63f7c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1227
},
"timestamp": "2026-02-24T06:06:48.382Z",
"answer": 3166
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7"... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
a881d2 | nt_min_crt_v1_677425708_1983 | Let $S$ be the set of all positive real solutions $x$ to the equation $x^2 - 144x - 10441 = 0$. Let $P$ be the product of all elements in $S$. Consider all ordered pairs $(x, y)$ of positive real numbers such that $xy = P$. Let $M$ be the minimum value of $x + y$ over all such pairs. Determine the smallest positive int... | 13 | graphs = [
Graph(
let={
"m": Const(3),
"k": Const(8),
"a": Const(1),
"b": Const(5),
"upper": 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 | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM/B3"
] | d036a4 | nt_min_crt_v1 | null | 7 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.016 | 2026-02-08T04:42:08.622973Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T04:42:08.639447Z"
} | 67182c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 1607
},
"timestamp": "2026-02-10T04:01:11.304Z",
"answer": 13
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
3ba9a4 | geo_count_lattice_triangle_v1_1470522791_1773 | Let $A$ be the set of all integers $t$ such that $9 \le t \le 141$ and there exist positive integers $a$ and $b$ with $1 \le a \le 13$, $1 \le b \le 19$, and $t = 5a + 4b$. Let $N = 121$. Define
\[
\text{area}_{2x} = \left| 121 \cdot |A| - 99 \cdot 24 \right|.
\]
Let
\[
\text{boundary} = \gcd(121, 24) + \gcd(|99 - 121|... | 6,127 | graphs = [
Graph(
let={
"_n": Const(121),
"area_2x": Abs(arg=Sum(Mul(CountOverSet(set=SolutionsSet(var=Var(name='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=Con... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T13:57:45.079960Z | {
"verified": true,
"answer": 6127,
"timestamp": "2026-02-08T13:57:45.089888Z"
} | f27527 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 5332
},
"timestamp": "2026-02-15T22:29:04.694Z",
"answer": 6127
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b05f3d | sequence_fibonacci_compute_v1_717093673_2842 | Let $n_1$ range over all positive integers that are multiples of $23$ and at most the largest prime number not exceeding $26$. Define $n$ to be the sum of all such $n_1$. 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 the remainder when $26617 \c... | 4,417 | graphs = [
Graph(
let={
"_n": Const(23),
"n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(2)), Leq(Var("n2"), Const(26)), IsPrime(Var("n2")))))), Eq(Mod... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/SUM_DIVISIBLE"
] | 831ad4 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 2 | 0.005 | 2026-02-08T17:13:40.683895Z | {
"verified": true,
"answer": 4417,
"timestamp": "2026-02-08T17:13:40.688777Z"
} | c2bfab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 2586
},
"timestamp": "2026-02-17T21:54:28.417Z",
"answer": 4417
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1789da | comb_count_permutations_fixed_v1_1978505735_5639 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 896$ and $\binom{896}{j}$ is odd. Compute $\binom{n}{0} \cdot !(n - 0)$, where $!k$ denotes the number of derangements of $k$ elements. | 14,833 | graphs = [
Graph(
let={
"_n": Const(896),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(896), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k": C... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"V8"
] | 1 | 0.004 | 2026-02-08T19:08:23.353762Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T19:08:23.357995Z"
} | 793983 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1737
},
"timestamp": "2026-02-18T21:22:55.715Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
3ae17e | comb_count_derangements_v1_898971024_571 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 200$ and $\binom{200}{j}$ is odd. The subfactorial $!n$ is the number of derangements of $n$ elements. Compute $!n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(200),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(200), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"resul... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T15:32:30.980947Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T15:32:30.982627Z"
} | 01b93e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1051
},
"timestamp": "2026-02-24T17:57:18.364Z",
"answer": 14833
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
9ea1e1 | nt_lcm_compute_v1_1439011603_553 | Let $a = 1165$ and $b = 2530$. Let $L = \mathrm{lcm}(a, b)$. Let $m$ be the largest prime number $n$ such that $2 \le n \le 2027$. Compute the remainder when $m - L$ is divided by $89979$. | 42,390 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1165),
"b": Const(2530),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(2027)), IsPr... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | nt_lcm_compute_v1 | negation_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T15:34:51.461901Z | {
"verified": true,
"answer": 42390,
"timestamp": "2026-02-08T15:34:51.465455Z"
} | 4c4145 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1501
},
"timestamp": "2026-02-16T10:07:30.219Z",
"answer": 42390
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0a600a | antilemma_k3_v1_458359167_5666 | Let $x = \sum_{d \mid 77041} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $30352x$ is divided by $69829$. | 54,538 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=77041), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(30352), Ref("x")), modulus=Const(69829)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:38:48.179487Z | {
"verified": true,
"answer": 54538,
"timestamp": "2026-02-08T12:38:48.180173Z"
} | ab5794 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 1750
},
"timestamp": "2026-02-15T03:12:27.848Z",
"answer": 54538
