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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0f0e66 | nt_count_divisible_and_v1_168721529_1035 | Let $\mu(n)$ denote the Möbius function, and let $F_k$ denote the $k$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Define $S$ to be the set of all positive integers $n \leq 35694$ such that $n$ is divisible by 6 and the remainder when $n$ is divided by 9 equals $\sum_{d... | 995 | graphs = [
Graph(
let={
"upper": Const(35694),
"d1": Const(6),
"d2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(Mo... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"MOBIUS_SUM"
] | 518e32 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"MOBIUS_SUM"
] | 1 | 1.185 | 2026-02-08T13:25:55.496409Z | {
"verified": true,
"answer": 995,
"timestamp": "2026-02-08T13:25:56.681604Z"
} | 8e8db5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 6052
},
"timestamp": "2026-02-09T12:49:54.744Z",
"answer": 995
},
{
"id... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
e34699 | modular_modexp_compute_v1_153355830_398 | Let $a = 5$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 3694084$. Define $e$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $m = 88209$. Compute the value of $a^e \bmod m$. | 7,555 | graphs = [
Graph(
let={
"a": Const(5),
"e": 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(3694084)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:05:10.380772Z | {
"verified": true,
"answer": 7555,
"timestamp": "2026-02-08T03:05:10.382552Z"
} | fdab72 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 3523
},
"timestamp": "2026-02-10T12:37:25.890Z",
"answer": 7555
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.16,
"hi": 5.68
} | ||
abb5ce | nt_sum_gcd_range_mod_v1_971394319_730 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 172$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 28224$. Define $M = 11059$ and let
$$
\sum_{n=1}^{N} \gcd(n, k)
$$
be the sum of the greatest common divisors ... | 85,913 | graphs = [
Graph(
let={
"_n": Const(28224),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(172)))), expr=Mul(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B1 | [
"B1",
"B3"
] | 655d51 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.39 | 2026-02-08T13:17:12.958008Z | {
"verified": true,
"answer": 85913,
"timestamp": "2026-02-08T13:17:13.347997Z"
} | e96a5a | 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": 2876
},
"timestamp": "2026-02-15T11:49:05.167Z",
"answer": 85913
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5d9682 | nt_count_intersection_v1_1431428450_294 | Let $N = 100000$ and $a = 3$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 100$. Let $b$ be the minimum value of $x + y$ over all pairs in $S$. Compute the number of positive integers $n \leq N$ such that $3$ divides $n$ and $\gcd(n, b) = 1$. | 13,334 | graphs = [
Graph(
let={
"_n": Const(100),
"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=Var(name='y')), Eq(Mul(Var("x"), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 9.076 | 2026-02-08T13:23:08.990055Z | {
"verified": true,
"answer": 13334,
"timestamp": "2026-02-08T13:23:18.066534Z"
} | 6e2883 | 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": 1130
},
"timestamp": "2026-02-15T13:58:02.087Z",
"answer": 13334
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
deae44 | modular_modexp_compute_v1_1874849503_1441 | Let $a$ be the largest prime number between 2 and 16, inclusive. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 160000$. Define $e$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Compute the remainder when $a^e$ is divided by $30625$. Determine the value of this rem... | 15,751 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(16)), IsPrime(Var("n"))))),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditi... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | modular_modexp_compute_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T13:54:07.444074Z | {
"verified": true,
"answer": 15751,
"timestamp": "2026-02-08T13:54:07.447409Z"
} | 2de8cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 5242
},
"timestamp": "2026-02-10T04:27:56.633Z",
"answer": 15751
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
685088 | sequence_lucas_compute_v1_1915831931_1221 | Let $m = 2$. Let $n$ be the smallest positive divisor of $190969$ that is at least as large as the largest positive integer $d \leq m$ that divides $10$. Determine the value of the $n$th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(10))))),
"n": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/MIN_PRIME_FACTOR"
] | b50ecd | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MAX_DIVISOR",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T15:57:19.388258Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T15:57:19.390601Z"
} | f8178a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 1530
},
"timestamp": "2026-02-16T17:21:57.841Z",
"answer": 9349
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ec10d6 | alg_qf_psd_orbit_v1_1218484723_382 | Let $B = \left|\{ (a_1, b_1) \in \mathbb{Z}^+ \times \mathbb{Z}^+ : a_1 \leq 25,\ b_1 \leq 25,\ 2b_1^2 + 13a_1^2 - 2a_1b_1 \leq 2533 \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers such that $1 \leq a \leq b \leq B$ and $2a^2 + 2b^2 - 4ab = 66248$. | 152 | graphs = [
Graph(
let={
"_n": Const(334),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a... | ALG | null | COUNT | sympy | POLY3_MIN | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"POLY3_MIN",
"QF_PSD_COUNT_LEQ"
] | 2 | 2.152 | 2026-02-25T02:05:08.893986Z | {
"verified": true,
"answer": 152,
"timestamp": "2026-02-25T02:05:11.045677Z"
} | fdfea8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 5386
},
"timestamp": "2026-03-28T22:27:25.077Z",
"answer": 152
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
b9c48d | modular_min_linear_v1_1520064083_5821 | Let $m = 68994$, $a = 32974$, and $b = 4950$. Let $x_0$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. Let $C$ be the number of positive integers $n$ such that $1 \leq n \leq 14283$ and the sum of the decimal digits of $n$ is even. Compute the remainder when $C \cdot x_0$ i... | 40,761 | graphs = [
Graph(
let={
"_n": Const(87111),
"a": Const(32974),
"b": Const(4950),
"m": Const(68994),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | 3e99ac | modular_min_linear_v1 | affine_mod | 5 | 0 | [
"L3B"
] | 1 | 2.85 | 2026-02-08T07:40:16.879634Z | {
"verified": true,
"answer": 40761,
"timestamp": "2026-02-08T07:40:19.729845Z"
} | d4a53a | 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": 4839
},
"timestamp": "2026-02-13T11:35:34.074Z",
"answer": 40761
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7a4250 | comb_factorial_compute_v1_1248542787_326 | Let $M$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 154$. Let $n$ be the smallest integer $d \geq 2$ that divides $M$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(154)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/MIN_PRIME_FACTOR"
] | 37b65c | comb_factorial_compute_v1 | null | 5 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T03:03:40.128973Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T03:03:40.130456Z"
} | edfac8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 511
},
"timestamp": "2026-02-09T02:55:45.651Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
03fcce | alg_poly4_min_v1_601307018_7625 | Find the minimum value of $-99072a b^{3} + 100104 b^{4} + 222912 a^{2} b^{2} + 83592 a^{4} - 222912 a^{3} b$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 466$ and $1 \leq b \leq \left|\{ (a_1, b_1) : a_1 \geq 1, a_1 \leq 40, b_1 \geq 1, b_1 \leq 40,\ 25 b_1^{2} + 10 a_1^{2} - 18 a_1 b_1 \leq... | 84,624 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(466)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/QF_PSD_COUNT_LEQ"
] | 26c09d | alg_poly4_min_v1 | null | 7 | 0 | [
"B3_CLOSEST",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.665 | 2026-03-10T08:09:47.704258Z | {
"verified": true,
"answer": 84624,
"timestamp": "2026-03-10T08:09:48.369021Z"
} | f251b5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 16005
},
"timestamp": "2026-04-19T07:09:48.159Z",
"answer": 84624
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "V1",
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
dfc433 | geo_count_lattice_rect_v1_1874849503_1000 | Let $a = 70$ and $b = 17$. Define a lattice point as a point in the plane with integer coordinates. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary.