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ad2cc3 | geo_count_lattice_triangle_v1_655260480_6001 | Let $A$ be the area of the triangle with vertices at $(120, 44)$, $(169, 210)$, and $(0, 0)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle, computed as the sum of the greatest common divisors of the absolute differences of the coordinates along each edge. Compute the value o... | 11,686 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=210)), Mul(Const(value=169), Sub(left=Const(value=0), right=Const(value=44))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=44))), GCD(a=Abs(arg=Sub(left=Const(value=169), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.005 | 2026-02-08T18:46:25.977215Z | {
"verified": true,
"answer": 11686,
"timestamp": "2026-02-08T18:46:25.982086Z"
} | 36c951 | 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": 2878
},
"timestamp": "2026-02-18T19:30:09.671Z",
"answer": 11686
},
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
7a98c6 | antilemma_k3_v1_124444284_5313 | Let $n = 27711$. Compute the sum
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $n$. | 27,711 | graphs = [
Graph(
let={
"_n": Const(27711),
"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 | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T06:32:18.237441Z | {
"verified": true,
"answer": 27711,
"timestamp": "2026-02-08T06:32:18.237904Z"
} | b291c3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 808
},
"timestamp": "2026-02-15T17:33:33.662Z",
"answer": 18399
},
{
"id": 11,... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
475758 | comb_count_partitions_v1_677425708_1209 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 58$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 8$, satisfying $t = 7a + 2b$. Let $n$ be the number of elements in $T$. Compute the number of integer partitions of $n$. | 75,175 | graphs = [
Graph(
let={
"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=6)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:02:10.741925Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T04:02:10.743508Z"
} | c66aca | 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": 1755
},
"timestamp": "2026-02-09T17:03:42.976Z",
"answer": 75175
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"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... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
a23347_l | nt_count_gcd_equals_v1_1116507919_254 | Let $k$ be the number of positive integers $t$ such that $8 \leq t \leq 192$ and $t = 3a + 5b$ for some positive integers $a \leq 19$ and $b \leq 27$. Let $d = 177$ and let $\text{result}$ be the number of positive integers $n \leq 26569$ such that $\gcd(n, k) = d$. Let $Q$ be the remainder when $\text{result}$ multipl... | 0 | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | nt_count_gcd_equals_v1 | affine_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.933 | 2026-02-08T02:29:58.490796Z | {
"verified": false,
"answer": 25542,
"timestamp": "2026-02-08T02:30:00.424241Z"
} | cdc21b | a23347 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T13:58:12.939Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 4.86,
"mid": 6.35,
"hi": 8.29
} | |
4fb82f | modular_count_residue_v1_655260480_945 | Let $r = \sum_{k=0}^{2} (-1)^k \binom{2}{k}$. Compute the number of positive integers $n$ such that $1 \leq n \leq 51984$ and
$$
n \equiv r \pmod{2}.
$$ | 25,992 | graphs = [
Graph(
let={
"upper": Const(51984),
"m": Const(2),
"r": Summation(var="k", start=Const(0), end=Const(2), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(2), k=Var("k")))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | modular_count_residue_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 1.949 | 2026-02-08T15:46:47.699694Z | {
"verified": true,
"answer": 25992,
"timestamp": "2026-02-08T15:46:49.649172Z"
} | 9bc846 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 416
},
"timestamp": "2026-02-24T18:32:11.309Z",
"answer": 25992
},
{
"... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
fed6c5 | nt_count_divisors_in_range_v1_1915831931_2624 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 176400$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all positive integers $t$ such that $27 \leq t \leq 672$ and $t = 21a + 6b$ for some integers $a, b$ with $1 \leq a \leq 28$ and $1 \le... | 40,725 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": 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(176400)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.013 | 2026-02-08T17:00:25.141666Z | {
"verified": true,
"answer": 40725,
"timestamp": "2026-02-08T17:00:25.154270Z"
} | cc7c91 | 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": 4000
},
"timestamp": "2026-02-17T17:13:46.607Z",
"answer": 40725
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
37a51a | antilemma_k2_v1_784195855_7862 | Let $c = 3300$ and $m = 133$. Let $n = \sum_{d \mid m} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $k_0$ be the sum of all real solutions $x$ to the equation $x^2 - 133x + 3300 = 0$. Compute $\sum_{k=1}^{k_0} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$. | 8,911 | graphs = [
Graph(
let={
"_c": Const(3300),
"_m": Const(133),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), ... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K3/K2",
"K2"
] | 4108ea | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T09:34:02.068756Z | {
"verified": true,
"answer": 8911,
"timestamp": "2026-02-08T09:34:02.070778Z"
} | df0c3a | 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": 805
},
"timestamp": "2026-02-14T05:04:54.444Z",
"answer": 8911
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
43f16c | algebra_poly_eval_v1_1218484723_561 | Let $z = 19$. Compute
\[
\frac{120z^5 - 278z^4 + 29z^3 + 320z^2 - 233z + 42}{\min\{ x + y : x > 0, y > 0, xy = 10316944 \}}.
\] | 40,662 | graphs = [
Graph(
let={
"_n": Const(5),
"z": Const(19),
"result": Div(Sum(Mul(Const(120), Pow(Ref("z"), Ref("_n"))), Mul(Const(-278), Pow(Ref("z"), Const(4))), Mul(Const(29), Pow(Ref("z"), Const(3))), Mul(Const(320), Pow(Ref("z"), Const(2))), Mul(Const(-233), Ref("z")), C... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-25T02:13:06.349017Z | {
"verified": true,
"answer": 40662,
"timestamp": "2026-02-25T02:13:06.354071Z"
} | ebb2d5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2342
},
"timestamp": "2026-03-28T23:10:47.092Z",
"answer": 40662
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
44d636 | nt_count_divisors_in_range_v1_809748730_12 | Let $n = 498960$, $a = 11$, and $b = 3249$. Define $r$ to be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 484$. Compute $r^2 + 2r + s$. | 18,268 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(498960),
"a": Const(11),
"b": Const(3249),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), R... | NT | null | COUNT | sympy | B3 | [
"B3"
] | d720b5 | nt_count_divisors_in_range_v1 | quadratic_mod | 4 | 0 | [
"B3"
] | 1 | 0.033 | 2026-02-08T11:17:28.387707Z | {
"verified": true,
"answer": 18268,
"timestamp": "2026-02-08T11:17:28.420236Z"
} | 3ef271 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 4623
},
"timestamp": "2026-02-14T11:36:33.452Z",
"answer": 18268
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1e0de2 | alg_sym_quad_system_v1_1218484723_6911 | Consider all ordered triples $(a,b,c)$ of positive integers satisfying
$$a^{2} + b^{2} + c^{2} = ab + bc + ca$$
and
$$5a + 9b + 4c = \left|\{n : 1 \le n \le 34146,\ n \equiv \lfloor n/2 \rfloor \pmod{7}\}\right|.$$
For each such triple, form $a^{3} + b^{3} + c^{3}$ and take the sum over all these triples. Find the rema... | 141 | graphs = [
Graph(
let={
"_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"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | alg_sym_quad_system_v1 | null | 7 | 0 | [
"L3C"
] | 1 | 0.014 | 2026-02-25T08:22:13.485115Z | {
"verified": true,
"answer": 141,
"timestamp": "2026-02-25T08:22:13.499112Z"
} | cce2a8 | 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": 4633
},
"timestamp": "2026-03-30T03:08:49.342Z",
"answer": 141
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
3d1730 | antilemma_k2_v1_677425708_4141 | Let $m = 2$. Let $n$ be the sum of all real solutions $x$ to the equation $x^m - 369x - 31752 = 0$. Compute $$\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{369}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 68,265 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-369), Var("x")), Const(-31752)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k"))... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T06:27:45.410217Z | {
"verified": true,
"answer": 68265,
"timestamp": "2026-02-08T06:27:45.411018Z"
} | c103b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 797
},
"timestamp": "2026-02-13T00:26:04.514Z",
"answer": 68265
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4776c4 | comb_count_partitions_v1_124444284_5502 | Let $ S $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq 39 $ and $ n $ is divisible by 39. Let $ s $ be the sum of all elements in $ S $. Let $ p(s) $ denote the number of integer partitions of $ s $. Compute the remainder when $ 29890 - p(s) $ is divided by 89681. | 88,386 | graphs = [
Graph(
let={
"_n": Const(89681),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(39)), Eq(Mod(value=Var("n"), modulus=Const(39)), Const(0))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mo... | COMB | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_count_partitions_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T06:37:58.484611Z | {
"verified": true,
"answer": 88386,
"timestamp": "2026-02-08T06:37:58.486035Z"
} | 43b3ed | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1620
},
"timestamp": "2026-02-24T06:52:00.879Z",
"answer": 88386
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
763701 | nt_count_intersection_v1_655260480_498 | Define $b$ to be
$$
\frac{5}{40} \sum_{k=1}^{4} \sum_{j=1}^{8} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n \leq 20000$ such that $7$ divides $n$ and $\gcd(n, b) = 1$. | 1,143 | graphs = [
Graph(
let={
"_n": Const(4),
"N": Const(20000),
"a": Const(7),
"b": Div(Mul(Const(5), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1),... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | nt_count_intersection_v1 | null | 6 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.858 | 2026-02-08T15:24:47.421935Z | {
"verified": true,
"answer": 1143,
"timestamp": "2026-02-08T15:24:48.279881Z"
} | e45601 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1459
},
"timestamp": "2026-02-16T05:31:39.062Z",
"answer": 1143
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
12ae59 | diophantine_fbi2_count_v1_717093673_3930 | Let $d$ be a positive integer. Define $k = 240$. Let $T$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 26$, $1 \le b \le 5$, $14 \le t \le 280$, and $t = 10a + 4b$. Let $m$ be the number of elements in $T$. Determine the number of divisors $d$ of $k$ such that $d \ge ... | 15 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(nam... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.019 | 2026-02-08T17:58:16.612720Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T17:58:16.631237Z"
} | 342f39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 3755
},
"timestamp": "2026-02-18T10:50:52.422Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
53b29c | nt_count_divisors_in_range_v1_124444284_9099 | Let $n = 83160$. Let $a$ be the number of integers $t$ such that $15 \le t \le 78$ and there exist positive integers $a'$ and $b'$ with $1 \le a' \le 2$, $1 \le b' \le 10$, and $t = 9a' + 6b'$. Let $b = 2527$. Compute the number of positive divisors $d$ of $n$ such that $a \le d \le b$. | 91 | graphs = [
Graph(
let={
"n": Const(83160),
"a": 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=2)), Geq(left=Var... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.224 | 2026-02-08T12:13:29.119546Z | {
"verified": true,
"answer": 91,
"timestamp": "2026-02-08T12:13:29.343826Z"
} | b9a835 | 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": 3453
},
"timestamp": "2026-02-14T23:24:48.763Z",
"answer": 91