\boxed{1206} | 1,278 | graphs = [
Graph(
let={
"a": Const(70),
"b": Const(17),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T13:30:07.725411Z | {
"verified": true,
"answer": 1278,
"timestamp": "2026-02-08T13:30:07.726626Z"
} | cb1285 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1132
},
"timestamp": "2026-02-09T23:37:25.805Z",
"answer": 1278
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
d22263 | nt_sum_divisors_mod_v1_153355830_1530 | 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 in $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $10831$. | 8,513 | 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(1083... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T06:28:58.089831Z | {
"verified": true,
"answer": 8513,
"timestamp": "2026-02-08T06:28:58.093122Z"
} | 3be62e | CC BY 4.0 | [
{
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{... | 1 | [
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}
] | {
"lo": -3.44,
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} | ||
afaae1 | comb_bell_compute_v1_2051736721_3340 | Let $n_1 = 0$ and $n_2 = 5 + 4$. Define
$$
c = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}
\quad\text{and}\quad
w = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 16$. Let $r = B_n$, the $n$-th Bell number. Compute the re... | 57,071 | graphs = [
Graph(
let={
"_n": Const(128),
"a": Const(5),
"b": Const(4),
"n2": Sum(Ref("a"), Ref("b")),
"w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Con... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | e741ba | comb_bell_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.003 | 2026-02-08T17:15:18.402292Z | {
"verified": true,
"answer": 57071,
"timestamp": "2026-02-08T17:15:18.405783Z"
} | a8a97f | CC BY 4.0 | [
{
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},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 779
},
"timestamp": "2026-02-17T22:29:52.325Z",
"answer": 57071
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_R... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
5220af | modular_count_residue_v1_1874849503_917 | Let $m = 49$ and let $n = \sum_{d \mid 49} \phi(d)$, where $\phi$ is Euler's totient function. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy$ equals the sum of all positive integers $k$ satisfying $1 \leq k \leq m$ and $n \mid k$. Let $m'$ be the minimum value of $x + y$ over all p... | 3,746 | graphs = [
Graph(
let={
"_m": Const(49),
"_n": SumOverDivisors(n=Const(value=49), var='d', expr=EulerPhi(n=Var(name='d'))),
"upper": Const(52441),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositiv... | NT | null | COUNT | sympy | K3 | [
"K3/SUM_DIVISIBLE/B3"
] | 7c62d8 | modular_count_residue_v1 | null | 7 | 0 | [
"B3",
"K3",
"SUM_DIVISIBLE"
] | 3 | 2.235 | 2026-02-08T13:24:50.611729Z | {
"verified": true,
"answer": 3746,
"timestamp": "2026-02-08T13:24:52.846394Z"
} | 2f24d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 996
},
"timestamp": "2026-02-09T22:40:33.252Z",
"answer": 3746
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
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},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
74063f_l | nt_gcd_compute_v1_124444284_297 | Let $a = 28945$ and $b = 63679$. Let $g$ be the greatest common divisor of $a$ and $b$. Let $p$ be the largest prime number less than or equal to the smallest divisor of 41327 that is at least 2. Define $m = |g| \bmod p$. Compute the $m$-th Bell number, and denote this value by $Q$. Find the value of $Q$. | 1 | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | 8ad15a | nt_gcd_compute_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T03:09:07.392327Z | {
"verified": false,
"answer": 5,
"timestamp": "2026-02-08T03:09:07.395319Z"
} | 60df5a | 74063f | legacy_text | CC BY 4.0 | [
{
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"score": 3,
"correct": {
"strict": true,
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"relaxed": true
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"prompt_tokens": 208,
"completion_tokens": 675
},
"timestamp": "2026-02-09T15:47:10.963Z",
"answer": 5
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
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},
{
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"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status":... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | |
9410ce | alg_poly_orbit_count_v1_601307018_946 | For a non-negative integer $a$, define the sequence $N, M, R, S, T$ recursively by $$N = (a^3 + 2a^2 + 2a - 1) \bmod 73,$$ $$M = (N^3 + 2N^2 + 2N - 1) \bmod 73,$$ $$R = (M^3 + 2M^2 + 2M - 1) \bmod 73,$$ $$S = (R^3 + 2R^2 + 2R - 1) \bmod 73,$$ $$T = (S^3 + 2S^2 + 2S - 1) \bmod 73.$$ Find the number of integers $a$ with ... | 2,660 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(2), Pow(Var("a"), Const(2))), Mul(Const(2), Var("a")), Const(-1)), modulus=Const(73)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(2), Pow(Ref("p1"), Const(2))), Mul(Const(2), Ref("p1")), Const... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.127 | 2026-03-10T01:32:37.557922Z | {
"verified": true,
"answer": 2660,
"timestamp": "2026-03-10T01:32:37.685419Z"
} | b3f726 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 326,
"completion_tokens": 23052
},
"timestamp": "2026-03-29T00:41:43.252Z",
"answer": 2660
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
960d94 | nt_max_prime_below_v1_865884756_6011 | Let $n$ be an integer. Consider the set of all prime numbers $n$ such that $2 \leq n \leq 38809$. Let $p$ be the largest prime in this set. Let $d$ be the smallest divisor of $41327$ that is at least $2$. Compute the Bell number $B_r$, where $r$ is the remainder when $|p|$ is divided by $d$. Find the value of this Bell... | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(38809),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modul... | NT | COMB | EXTREMUM | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_max_prime_below_v1 | bell_mod | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 4.609 | 2026-02-08T18:55:05.522612Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T18:55:10.131679Z"
} | 8197aa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 4079
},
"timestamp": "2026-02-18T20:35:00.104Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cb2f1a | sequence_count_fib_divisible_v1_1978505735_6872 | Let $n$ be a positive integer such that $1 \leq n \leq 1836$ and the sum of the digits of $n$ is divisible by 2. Define $u$ to be the number of such integers $n$.