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0dd3a3 | alg_poly4_min_v1_1218484723_927 | Let $s = \min\{x+y \mid x,y > 0,\, xy = 13741849\}$ and $t = \min\{x_1+y_1 \mid x_1,y_1 > 0,\, x_1y_1 = 7991929\}$. Find the minimum value of $s b^4 + t a^4 + 34980 a^2 b^2 + 24904 a b^3 + 22792 a^3 b$ over all positive integers $a, b$ with $1 \leq a, b \leq 490$. | 95,744 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(3),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(490)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(490)))), e... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.546 | 2026-02-25T02:37:41.743821Z | {
"verified": true,
"answer": 95744,
"timestamp": "2026-02-25T02:37:42.289357Z"
} | de4a03 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1855
},
"timestamp": "2026-03-10T02:57:08.222Z",
"answer": 95744
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
868249 | modular_count_residue_v1_1520064083_5355 | Let $ m = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor $, where $\phi$ denotes Euler's totient function. Let $ N $ be the number of positive integers $ n $ such that $ 1 \leq n \leq 60516 $ and $ n \equiv 1 \pmod{m} $. Compute the value of $ N $. | 6,052 | graphs = [
Graph(
let={
"upper": Const(60516),
"m": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"r": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 4 | 0 | [
"K2"
] | 1 | 3.673 | 2026-02-08T06:45:15.134620Z | {
"verified": true,
"answer": 6052,
"timestamp": "2026-02-08T06:45:18.807408Z"
} | 52ff25 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 619
},
"timestamp": "2026-02-13T04:11:12.448Z",
"answer": 6052
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2743ec | nt_count_divisible_v1_238844314_143 | Let $d = \sum_{k=1}^{2} k$. Compute the number of positive integers $n$ such that $1 \leq n \leq 53361$ and $n$ is divisible by $d$. Find the value of this count. | 17,787 | graphs = [
Graph(
let={
"upper": Const(53361),
"divisor": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modu... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 2.258 | 2026-02-08T13:08:17.151241Z | {
"verified": true,
"answer": 17787,
"timestamp": "2026-02-08T13:08:19.408760Z"
} | 4dc757 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 255
},
"timestamp": "2026-02-16T04:26:13.864Z",
"answer": 17787
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
c3f0b5 | nt_count_with_divisor_count_v1_1978505735_1744 | Let $m = 5$. Let $n$ be the largest prime number such that $2 \leq n \leq 6$. Define
$$
d = \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 20000$ and the number of positive d... | 19 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))),
"upper": Const(20000),
"div_count": Summation(var="k", start=Const(1), end=Ref("_m"), ... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 4.846 | 2026-02-08T16:22:59.034729Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T16:23:03.880461Z"
} | a4c4b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 3278
},
"timestamp": "2026-02-17T02:21:32.653Z",
"answer": 19
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2d9a59 | nt_gcd_compute_v1_124444284_372 | Let $n_1 = 6859$. Define $c$ to be the number of distinct prime factors of $n_1$. Let $w$ be the sum of $\mu(d)$ over all positive divisors $d$ of $1$, where $\mu$ denotes the Möbius function. Define $a = 84280$ and $b = 189630 \cdot c \cdot w$. Compute $\gcd(a, b)$. | 21,070 | graphs = [
Graph(
let={
"n1": Const(6859),
"c": SmallOmega(n=Ref(name='n1')),
"n": Const(1),
"w": SumOverDivisors(n=Ref(name='n'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"a": Const(84280),
"b": Mul(Const(189630), Ref("c"), Ref("w"))... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"OMEGA_ONE"
] | f75c62 | nt_gcd_compute_v1 | null | 3 | 2 | [
"MOBIUS_SUM",
"OMEGA_ONE"
] | 2 | 0.001 | 2026-02-08T03:13:47.082044Z | {
"verified": true,
"answer": 21070,
"timestamp": "2026-02-08T03:13:47.083115Z"
} | 7b2e6f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 570
},
"timestamp": "2026-02-09T01:26:04.867Z",
"answer": 21070
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "OMEGA_ONE",
"status": "ok"
},
{
"lemma": "... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
f346ed | comb_count_partitions_v1_151522320_1291 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 64$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 6$, and $t = 5a + 4b$. Compute the number of integer partitions of $n$. | 75,175 | graphs = [
Graph(
let={
"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=8)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:52:20.313441Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T03:52:20.315703Z"
} | b67722 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1832
},
"timestamp": "2026-02-10T16:18:25.304Z",
"answer": 75175
},
{
"... | 1 | [
{
"lemma": "C2",
"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",
"status": "no"
... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
23f7b9 | nt_gcd_compute_v1_1116507919_436 | Let $p_1 = 13$. Compute $m = \left((p_1 - 1)! + 1\right) \bmod p_1$. Let $p$ be the largest prime number at most $41$. Let $s$ be the number of prime factors of $p$, counted with multiplicity. Let $a = 289160$ and $b = 636152 \cdot s$. Compute $g = \gcd(a, b)$. Find the remainder when $(53147 + m) \cdot g$ is divided b... | 20,808 | graphs = [
Graph(
let={
"p1": Const(13),
"m": Mod(value=Sum(Factorial(Sub(Ref("p1"), Const(1))), Const(1)), modulus=Ref("p1")),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(41)), IsPrime(Var("n"))))),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/BIG_OMEGA_ONE",
"WILSON"
] | 374b5a | nt_gcd_compute_v1 | null | 4 | 2 | [
"BIG_OMEGA_ONE",
"MAX_PRIME_BELOW",
"WILSON"
] | 3 | 0.003 | 2026-02-08T02:34:11.663731Z | {
"verified": true,
"answer": 20808,
"timestamp": "2026-02-08T02:34:11.666671Z"
} | 8abf86 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2130
},
"timestamp": "2026-02-08T19:33:00.172Z",
"answer": 20808
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
5d52bc | modular_inverse_v1_1456120455_81 | Let $a = 189$. Define $T$ as the set of all integers $t$ such that there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 88$, $1 \leq b' \leq 105$, and $t = 2a' + 3b'$, and such that $5 \leq t \leq 491$. Let $m$ be the largest prime number $n$ satisfying $2 \leq n \leq |T|$. Define $S$ as the set of all posi... | 37 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(189),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b')... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | modular_inverse_v1 | null | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.314 | 2026-02-08T02:53:03.692463Z | {