Now consider the Fibonacci sequence, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $r$ be the number of positive integers $n... | 153 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1836)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(0))))),
"d": Const(8),
"result": CountOve... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.042 | 2026-02-08T19:52:12.574642Z | {
"verified": true,
"answer": 153,
"timestamp": "2026-02-08T19:52:12.616725Z"
} | 25b95d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 3280
},
"timestamp": "2026-02-18T23:37:57.537Z",
"answer": 153
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e1e9b7 | comb_binomial_compute_v1_865884756_79 | Let $n$ be the number of integers $t$ with $16 \leq t \leq 30$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 3$, and $t = 2a + 3b + 11$. Let $k$ be the largest integer such that $47^k$ divides $4879681 \cdot 47$. Define $c = \binom{n}{k}$ and let $Q = 80656 - c$. Find t... | 79,369 | graphs = [
Graph(
let={
"_n": Const(47),
"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=5)), Geq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"K13"
] | 11ea0b | comb_binomial_compute_v1 | null | 6 | 0 | [
"K13",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T15:09:23.211670Z | {
"verified": true,
"answer": 79369,
"timestamp": "2026-02-08T15:09:23.215919Z"
} | 460516 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 2334
},
"timestamp": "2026-02-10T03:38:08.451Z",
"answer": 79369
}
] | 2 | [
{
"lemma": "K13",
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},
{
"lemma": "K5",
"status": "no"
},
{
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"status": "ok"
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{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemm... | {
"lo": 2.19,
"mid": 6.06,
"hi": 9.93
} | ||
654330 | sequence_fibonacci_compute_v1_1820931509_728 | Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 136$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 14$, $1 \leq b \leq 22$, and $t = 5a + 3b$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = |T|$. Compute the value of the $n$-th Fi... | 17,711 | 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=14)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.16 | 2026-02-08T11:50:28.299489Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T11:50:28.459984Z"
} | 76343d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 4600
},
"timestamp": "2026-02-14T19:33:12.537Z",
"answer": 17711
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bbf3a9 | antilemma_cartesian_v1_677425708_1491 | Let $x$ be the number of ordered pairs $(a,b)$ such that $a$ is an integer with $1 \leq a \leq 21$ and $b$ is an integer with $1 \leq b \leq 31$. Compute the remainder when $44121 \cdot x$ is divided by $93341$. | 67,084 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(31)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(93341)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:13:42.757884Z | {
"verified": true,
"answer": 67084,
"timestamp": "2026-02-08T04:13:42.758765Z"
} | dea8a5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 6732
},
"timestamp": "2026-02-09T20:43:55.070Z",
"answer": 67084
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
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},
{
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},
{
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"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
045537 | nt_count_divisors_in_range_v1_717093673_653 | Let $n = 166320$, $a = 6$, and $b = 6166$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 135 | graphs = [
Graph(
let={
"n": Const(166320),
"a": Const(6),
"b": Const(6166),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
},
... | NT | null | COUNT | sympy | B3 | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"B3",
"COUNT_COPRIME_GRID"
] | 2 | 0.398 | 2026-02-08T15:35:21.174489Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T15:35:21.572357Z"
} | 145f1b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 2951
},
"timestamp": "2026-02-16T10:32:21.328Z",
"answer": 135
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a7e451 | antilemma_sum_equals_v1_548369836_50 | Let $m = 38$. Define $n$ to be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = m$. Compute the remainder when $44121$ times the number of ordered pairs $(i, j)$ of integers with $1 \leq i, j \leq 18$ and $i + j = n$ is divided by $61856$. | 51,906 | graphs = [
Graph(
let={
"_m": Const(38),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.041 | 2026-02-08T02:44:41.765941Z | {
"verified": true,
"answer": 51906,
"timestamp": "2026-02-08T02:44:41.807221Z"
} | 80ef10 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2637
},
"timestamp": "2026-02-08T19:45:13.342Z",
"answer": 51906
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
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},
{
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{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": ... | {
"lo": 0.52,
"mid": 2,
"hi": 3.36
} | ||
8c3ce4 | nt_count_gcd_equals_v1_784195855_4644 | Let $d$ be the number of positive integers $n$ such that $1 \leq n \leq 272$ and $\gcd(n, 15) = 1$. Determine the number of positive integers $n$ such that $1 \leq n \leq 10080$ and $\gcd(n, 146) = d$. Let $Q$ be the remainder when $44121$ times this number is divided by $57373$. Compute $Q$. | 3,580 | graphs = [
Graph(
let={
"_n": Const(57373),
"upper": Const(10080),
"k": Const(146),
"d": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(272)), Eq(GCD(a=Var("n"), b=Const(15)), Const(1))))),
"r... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.984 | 2026-02-08T07:14:04.504170Z | {
"verified": true,
"answer": 3580,
"timestamp": "2026-02-08T07:14:05.487802Z"
} | 271088 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1072
},
"timestamp": "2026-02-13T09:00:36.423Z",
"answer": 3580
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3a1a61 | antilemma_cartesian_v1_784195855_515 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 43$ and $1 \leq b \leq 47$. Compute the remainder when $60351 \cdot x$ is divided by $92492$. | 64,915 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(43)), right=IntegerRange(start=Const(1), end=Const(47)))),
"_c": Const(60351),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(92492)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T04:25:06.600255Z | {
"verified": true,
"answer": 64915,
"timestamp": "2026-02-08T04:25:06.600593Z"
} | 358676 | 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": 11881
},
"timestamp": "2026-02-24T00:33:19.402Z",
"answer": 64915
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
458461 | nt_count_divisible_and_v1_1520064083_2507 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $$
x \cdot y = \sum_{k=1}^{8} \phi(k) \left\lfloor \frac{8}{k} \right\rfloor.$$
Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Define $d_2$ to be the minimum element of $T$.
Now let $N$ be the number of positive integers $n... | 1,384 | graphs = [
Graph(
let={
"upper": Const(33216),
"d1": Const(8),
"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")), Summation(var=... | NT | null | COUNT | sympy | K2 | [
"K2/B3"
] | 56e545 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 1.096 | 2026-02-08T04:50:22.531452Z | {
"verified": true,
"answer": 1384,
"timestamp": "2026-02-08T04:50:23.627442Z"
} | af96a2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 950
},
"timestamp": "2026-02-11T22:13:40.643Z",
"answer": 1384
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
9dd059 | alg_poly4_sum_v1_601307018_9530 | Find the remainder when $$\sum_{\substack{1 \leq a \leq 116 \\ 1 \leq b \leq 116}} \left( 82b^4 - 448a b^3 - 1024a^3 b + \min_{\substack{1 \leq a_1 \leq 5 \\ 1 \leq b_1 \leq 5}} \left\{ 256b_1^4 + \left| \left\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 35,\ -2a_2 b_2 + 13a_2^2 + 2b_2^2 \leq 1537 \right\} \right| \cdot a_1^4 \... | 16,440 | graphs = [
Graph(
let={
"_m": Const(1537),
"_n": Const(116),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Co... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/POLY4_MIN"
] | 469f6e | alg_poly4_sum_v1 | null | 8 | 0 | [
"POLY4_MIN",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.06 | 2026-03-10T09:57:14.563611Z | {
"verified": true,
"answer": 16440,
"timestamp": "2026-03-10T09:57:14.624038Z"
} | 86932c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 7781
},
"timestamp": "2026-04-19T11:31:16.742Z",
"answer": 16440
},
{
... | 1 | [
{
"lemma": "POLY4_MIN",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
079ea2 | comb_count_permutations_fixed_v1_655260480_2418 | Let $n$ be the smallest prime divisor of $35$. Let $k = 0$. Define $R = \binom{n}{k} \cdot !\left(n - k\right)$, where $!m$ denotes the number of derangements of $m$ elements. Find the remainder when $44121 \cdot R$ is divided by $67030$. | 64,484 | graphs = [
Graph(
let={
"_n": Const(35),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(le... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T16:42:47.640288Z | {
"verified": true,
"answer": 64484,
"timestamp": "2026-02-08T16:42:47.643229Z"
} | 158c60 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1171
},
"timestamp": "2026-02-17T11:17:33.129Z",
"answer": 64484
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ac46b9 | nt_count_divisible_v1_168721529_273 | Let $\text{upper} = 30109$. Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n$ is divisible by $8$.