"verified": true,
"answer": 37,
"timestamp": "2026-02-08T02:53:04.006708Z"
} | b22ecf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 4732
},
"timestamp": "2026-02-08T20:02:39.056Z",
"answer": 37
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": 0.24,
"mid": 2.75,
"hi": 4.89
} | ||
2b70ea | comb_binomial_compute_v1_1978505735_6960 | Let $n = 15$ and $k = 6$. Define $a = \binom{n}{k}$. Let $s$ be the sum $\sum_{i=0}^{d-1} d_i (i+1)^2$, where $d_i$ is the $i$-th decimal digit of $a$ (starting from the units digit as $i=0$) and $d$ is the number of digits in $a$. Let $t$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such tha... | 213 | graphs = [
Graph(
let={
"_n": Const(4096),
"n": Const(15),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 8e300c | comb_binomial_compute_v1 | digits_weighted_mod | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T19:54:43.816287Z | {
"verified": true,
"answer": 213,
"timestamp": "2026-02-08T19:54:43.819144Z"
} | c7df61 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1145
},
"timestamp": "2026-02-18T23:44:19.494Z",
"answer": 213
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
fa7c12 | lin_form_endings_v1_124444284_9467 | Let $a = 30$ and $b = 42$. Define $r = \left\lfloor \frac{42}{\gcd(a, b)} \right\rfloor$. Let $s = 18239 \cdot r$. Compute the remainder when $s$ is divided by 75123. | 52,550 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(42),
"_inner_result": Floor(Div(Const(42), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(18239),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:30:43.541729Z | {
"verified": true,
"answer": 52550,
"timestamp": "2026-02-08T12:30:43.542451Z"
} | 40edd2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 236
},
"timestamp": "2026-02-16T03:47:40.840Z",
"answer": 52550
},
{
"id": 11,
... | 2 | [
{
"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": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
402b62 | nt_sum_gcd_range_mod_v1_397696148_1863 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1587600$. Let $T$ be the set of all values $x + y$ as $(x,y)$ ranges over $S$. Let $N$ be the sum of $\phi(d)$ over all positive divisors $d$ of the minimum element of $T$, where $\phi$ denotes Euler's totient function. Define $k = 480... | 4,246 | graphs = [
Graph(
let={
"N": SumOverDivisors(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Mul(Var(name='x'), Var(name='y')), right=Const(value=1587600)))), expr... | NT | null | COMPUTE | sympy | B3 | [
"B3/K3"
] | 4a4ef2 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3",
"K3"
] | 2 | 0.12 | 2026-02-08T12:48:31.996398Z | {
"verified": true,
"answer": 4246,
"timestamp": "2026-02-08T12:48:32.116077Z"
} | 7c2a4e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 3719
},
"timestamp": "2026-02-15T05:50:10.249Z",
"answer": 4246
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
4514c2 | diophantine_fbi2_min_v1_717093673_3231 | Let $k = 14$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Define $s_{\text{min}}$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $D$ be the set of all positive integers $d$ such that $d \geq s_{\text{min}}$, $d \leq 24$, $d$ divides $k$, and $\frac{k}{d... | 18 | graphs = [
Graph(
let={
"k": Const(14),
"upper": Const(24),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), Is... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"ONE_PHI_2"
] | 2 | 0.047 | 2026-02-08T17:26:54.506896Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T17:26:54.553809Z"
} | 123e59 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 377
},
"timestamp": "2026-02-16T09:43:25.292Z",
"answer": 18
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
513859 | nt_count_coprime_v1_579913215_82 | Let $k$ be the number of integers $t$ such that $13 \leq t \leq 38$ and there exist integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 2$, and $t = 2a + 5b + 6$. Let $Q$ be the remainder when $44121$ times the number of positive integers $n \leq 64516$ satisfying $\gcd(n, k) = 1$ is divided by $56183$. Comput... | 10,018 | graphs = [
Graph(
let={
"upper": Const(64516),
"k": 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=11)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 16.846 | 2026-02-08T12:50:42.847631Z | {
"verified": true,
"answer": 10018,
"timestamp": "2026-02-08T12:50:59.693378Z"
} | e17203 | 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": 2942
},
"timestamp": "2026-02-15T06:13:22.302Z",
"answer": 10018
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ea7162 | algebra_quadratic_discriminant_v1_655260480_3903 | Let $a = 2$, $b = 0$, and $c = 0$. Define the discriminant $D = b^2 - 4ac$. Let $\alpha = 1$ if $D > 0$, and $\alpha = 0$ otherwise. Let $\beta = 1$ if $D = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, and $\beta = 0$ otherwise. Compute $2\alpha + \beta$. | 1 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(0),
"c": Const(0),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Summat... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.004 | 2026-02-08T17:36:40.858366Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:36:40.862236Z"
} | 4aeea9 | 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": 540
},
"timestamp": "2026-02-24T22:49:29.622Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
784cbc | nt_sum_gcd_range_mod_v1_153355830_2943 | Let $N = 2281$ and let $k = \sum_{d \mid 540} \phi(d)$, where the sum is over all positive divisors $d$ of 540. Compute
\[
\sum_{n=1}^{N} \gcd(n, k),
\]
and let $r$ be the remainder when this sum is divided by $11731$. Find the remainder when $95455 \cdot r$ is divided by 92002. | 70,639 | graphs = [
Graph(
let={
"N": Const(2281),
"k": SumOverDivisors(n=Const(value=540), var='d', expr=EulerPhi(n=Var(name='d'))),
"M": Const(11731),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.201 | 2026-02-08T07:29:01.149838Z | {
"verified": true,
"answer": 70639,
"timestamp": "2026-02-08T07:29:01.351277Z"
} | 077ee5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 3173
},
"timestamp": "2026-02-13T10:31:28.090Z",
"answer": 70639
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
c90be4 | modular_modexp_compute_v1_1125832087_685 | Let $a = 5$ and $n = 176$. Let $e$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $m = 41616$, and define
$$
r = a^e \bmod m.