Let $Q$ be the remainder when
$$
\left| \left\{ j \in \mathbb{Z}^+ : 1 \leq j \leq 99 \text{ and } j^5 \leq 9509900499 \right\} \right| - \text{result}
$$
is ... | 86,297 | graphs = [
Graph(
let={
"_n": Const(89961),
"upper": Const(30109),
"divisor": Const(8),
"result": CountOverSet(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 | COUNT | sympy | C3 | [
"C3"
] | a45c54 | nt_count_divisible_v1 | negation_mod | 3 | 0 | [
"C3"
] | 1 | 1.155 | 2026-02-08T12:56:33.601071Z | {
"verified": true,
"answer": 86297,
"timestamp": "2026-02-08T12:56:34.755967Z"
} | 7b6408 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1680
},
"timestamp": "2026-02-09T03:06:14.013Z",
"answer": 86297
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
b89832 | sequence_lucas_compute_v1_1742523217_359 | Let $n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $L_n$ denote the $n$-th Lucas number. Define $Q$ to be the sum of $77$ and the sum over each digit of $|L_n|$, where each digit in position $i$ (starting from the units digit at $i=0$) is multipli... | 261 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Lucas(arg=Ref(name='n')),
"_c": Const(77),
"Q": Sum(Summation(var="i", start=C... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_lucas_compute_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T02:59:43.974699Z | {
"verified": true,
"answer": 261,
"timestamp": "2026-02-08T02:59:43.976579Z"
} | a1acf2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1036
},
"timestamp": "2026-02-09T16:53:11.989Z",
"answer": 261
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
470866 | comb_catalan_compute_v1_1125832087_352 | Let $n$ be the number of integers $t$ such that $35 \leq t \leq 71$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 6a + 9b + 20$. Compute the remainder when $44121$ times the $n$th Catalan number is divided by $80723$. | 67,116 | graphs = [
Graph(
let={
"_n": Const(80723),
"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=4)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:02:18.119127Z | {
"verified": true,
"answer": 67116,
"timestamp": "2026-02-08T03:02:18.120984Z"
} | 2aed6b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 3622
},
"timestamp": "2026-02-10T12:33:45.534Z",
"answer": 67116
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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",
"s... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
bf3d46 | alg_poly3_min_v1_1218484723_2665 | Let $D = \left|\left\{ (a_1, b_1) : 1 \le a_1 \le b_1 \le 40,\ 2a_1^2 - 4a_1b_1 + 2b_1^2 = \min\{x + y : x > 0, y > 0,\ xy = 2085136\} \right\}\right|$. Find the remainder when $$\min_{\substack{1 \le a, b, c \le 50}} \left( -101a^3 - 327a^2b + 96a^2c + 33ab^2 - 288abc - 408ac^D - 189b^3 - 144b^2c + 98c^3 - 108bc^2 \ri... | 26,650 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(40),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(50)), Geq(Var("b"), Const(1)), Leq(Var("b... | ALG | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_ORBIT"
] | cb4069 | alg_poly3_min_v1 | null | 6 | 0 | [
"B3",
"QF_PSD_ORBIT"
] | 2 | 0.287 | 2026-02-25T04:24:08.469431Z | {
"verified": true,
"answer": 26650,
"timestamp": "2026-02-25T04:24:08.756109Z"
} | d188f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 303,
"completion_tokens": 6527
},
"timestamp": "2026-03-29T05:57:51.808Z",
"answer": 26650
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
4bd814 | comb_count_surjections_v1_2051736721_4233 | Let $m = 14$. Define $a$ to be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 12$, $1 \le j \le 12$, and $i + j = m$. Define $n$ to be the number of ordered pairs $(i_1, j_1)$ of integers with $1 \le i_1 \le 9$, $1 \le j_1 \le 9$, and $i_1 + j_1 = a$. Let $k = 4$. Compute the smallest positive intege... | 2,553 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Co... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS"
] | 756129 | comb_count_surjections_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.021 | 2026-02-08T17:50:13.059263Z | {
"verified": true,
"answer": 2553,
"timestamp": "2026-02-08T17:50:13.080237Z"
} | 625773 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 3610
},
"timestamp": "2026-02-18T08:35:52.787Z",
"answer": 2553
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
2e71e0 | comb_factorial_compute_v1_1439011603_3113 | Let $N$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 24578$ and $\binom{24578}{j}$ is odd. Let $f = N!$.
Compute the remainder when $50034 \cdot f$ is divided by $57727$. | 43,138 | graphs = [
Graph(
let={
"_n": Const(24578),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(24578)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T17:15:06.526591Z | {
"verified": true,
"answer": 43138,
"timestamp": "2026-02-08T17:15:06.529194Z"
} | edfd29 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 2398
},
"timestamp": "2026-02-17T23:15:18.766Z",
"answer": 43138
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
99551e | nt_num_divisors_compute_v1_677425708_413 | Let $m = 2$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 7338681$. Let $s$ be the minimum value of $x + y$ over all such pairs. Define $n$ to be the sum of all positive integers $x$ satisfying the equation $x^m - 169x + s = 0$. Let $d$ be the number of positive divisors of $n$.... | 5 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(7338681)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"B3/VIETA_SUM"
] | 634c8f | nt_num_divisors_compute_v1 | null | 7 | 0 | [
"B3",
"ONE_PHI_1",
"VIETA_SUM"
] | 3 | 0.006 | 2026-02-08T03:31:58.483590Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T03:31:58.489610Z"
} | 915a2d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 2502
},
"timestamp": "2026-02-08T20:33:54.933Z",
"answer": 5
},
{
"id":... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
987eff | nt_count_divisible_v1_1520064083_4537 | Let $a = 5$ and $b = 7$. Define $d_0 = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ denotes the M\"obius function. Let $S$ be the set of all integers $n$ such that $n \geq d_0$, $n \leq 30203$, and $n$ is divisible by 17. Compute the number of elements in $S$. | 1,776 | graphs = [
Graph(
let={
"upper": Const(30203),
"divisor": Const(17),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=5), b=Const(value=7)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Ref(... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 1.276 | 2026-02-08T06:19:02.591337Z | {
"verified": true,
"answer": 1776,
"timestamp": "2026-02-08T06:19:03.867705Z"
} | 67b1e6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 366
},
"timestamp": "2026-02-19T03:34:40.303Z",
"answer": 1776
}
] | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
19073a | nt_sum_totient_over_divisors_v1_717093673_1063 | Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 48$ and $1 \leq j \leq 170$ such that $\gcd(i, j) = 1$. Define $\text{result} = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $m$ be the smallest divisor of $537251$ that is at least $2$. Compute the Bell numb... | 21,147 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(48)), right=IntegerRange(start=Const(1), end=C... | NT | COMB | COMPUTE | sympy | L3B | [
"MIN_PRIME_FACTOR",
"COUNT_COPRIME_GRID"
] | 4dd972 | nt_sum_totient_over_divisors_v1 | bell_mod | 7 | 0 | [
"COUNT_COPRIME_GRID",
"L3B",
"MIN_PRIME_FACTOR"
] | 3 | 0.012 | 2026-02-08T15:50:06.682564Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T15:50:06.694223Z"
} | 6c5023 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 3847
},
"timestamp": "2026-02-16T15:17:53.575Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c7e1ce | nt_min_coprime_above_v1_784195855_9738 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 484$. Let $s_{\text{min}}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Now let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s_{\text{min}}$. Define $m$ to be the maximum value o... | 26,897 | graphs = [
Graph(
let={
"start": Const(26896),
"upper": Const(27390),
"modulus": 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")), Mi... | NT | null | EXTREMUM | sympy | B3 | [
"B3/B1"
] | 7f76f7 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.044 | 2026-02-08T17:01:23.882449Z | {
"verified": true,
"answer": 26897,
"timestamp": "2026-02-08T17:01:23.926187Z"
} | e824d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 890
},
"timestamp": "2026-02-17T21:10:34.564Z",
"answer": 26897
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e12eb9 | nt_count_intersection_v1_124444284_7698 | Let $N$ be the number of integers $t$ such that $8 \leq t \leq 10015$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 110$, $1 \leq b \leq 3155$, and $t = 5a + 3b$. Let $a$ be the number of integers $t$ such that $15 \leq t \leq 45$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq ... | 477 | 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=110)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.337 | 2026-02-08T09:17:10.939403Z | {
"verified": true,
"answer": 477,
"timestamp": "2026-02-08T09:17:11.275991Z"
} | f4a4c4 | 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": 3156
},
"timestamp": "2026-02-14T02:56:33.815Z",
"answer": 477
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2a48cd | antilemma_sum_equals_v1_1918700295_3115 | Let $t$ be an integer satisfying $21 \le t \le 117$. A pair $(a,b)$ of positive integers is called valid if $1 \le a \le 3$, $1 \le b \le 12$, and $t = 15a + 6b$. Let $m$ be the number of values of $t$ for which at least one valid pair $(a,b)$ exists. Compute the number of ordered pairs $(i,j)$ of positive integers suc... | 26 | 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=3)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.017 | 2026-02-08T08:23:24.205329Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T08:23:24.222196Z"
} | 7f8cfe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 4743
},
"timestamp": "2026-02-24T09:31:37.314Z",
"answer": 26
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
1074ff | geo_visible_lattice_v1_865884756_7037 | Let $n = 80$. Define a visible lattice point $(x, y)$ as a point with integer coordinates such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $L$ be the number of visible lattice points for this $n$. Compute the remainder when $30237 \cdot L$ is divided by $78796$. | 37,279 | graphs = [
Graph(
let={
"n": Const(80),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(30237), Ref("result")), modulus=Const(78796)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.129 | 2026-02-08T19:36:07.576257Z | {
"verified": true,
"answer": 37279,
"timestamp": "2026-02-08T19:36:07.704921Z"
} | 9e1ffa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 5579
},
"timestamp": "2026-02-18T22:49:41.246Z",
"answer": 37279
},
... | 1 | [] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||||
5f8e4b | nt_num_divisors_compute_v1_458359167_4629 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 60$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 16$, $1 \leq b \leq 3$, and $t = 3a + 4b$. Let $n$ be the number of elements in $T$. Determine the number of positive divisors of $n$. | 10 | 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=16)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:57:06.326787Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T11:57:06.327877Z"
} | d26108 | 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": 2636
},
"timestamp": "2026-02-14T21:17:49.738Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8b421a | comb_binomial_compute_v1_865884756_6397 | Let $n = \sum_{k_1=1}^{5} \phi(k_1) \left\lfloor \frac{5}{k_1} \right\rfloor$ and let $k = \sum_{k_2=1}^{3} \phi(k_2) \left\lfloor \frac{3}{k_2} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $\binom{n}{k}$. | 5,005 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k1", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(5), Var("k1"))))),
"k": Summation(var="k2", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k2")), Floor(Div(Ref("_n"), Va... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T19:10:20.125281Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T19:10:20.127971Z"
} | 4e2e2d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1127
},
"timestamp": "2026-02-18T21:30:15.968Z",
"answer": 5005
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d3e6f2 | comb_count_surjections_v1_458359167_3425 | Let $n = 7$ and $k = 3$. Define $S = k! \cdot S(n,k)$, where $S(n,k)$ is the Stirling number of the second kind. Let $d$ be the number of decimal digits of $|S|$, and for $i = 0$ to $d-1$, let $d_i$ denote the $i$th digit of $|S|$ (starting from the units digit as $i=0$). Define $$
A = \sum_{i=0}^{d-1} d_i \cdot (i + 0... | 455 | graphs = [
Graph(
let={
"_n": Const(722),
"n": Const(7),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), ba... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1",
"ONE_FACTORIAL_0"
] | 85810a | comb_count_surjections_v1 | digits_weighted_mod | 6 | 0 | [
"COMB1",
"ONE_FACTORIAL_0"
] | 2 | 0.003 | 2026-02-08T08:20:55.554679Z | {
"verified": true,
"answer": 455,
"timestamp": "2026-02-08T08:20:55.557862Z"
} | c45445 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 1719
},
"timestamp": "2026-02-24T09:26:22.649Z",
"answer": 455
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
840700 | nt_min_coprime_above_v1_865884756_5443 | Let $S$ be the set of all integers $n$ such that $6400 < n \leq 6758$ and $\gcd(n, 348) = 1$. Let $m$ be the smallest element of $S$. Compute the remainder when the Bell number $B_{|m| \bmod 11}$ is divided by $71208$. | 44,767 | graphs = [
Graph(
let={
"start": Const(6400),
"upper": Const(6758),
"modulus": Const(348),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(1)... | NT | COMB | EXTREMUM | sympy | COUNT_PRIMES | [
"MIN_PRIME_FACTOR/C4",
"B3"
] | 61a2c4 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B3",
"C4",
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 4 | 0.515 | 2026-02-08T18:36:01.949882Z | {
"verified": true,
"answer": 44767,
"timestamp": "2026-02-08T18:36:02.465159Z"
} | a187b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1187
},
"timestamp": "2026-02-18T18:08:49.439Z",
"answer": 44767
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7732c8 | diophantine_fbi2_min_v1_1439011603_509 | Find the smallest integer $d$ such that $2 \leq d \leq 42$, $d$ divides $32$, and $\frac{32}{d} \geq 5$. | 2 | graphs = [
Graph(
let={
"k": Const(32),
"a": Const(1),
"b": Const(4),
"upper": Const(42),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.12 | 2026-02-08T15:32:02.349535Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:32:02.469881Z"
} | f19566 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 475
},
"timestamp": "2026-02-16T06:06:35.692Z",
"answer": 2
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
7f81bf | modular_modexp_compute_v1_1439011603_3022 | Let $a = 5$. Consider the set of all ordered pairs $(i,j)$ such that $1 \leq i \leq 21$ and $1 \leq j \leq 37$. Let $e$ be the number of elements in this set. Define $m = 12100$ and let $r$ be the remainder when $a^e$ is divided by $m$.
Compute $r$. | 5,525 | graphs = [
Graph(
let={
"a": Const(5),
"e": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(37)))),
"m": Const(12100),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_modexp_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T17:10:39.268829Z | {
"verified": true,
"answer": 5525,
"timestamp": "2026-02-08T17:10:39.269884Z"
} | 4d1dae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1445
},
"timestamp": "2026-02-17T22:01:42.569Z",
"answer": 5525
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b29f69 | lin_form_endings_v1_1440796553_532 | Let $a = 30$ and $b = 42$. Let $L$ be the least common multiple of $a$ and $b$. Define $x = 5L + a + b$.
Compute the value of $x$. | 1,122 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(42),
"k_val": Const(5),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"x": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
},
goal=Ref("x... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T11:51:00.324341Z | {
"verified": true,
"answer": 1122,
"timestamp": "2026-02-08T11:51:00.326841Z"
} | ee36e7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 256
},
"timestamp": "2026-02-16T03:26:22.282Z",
"answer": 2172
},
{
"id": 11,... | 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": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
9f7b52 | lin_form_endings_v1_1874849503_1059 | Let $a = 98$ and $b = 56$. Define $\delta = \gcd(a, b)$. Let $k = 210$ and define
$$
r = \left\lfloor \frac{k}{\gcd(k, \delta)} \right\rfloor.