$$
Compute the remainder when $44121 \cdot r$ is divided by $68011$. | 25,944 | graphs = [
Graph(
let={
"_n": Const(176),
"a": Const(5),
"e": 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 | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T03:13:01.463343Z | {
"verified": true,
"answer": 25944,
"timestamp": "2026-02-08T03:13:01.465488Z"
} | 450a3d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2228
},
"timestamp": "2026-02-10T13:31:18.958Z",
"answer": 25944
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
127221 | algebra_quadratic_discriminant_v1_601307018_4027 | Let $b$ be the largest positive integer $d$ such that $d^2 \le \max\{ d_1 : d_1 \ge 1,\, d_1 \mid 12430,\, d_1^2 \le 12430 \}$ and $d \mid 110$. Let $M = b^2 - 180$. Compute $\sum_{n=1}^{|M|} \varphi(n)$. | 1,966 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(5),
"b": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(110)), Leq(Mul(Var("d"), Var("d")), MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=A... | NT | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"B3_CLOSEST/B3_CLOSEST"
] | 13f355 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.125 | 2026-03-10T04:38:07.251890Z | {
"verified": true,
"answer": 1966,
"timestamp": "2026-03-10T04:38:07.376800Z"
} | 727976 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 3187
},
"timestamp": "2026-03-29T10:47:50.443Z",
"answer": 1966
},
{
"i... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
e3986d | diophantine_product_count_v1_168721529_1871 | Let $n = 40$, $k = 120$, and $\text{upper} = 106$. Define $\text{result}$ to be the number of positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$. Let $c = 10$. Compute the value of $\text{result}^2 + \left(\sum_{d \mid n} \phi(d)\right) \cdot \text{result}... | 766 | graphs = [
Graph(
let={
"_n": Const(40),
"k": Const(120),
"upper": Const(106),
"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(Ref("... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 373090 | diophantine_product_count_v1 | quadratic_mod | 4 | 0 | [
"K3"
] | 1 | 0.013 | 2026-02-08T13:58:21.242840Z | {
"verified": true,
"answer": 766,
"timestamp": "2026-02-08T13:58:21.255907Z"
} | f4f889 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1378
},
"timestamp": "2026-02-09T22:49:55.409Z",
"answer": 766
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
1ddfb9 | nt_sum_divisors_mod_v1_124444284_10348 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 8100$. Let $\sigma$ be the sum of all positive divisors of $n$. Let $M = 11351$. Compute the remainder when $\sigma$ is divided by $M$. Let $c$ be the largest prime number not exceeding $2010$. Let $r_1$ be the remainder whe... | 14,576 | graphs = [
Graph(
let={
"_n": Const(2010),
"n": 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(8100)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 45e23c | nt_sum_divisors_mod_v1 | two_moduli | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T12:59:15.542100Z | {
"verified": true,
"answer": 14576,
"timestamp": "2026-02-08T12:59:15.547002Z"
} | 81634b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2074
},
"timestamp": "2026-02-15T09:01:40.909Z",
"answer": 14576
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f8382d | comb_count_derangements_v1_784195855_416 | Let $n = 7$ and define $r = !n$, the number of derangements of $n$ elements. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 62500$. Define $s$ to be the minimum value of $x + y$ over all such pairs.
Let $Q$ be the remainder when $s - r$ is divided by $95357$.
Find the val... | 94,003 | graphs = [
Graph(
let={
"_n": Const(62500),
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositiv... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | comb_count_derangements_v1 | negation_mod | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:21:49.737436Z | {
"verified": true,
"answer": 94003,
"timestamp": "2026-02-08T04:21:49.739171Z"
} | 5cd23a | 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": 2227
},
"timestamp": "2026-02-24T00:17:40.636Z",
"answer": 94003
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
2b38a1 | comb_sum_binomial_row_v1_1915831931_3276 | Let $m = 2$. Let $t$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 3$ and $1 \leq b \leq 5$. Let $p$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number that is at least $p$ and at... | 8,192 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(5)))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), CountOverSet(s... | NT | null | SUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/MAX_PRIME_BELOW",
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 266339 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"COUNT_CARTESIAN",
"MAX_PRIME_BELOW"
] | 3 | 0.005 | 2026-02-08T17:31:39.833115Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T17:31:39.838163Z"
} | 18b713 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 189
},
"timestamp": "2026-02-16T11:23:11.719Z",
"answer": 8192
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_la... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
efce7c | comb_count_partitions_v1_1742523217_4946 | Let $ m $ be the maximum value of $ xy $ over all pairs of positive integers $ (x, y) $ such that $ x + y = 44 $. Let $ s $ be the minimum value of $ x + y $ over all pairs of positive integers $ (x, y) $ such that $ xy = m $. Compute the remainder when $ 87805 $ times the number of integer partitions of $ s $ is divid... | 13,483 | graphs = [
Graph(
let={
"_n": Const(74981),
"n": 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")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var... | COMB | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_count_partitions_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T10:40:51.218245Z | {
"verified": true,
"answer": 13483,
"timestamp": "2026-02-08T10:40:51.219909Z"
} | 8f5159 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1496
},
"timestamp": "2026-02-24T12:13:29.515Z",
"answer": 13483
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e4bc4b | comb_factorial_compute_v1_784195855_4497 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 110250$, $\gcd(p, q) = 1$, and $p < q$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"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(name='q')), right=Const(value=110250)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T07:08:48.872111Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T07:08:48.873333Z"
} | 233a56 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1337
},
"timestamp": "2026-02-13T08:12:54.188Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a5d219 | comb_count_derangements_v1_1820931509_512 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 2208$ and $\binom{2208}{j}$ is odd. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2208)), Eq(Mod(value=Binom(n=Const(2208), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T11:40:37.166160Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T11:40:37.167029Z"
} | 3d295a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1128
},
"timestamp": "2026-02-24T14:34:33.132Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7bccbd | diophantine_fbi2_min_v1_153355830_2858 | Let $k = 72$. Consider the set of all integers $d$ such that $4 \leq d \leq 82$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Compute the minimum value of $d$ in this set. | 4 | graphs = [
Graph(
let={
"k": Const(72),
"a": Const(3),
"b": Const(3),
"upper": Const(82),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | B3 | [
"B3/COMB1"
] | e26f7e | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"B3",
"COMB1"
] | 2 | 0.041 | 2026-02-08T07:26:43.791669Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T07:26:43.833116Z"
} | 104b53 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 336
},
"timestamp": "2026-02-15T18:59:19.126Z",
"answer": 6
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
116f12 | algebra_poly_eval_v1_1431428450_144 | Let $n = 12$ and let $p_{\text{max}}$ be the largest prime number $p$ such that $2 \le p \le 6$.
Compute the value of $2n^4 + 9n^3 + p_{\text{max}} \cdot n^2 + 2n + 7$. | 57,775 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"result": Sum(Mul(Const(2), Pow(Ref("n"), Const(4))), Mul(Const(9), Pow(Ref("n"), Const(3))), Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(6)), IsPrime(Var... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.006 | 2026-02-08T13:16:44.299557Z | {
"verified": true,
"answer": 57775,
"timestamp": "2026-02-08T13:16:44.305480Z"
} | 166917 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 533
},
"timestamp": "2026-02-16T04:30:02.049Z",
"answer": 57775
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
a7c689 | antilemma_k2_v1_2051736721_2287 | Compute $$\sum_{k=1}^{229} \phi(k) \left\lfloor \frac{229}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function.\n\nFind the value of this sum. | 26,335 | graphs = [
Graph(
let={
"_n": Const(229),
"x": Summation(var="k", start=Const(1), end=Const(229), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T16:33:46.484975Z | {
"verified": true,
"answer": 26335,
"timestamp": "2026-02-08T16:33:46.485663Z"
} | 56c248 | 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": 744
},
"timestamp": "2026-02-17T06:37:03.501Z",
"answer": 26335
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0511a3 | alg_poly_preperiod_count_v1_1218484723_3139 | For a non-negative integer $a$, define $N = a^3 - 4a \bmod 73$, $M = N^3 - 4N \bmod 73$, $R = M^3 - 4M \bmod 73$, $S = R^3 - 4R \bmod 73$. Find the number of integers $a$ with $0 \le a \le 82343$ such that $S = M$ and $R \ne M$. | 9,024 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-4), Var("a"))), modulus=Const(73)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-4), Ref("p1"))), modulus=Const(73)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(-4), R... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.018 | 2026-02-25T04:51:19.688026Z | {
"verified": true,
"answer": 9024,
"timestamp": "2026-02-25T04:51:19.706035Z"
} | 8ed55f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 30292
},
"timestamp": "2026-03-29T08:39:46.634Z",
"answer": 6768
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