$$
Let $s = 14264 \cdot r$ and let $M = 86500$. Compute the remainder when $s$ is divided by $M$. Find the value of this remainder. | 40,960 | graphs = [
Graph(
let={
"a_coeff": Const(98),
"b_coeff": Const(56),
"k_val": Const(210),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:32:39.105118Z | {
"verified": true,
"answer": 40960,
"timestamp": "2026-02-08T13:32:39.105898Z"
} | 820df4 | 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": 803
},
"timestamp": "2026-02-10T00:28:40.252Z",
"answer": 40960
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
8cc921 | diophantine_fbi2_min_v1_124444284_8916 | Let $k = 64$. Consider all integers $d$ such that $7 \leq d \leq 74$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Find the minimum value of such $d$, and compute its absolute value modulo $57930$. | 8 | graphs = [
Graph(
let={
"k": Const(64),
"a": Const(6),
"b": Const(2),
"upper": Const(74),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(7)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LTE_DIFF_P2"
] | f850a7 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LTE_DIFF_P2",
"MIN_PRIME_FACTOR"
] | 2 | 0.031 | 2026-02-08T11:58:57.434941Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T11:58:57.465481Z"
} | 67c381 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 324
},
"timestamp": "2026-02-16T03:31:10.170Z",
"answer": 8
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
f4b3fb | antilemma_sum_equals_v1_717093673_2488 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 80$ and $1 \leq j \leq 81$. Let $n$ be the number of ordered pairs $(a, b)$ such that $1 \leq a, b \leq 9$. Compute the number of elements in $S$ for which $i + j = n$. | 80 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const(9)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.027 | 2026-02-08T16:52:52.703603Z | {
"verified": true,
"answer": 80,
"timestamp": "2026-02-08T16:52:52.730374Z"
} | 687a9f | 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": 915
},
"timestamp": "2026-02-24T22:00:23.659Z",
"answer": 80
},
{
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
73e8a6 | antilemma_product_of_sums_v1_865884756_650 | Let $S$ be the set of all ordered pairs of positive integers $(x_1, y)$ such that $x_1 \cdot y = 25$. Define $n_0$ to be the minimum value of $x_1 + y$ over all such pairs. Let $S_1$ be the sum of all $k$ where $k$ ranges from $1$ to $9$ and $j$ ranges from $1$ to $3$ in the Cartesian product. Let $S_2 = \sum_{k_1=1}^{... | 38,137 | graphs = [
Graph(
let={
"_m": Const(68981),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("y")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x1"), Var("y")), Const(25)))), expr=Sum(Var("x1"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3/PRODUCT_OF_SUMS/SUM_ARITHMETIC"
] | 2fc751 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"B3",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 3 | 0.004 | 2026-02-08T15:33:06.058136Z | {
"verified": true,
"answer": 38137,
"timestamp": "2026-02-08T15:33:06.061814Z"
} | 1b8d49 | CC BY 4.0 | null | null | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok... | {
"lo": -10,
"mid": -0.22,
"hi": 9.56
} | ||
764b4b | antilemma_sum_equals_v1_349078426_2011 | Let $\mathcal{T}$ be the set of all integers $t$ such that $11 \le t \le 28$ and there exist positive integers $a \le 7$ and $b \le 2$ satisfying $t = 2a + 5b + 4$. Let $n$ be the number of elements in $\mathcal{T}$. Let $S$ be the set of all ordered pairs $(i,j)$ where $i$ is an integer from 1 to 12 and $j$ is an inte... | 8,488 | 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=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.015 | 2026-02-08T14:03:51.207744Z | {
"verified": true,
"answer": 8488,
"timestamp": "2026-02-08T14:03:51.222565Z"
} | 5189cf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1797
},
"timestamp": "2026-02-24T19:36:42.713Z",
"answer": 8488
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -3.9,
"mid": -1.69,
"hi": 1.31
} | ||
3d98af | geo_count_lattice_rect_v1_48377204_380 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 233$ and $0 \leq y \leq 294$. | 69,030 | graphs = [
Graph(
let={
"a": Const(233),
"b": Const(294),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T15:22:40.353551Z | {
"verified": true,
"answer": 69030,
"timestamp": "2026-02-08T15:22:40.354459Z"
} | c52070 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 209
},
"timestamp": "2026-02-24T20:49:00.248Z",
"answer": 69030
},
{
"i... | 1 | [] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||||
d15c49 | sequence_fibonacci_compute_v1_1915831931_3173 | Let $m = 5184$. Let $n_0$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $n$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = n_0$. Let $\text{result} = F_n$, the $n$th Fibonacci number. Let $Q$ be the remaind... | 58,218 | graphs = [
Graph(
let={
"_m": Const(5184),
"_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")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:24:40.453451Z | {
"verified": true,
"answer": 58218,
"timestamp": "2026-02-08T17:24:40.455766Z"
} | 6ae443 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 1190
},
"timestamp": "2026-02-18T02:49:36.377Z",
"answer": 58218
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21b6f6 | nt_max_prime_below_v1_151522320_1032 | Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 5$ and $\gcd(n, 6) = 1$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 45369$. | 45,361 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(45369),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | 08d162 | nt_max_prime_below_v1 | null | 4 | 0 | [
"C4"
] | 1 | 2.417 | 2026-02-08T03:43:14.451255Z | {
"verified": true,
"answer": 45361,
"timestamp": "2026-02-08T03:43:16.868326Z"
} | b577c1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2394
},
"timestamp": "2026-02-10T14:16:13.103Z",
"answer": 45361
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
a81cae | algebra_poly_eval_v1_124444284_9558 | Let $t$ be an integer satisfying $9 \le t \le 399$. Define $T$ as the set of all such $t$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 98$, $1 \le b \le 29$, and $t = 2a + 7b$. Let $d$ be the smallest prime divisor of the number of elements in $T$ that is at least 2. Compute $7 \cdot 10^4 - 3 \... | 67,152 | graphs = [
Graph(
let={
"_n": Const(7),
"x": Const(10),
"result": Sum(Mul(Ref("_n"), Pow(Ref("x"), Const(4))), Mul(Const(-3), Pow(Ref("x"), Const(3))), Pow(Ref("x"), Const(2)), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(di... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | algebra_poly_eval_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T12:34:10.303430Z | {
"verified": true,
"answer": 67152,
"timestamp": "2026-02-08T12:34:10.308914Z"
} | 144217 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 4958
},
"timestamp": "2026-02-15T02:26:17.460Z",
"answer": 67152
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3735fe | nt_sum_divisors_mod_v1_1915831931_998 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10949$. | 2,880 | 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(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10949... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T15:49:21.990973Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T15:49:21.998265Z"
} | f53054 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1258
},
"timestamp": "2026-02-16T14:24:18.895Z",
"answer": 2880
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b4ab85 | alg_poly3_min_v1_1218484723_6273 | Let $P = \min\{ x + y : x, y > 0,\ xy = 8294400 \}$. Let $A = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 15,\ 10a_1^2 - 18a_1b_1 + 25b_1^2 \leq 1405 \}\right|$. Find the minimum value of $P \cdot a \cdot b^2 + 4440a^3 + 10080a^2b$ over all positive integers $a, b$ with $1 \leq a \leq A$ and $1 \leq b \leq 108$. | 20,280 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(10080),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3"
] | 3a349f | alg_poly3_min_v1 | null | 6 | 0 | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.031 | 2026-02-25T07:51:21.458752Z | {
"verified": true,
"answer": 20280,
"timestamp": "2026-02-25T07:51:21.490083Z"
} | 336fcc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T01:02:22.367Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
78409b | antilemma_product_of_sums_v1_1116507919_266 | Let $m = 3$. Define $n$ to be the smallest positive integer such that the highest power of $m$ dividing $n!$ is at least 6. Let $S_1$ be the sum of all integers from 1 to $n$. Let $S_2$ be the sum of $i \cdot j$ over all ordered pairs $(i, j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 4$. Define $x = S_1 \cdot S_2$. Co... | 58,336 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Ref("_m")), Const(6)), domain='Z_{>0}')),
"S1": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
... | NT | null | COMPUTE | sympy | V5 | [
"V5/PRODUCT_OF_SUMS/SUM_ARITHMETIC"
] | 9ca925 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC",
"V5"
] | 3 | 0.001 | 2026-02-08T02:30:12.807346Z | {
"verified": true,
"answer": 58336,
"timestamp": "2026-02-08T02:30:12.808486Z"
} | 5ac80f | 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": 777
},
"timestamp": "2026-02-08T19:20:18.449Z",
"answer": 58336
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok_later"
},
{
"lemma": "SUM_ARITHMETIC",
"stat... | {
"lo": -4.6,
"mid": 0.18,
"hi": 4.74
} | ||
caab1d | diophantine_product_count_v1_1520064083_9046 | Let $k$ be the number of integers $t$ with $8 \leq t \leq 735$ such that there exist positive integers $a \leq 130$ and $b \leq 69$ satisfying $t = 3a + 5b$. Let $\text{upper}$ be the number of integers $t$ with $10 \leq t \leq 471$ such that there exist positive integers $a \leq 5$ and $b \leq 148$ satisfying $t = 5a ... | 28 | graphs = [
Graph(
let={
"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=130)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.036 | 2026-02-08T10:30:41.893387Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T10:30:41.929621Z"
} | c24434 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 7027
},
"timestamp": "2026-02-14T07:39:16.402Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8f8e4e | sequence_count_fib_divisible_v1_151522320_1142 | Let $d$ be the number of integers $n$ such that $1 \le n \le 540$ and $20$ divides the $n$th Fibonacci number. Let $S$ be the set of integers $n$ such that $1 \le n \le 543$ and $d$ divides the $n$th Fibonacci number. Compute the number of elements in $S$. Let $Q$ be the remainder when $55741$ times this number is divi... | 45,585 | graphs = [
Graph(
let={
"_n": Const(54728),
"upper": Const(543),
"d": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(540)), Divides(divisor=Const(20), dividend=Fibonacci(arg=Var(name='n')))))),
"result": ... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.053 | 2026-02-08T03:49:12.234121Z | {
"verified": true,
"answer": 45585,
"timestamp": "2026-02-08T03:49:12.287080Z"
} | 564ff8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 3080
},
"timestamp": "2026-02-10T14:29:21.454Z",
"answer": 45585
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0a6fb0_l | algebra_quadratic_discriminant_v1_809748730_476 | Let $a = 2$, $b = 28$, and $c = 90$. Define the discriminant $D = b^2 - 4ac$. Let $\alpha = 1$ if $D > 0$, and $0$ otherwise. Let $\beta = 1$ if $D = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$, and $0$ otherwise. Let $r = 2\alpha + \beta$. Compute $105 - r$. | 102 | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T11:32:30.356607Z | {
"verified": false,
"answer": 103,
"timestamp": "2026-02-08T11:32:30.358528Z"
} | 25247b | 0a6fb0 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 295
},
"timestamp": "2026-02-24T14:13:21.807Z",
"answer": 103
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | |
fb4b99 | comb_sum_binomial_row_v1_1218484723_777 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 20$ such that
$$
384a b^2 + 128a^3 + \left|\{ v : 29 \leq v \leq 11600,\ \exists\, a,b \in [1,20] \text{ with } 2ab + 10b^2 + 17a^2 = v \}\right| \cdot a^2 b + 128b^3 = 3121792.
$$
Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(384), ... | COMB | null | SUM | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY3_COUNT"
] | 5dc0d1 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"POLY3_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.008 | 2026-02-25T02:30:47.231276Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-25T02:30:47.238918Z"
} | 3c7af7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T01:39:18.326Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_... | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
60d494 | nt_max_prime_below_v1_458359167_4381 | Let $c = 30227$ and let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $L \le n \le 10816$. Compute the remainder when $c... | 12,941 | graphs = [
Graph(
let={
"upper": Const(10816),
"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 | 4.773 | 2026-02-08T11:44:27.071149Z | {
"verified": true,
"answer": 12941,
"timestamp": "2026-02-08T11:44:31.843796Z"
} | e08401 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 3982
},
"timestamp": "2026-02-14T18:37:14.751Z",
"answer": 12941
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5bb455 | v7_endings_v1_677425708_1994 | Let $n = 4014$. Let $x$ be the number of integers $k$ such that $0 \leq k \leq 4014$ and $3$ divides $\binom{4014}{k}$. Compute the remainder when $44121 \times x$ is divided by $58903$. | 32,594 | graphs = [
Graph(
let={
"_n": Const(3),
"x": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(4014)), Divides(divisor=Ref("_n"), dividend=Binom(n=Const(4014), k=Var("k")))))),
"Q": Mod(value=Mul(Const(44121), Ref("x"))... | NT | COMB | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | 0 | [
"V7"
] | 1 | 0.001 | 2026-02-08T04:42:12.492329Z | {
"verified": true,
"answer": 32594,
"timestamp": "2026-02-08T04:42:12.493145Z"
} | 4271f6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1160
},
"timestamp": "2026-02-10T04:10:10.554Z",
"answer": 32594
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
d119c3 | algebra_quadratic_discriminant_v1_2051736721_5301 | Let $p$ and $q$ be positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $B$ be the set of all such integers $p$. Let $k$ be the number of elements in $B$. Compute $6^k - 4 \cdot 1 \cdot (-27)$. | 144 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(1),
"b": Const(6),
"c": Const(-27),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(l... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_1"
] | 2 | 0.038 | 2026-02-08T18:28:42.205793Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T18:28:42.243900Z"
} | d2c88d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 600
},
"timestamp": "2026-02-16T12:23:47.511Z",
"answer": 144
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
954d53 | modular_count_residue_v1_898971024_11 | Let $r$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $m = 16$. Determine the number of positive integers $n$ such that $1 \leq n \leq 30276$ and $n \equiv r \pmod{m}$. | 1,892 | graphs = [
Graph(
let={
"upper": Const(30276),
"m": Const(16),
"r": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), ex... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | modular_count_residue_v1 | null | 3 | 0 | [
"B1"
] | 1 | 3.309 | 2026-02-08T15:09:00.287566Z | {
"verified": true,
"answer": 1892,
"timestamp": "2026-02-08T15:09:03.596458Z"
} | 8eb005 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 654
},
"timestamp": "2026-02-16T00:53:48.848Z",
"answer": 1892
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8856fb | alg_qf_psd_min_v1_601307018_135 | Let $m = \min\{ x + y \mid x, y > 0,\, xy = 1580049,\, x \leq y \}$. Find the minimum value of $21369 b^2 + 12570 ab + m a^2$ over all positive integers $a, b$ with $1 \leq a \leq 174$ and $1 \leq b \leq 174$. | 36,453 | graphs = [
Graph(
let={
"_n": Const(12570),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), SumOverDivisors(n=GCD(a=Const(value=3), b=Const(value=5)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("a"), ... | NT | NT | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.065 | 2026-03-10T00:46:02.024558Z | {
"verified": true,
"answer": 36453,
"timestamp": "2026-03-10T00:46:02.089784Z"