825eab | nt_max_prime_below_v1_677425708_1634 | Let $n = 67129$. Define $P$ as the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $P$. Determine the largest prime number $n'$ such that $c \leq n' \leq 32768$. Compute the remainder when $44... | 34,033 | graphs = [
Graph(
let={
"_n": Const(67129),
"upper": Const(32768),
"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=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.624 | 2026-02-08T04:20:52.069724Z | {
"verified": true,
"answer": 34033,
"timestamp": "2026-02-08T04:20:53.693416Z"
} | 326027 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 8147
},
"timestamp": "2026-02-10T16:16:13.270Z",
"answer": 34033
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
c8d7c5 | diophantine_fbi2_count_v1_1742523217_618 | Let $k = 240$. Let $T$ be the set of all integers $n$ such that $1 \leq n \leq 396$ and the sum of the decimal digits of $n$ is even. Let $c$ be the number of elements in $T$. Let $D$ be the set of all positive integers $d$ such that $6 \leq d \leq 201$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq c$. Let $\text{resu... | 17,775 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(201)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(... | NT | null | COUNT | sympy | L3B | [
"L3B",
"B3"
] | e8deef | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3",
"L3B"
] | 2 | 0.011 | 2026-02-08T03:09:08.339127Z | {
"verified": true,
"answer": 17775,
"timestamp": "2026-02-08T03:09:08.350543Z"
} | afb422 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 2183
},
"timestamp": "2026-02-09T20:20:52.030Z",
"answer": 17775
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lem... | {
"lo": -3.55,
"mid": 0.8,
"hi": 4.81
} | ||
74f5b6 | geo_count_lattice_triangle_v1_865884756_2933 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(324,300)$, and $(90,111)$, multiplied by $2$. Compute $A = |324 \cdot 111 + 90 \cdot (-300)|$. Let $B$ be the number of lattice points on the boundary of this triangle, given by $B = \gcd(324,300) + \gcd(|90-324|, |111-300|) + \gcd(90,111)$. Using Pick's T... | 18,075 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=324), Const(value=111)), Mul(Const(value=90), Sub(left=Const(value=0), right=Const(value=300))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=324)), b=Abs(arg=Const(value=300))), GCD(a=Abs(arg=Sub(left=Const(value=90), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.005 | 2026-02-08T17:01:36.606766Z | {
"verified": true,
"answer": 18075,
"timestamp": "2026-02-08T17:01:36.611755Z"
} | be46b0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1470
},
"timestamp": "2026-02-17T17:26:48.877Z",
"answer": 18075
},
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
c5c191 | alg_qf_psd_min_v1_1218484723_2156 | Let $P$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 25$ such that $-2a_1b_1 + 2b_1^2 + 13a_1^2 \le 1097$. Let $B = |P|$. Find the minimum value of $457750a^2 - 366200ab + 91550b^2$ over all positive integers $a, b$ with $1 \le a \le 180$ and $1 \le b \le B$. | 91,550 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(180)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elem... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_min_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.061 | 2026-02-25T03:55:46.821812Z | {
"verified": true,
"answer": 91550,
"timestamp": "2026-02-25T03:55:46.882804Z"
} | dd6592 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 9242
},
"timestamp": "2026-03-29T03:18:13.261Z",
"answer": 91550
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
2d340f | antilemma_sum_equals_v1_124444284_5567 | Let $n = 89$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = n$, where $1 \le i \le 87$ and $1 \le j \le 88$. Let $x$ be the number of such ordered pairs. Compute the remainder when $|x|$ is divided by $94229$. | 87 | graphs = [
Graph(
let={
"_n": Const(89),
"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(87)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.031 | 2026-02-08T06:42:47.047173Z | {
"verified": true,
"answer": 87,
"timestamp": "2026-02-08T06:42:47.077681Z"
} | 825d52 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1671
},
"timestamp": "2026-02-24T06:52:14.603Z",
"answer": 87
},
{
"id"... | 2 | [
{
"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",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
f3d3b7 | nt_sum_over_divisible_v1_1431428450_643 | Let $n$ be a positive integer such that $1 \leq n \leq 5279$ and $n$ is divisible by 159. Compute the sum of all such $n$. | 89,199 | graphs = [
Graph(
let={
"upper": Const(5279),
"divisor": Const(159),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
},
go... | NT | null | SUM | sympy | ONE_PHI_1 | [
"MAX_PRIME_BELOW/COUNT_PRIMES"
] | bfe068 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 3 | 3.84 | 2026-02-08T13:35:56.637934Z | {
"verified": true,
"answer": 89199,
"timestamp": "2026-02-08T13:36:00.478216Z"
} | 66500f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 730
},
"timestamp": "2026-02-15T18:10:33.511Z",
"answer": 89199
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3d5471 | geo_count_lattice_triangle_v1_458359167_2313 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(484,256)$, and $(256,128)$, multiplied by 2. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates along each side of the triangle, specifically:
- $\gcd(|484 - 0|, |256 - 0|)$,
- $\gcd(|256 - 484|, |128 - 256|)... | 1,725 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=484), Const(value=128)), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=256))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=484)), b=Abs(arg=Const(value=256))), GCD(a=Abs(arg=Sub(left=Const(value=256), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.004 | 2026-02-08T05:18:32.605339Z | {
"verified": true,
"answer": 1725,
"timestamp": "2026-02-08T05:18:32.609465Z"
} | befd6c | 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": 908
},
"timestamp": "2026-02-12T06:05:05.859Z",
"answer": 1725
},
{
... | 1 | [] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||||
a4c6ad | nt_sum_divisors_mod_v1_153355830_2617 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Let $n$ be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $11399$. | 7,945 | graphs = [
Graph(
let={
"n": 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(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1139... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T07:14:47.852459Z | {
"verified": true,
"answer": 7945,
"timestamp": "2026-02-08T07:14:47.853849Z"
} | 56914f | 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": 1654
},
"timestamp": "2026-02-13T09:08:04.595Z",
"answer": 7945
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} |
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