} | 1e89ed | CC BY 4.0 | null | null | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lem... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
f68a90 | comb_sum_binomial_row_v1_865884756_2479 | Let $S_1$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S_1$. Let $d_{\text{min}}$ be the smallest divisor of $41327$ that is at least $m$. Let $S_2$ be the set of all positive integers $p_1... | 41,059 | graphs = [
Graph(
let={
"_n": Const(63463),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), 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=... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.008 | 2026-02-08T16:47:27.521559Z | {
"verified": true,
"answer": 41059,
"timestamp": "2026-02-08T16:47:27.529943Z"
} | be44ea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1988
},
"timestamp": "2026-02-17T11:48:05.307Z",
"answer": 41059
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
870c9d | algebra_quadratic_discriminant_v1_1440796553_1236 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 5$ and $1 \leq j \leq 5$ and $i + j = 5$. Let $N = |S|$. Compute the value of $0^2 - (-7)(-1)N$. Find the remainder when this value is divided by $70113$. | 70,085 | graphs = [
Graph(
let={
"_n": Const(5),
"a": Const(-7),
"b": Const(0),
"c": Const(-1),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n"... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"COUNT_SUM_EQUALS"
] | 75ab0f | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"MOBIUS_COPRIME"
] | 2 | 0.025 | 2026-02-08T12:15:19.502311Z | {
"verified": true,
"answer": 70085,
"timestamp": "2026-02-08T12:15:19.526823Z"
} | 58a398 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 384
},
"timestamp": "2026-02-16T04:52:20.170Z",
"answer": 69985
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"statu... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
7e36f7 | nt_count_divisors_in_range_v1_865884756_4969 | Let $m = 4$ and $n = 1351$. Define $b$ to be the number of positive integers $j$ such that $1 \leq j \leq n$ and $j^k \leq 2465846551$, where $k$ is the number of positive integers $\ell$ with $1 \leq \ell \leq m$ and the sum of the digits of $\ell$ is odd. Let $d$ be the number of positive divisors of $20160$ that are... | 72 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(1351),
"n": Const(20160),
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), CountOverSet(set=Soluti... | NT | null | COUNT | sympy | LIN_FORM | [
"L3B/C3"
] | 16113d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"C3",
"L3B",
"LIN_FORM"
] | 3 | 0.055 | 2026-02-08T18:18:20.762525Z | {
"verified": true,
"answer": 72,
"timestamp": "2026-02-08T18:18:20.817711Z"
} | 55cab7 | 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": 2837
},
"timestamp": "2026-02-18T16:10:45.027Z",
"answer": 72
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
380a0d | lin_form_endings_v1_458359167_662 | Let $a = 27$ and $b = 18$. Let $k = 5$ and $L = \mathrm{lcm}(a, b)$. Define $s = k \cdot L + a + b$. Compute the remainder when $7487 \cdot s$ is divided by $52779$. | 36,129 | graphs = [
Graph(
let={
"a_coeff": Const(27),
"b_coeff": Const(18),
"k_val": Const(5),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:29:27.249146Z | {
"verified": true,
"answer": 36129,
"timestamp": "2026-02-08T03:29:27.250506Z"
} | ff0f53 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 852
},
"timestamp": "2026-02-10T14:40:09.058Z",
"answer": 36129
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
49726f | alg_sym_quad_system_v1_1218484723_7008 | Let $T = \left|\{ n : 1 \le n \le 12964,\, \gcd(n, 15) = 1 \}\right|$ and $D = \left|\{ n_1 : 1 \le n_1 \le 12151,\, \gcd(n_1, 30) = 1 \}\right|$. Find the remainder when
$$
\sum_{\substack{a,b,c \ge 1 \\ a^2 + b^2 + c^2 = ab + bc + ca \\ 7a + 3b + 5c = T}} (a^4 + b^4 + c^4)
$$
is divided by $D$. | 1,900 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Ref("_n")), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | alg_sym_quad_system_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.019 | 2026-02-25T08:26:36.794435Z | {
"verified": true,
"answer": 1900,
"timestamp": "2026-02-25T08:26:36.813622Z"
} | 4d315b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 8576
},
"timestamp": "2026-03-30T03:38:01.988Z",
"answer": 1900
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
0a68ae | algebra_poly_eval_v1_153355830_515 | Let $\_c = 3$ and $\_m = 4$. Let $\_n$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $y$ be the smallest positive integer $d$ such that $d$ divides 91091 and $d \ge \_n$. Compute $y^4 - 5y^3 + 4y^{\_n} - 8y - 1$. | 825 | graphs = [
Graph(
let={
"_c": Const(3),
"_m": Const(4),
"_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=18)), Eq(left=GCD(a=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T03:08:26.704053Z | {
"verified": true,
"answer": 825,
"timestamp": "2026-02-08T03:08:26.708647Z"
} | 3361c0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1081
},
"timestamp": "2026-02-10T12:56:29.551Z",
"answer": 825
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma"... | {
"lo": -3.55,
"mid": 0.8,
"hi": 4.81
} | ||
0e0dd9 | nt_count_gcd_equals_v1_784195855_5625 | Let $ d = 107 $ and let $ S $ be the set of all integers $ n $ such that $ 1 \leq n \leq 46656 $ and $ \gcd(n, 107) = d $. Let $ \text{result} $ be the number of elements in $ S $. Compute the remainder when $ |\text{result}| $ is divided by $ 80527 $. | 436 | graphs = [
Graph(
let={
"upper": Const(46656),
"k": Const(107),
"d": Const(107),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 9.795 | 2026-02-08T08:00:16.956796Z | {
"verified": true,
"answer": 436,
"timestamp": "2026-02-08T08:00:26.752103Z"
} | 3b426c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 637
},
"timestamp": "2026-02-15T19:08:43.858Z",
"answer": 45780
},
{
"id": 11... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f8e9af | geo_count_lattice_triangle_v1_717093673_1814 | Consider the triangle with vertices at $(100, 233)$, $(169, 240)$, and $(0, 0)$. Let $A$ be twice the area of this triangle. Let $B$ be the number of lattice points on the boundary of the triangle, computed as the sum of the greatest common divisors of the absolute differences in coordinates along each side. Compute th... | 7,688 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=240)), Mul(Const(value=169), Sub(left=Const(value=0), right=Const(value=233))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=233))), GCD(a=Abs(arg=Sub(left=Const(value=169), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 3 | 0 | null | null | 0.013 | 2026-02-08T16:20:37.028152Z | {
"verified": true,
"answer": 7688,
"timestamp": "2026-02-08T16:20:37.040952Z"
} | 1fb0f8 | 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": 1933
},
"timestamp": "2026-02-17T01:29:07.867Z",
"answer": 7688
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
da7823 | nt_count_gcd_equals_v1_784195855_7461 | Let $d$ be a positive divisor of $360$. Define $\phi(d)$ to be the number of positive integers less than or equal to $d$ that are relatively prime to $d$. Compute
$$
\sum_{d \mid 360} \phi(d).
$$
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 5087$ and $\gcd(n, 40) = 40$. Determine the value o... | 233 | graphs = [
Graph(
let={
"upper": Const(5087),
"k": Const(40),
"d": Const(40),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"Q... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 91dc2d | nt_count_gcd_equals_v1 | negation_mod | 4 | 0 | [
"K3"
] | 1 | 0.393 | 2026-02-08T09:20:13.800080Z | {
"verified": true,
"answer": 233,
"timestamp": "2026-02-08T09:20:14.192742Z"
} | 4883af | 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": 718
},
"timestamp": "2026-02-14T02:38:02.526Z",
"answer": 233
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
987839 | comb_count_permutations_fixed_v1_168721529_1225 | Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 93$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 5$, and $t = 6a + 9b$. Let $s$ be the number of elements in $T$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = s$. Let $n$ be ... | 32,487 | graphs = [
Graph(
let={
"_n": Const(89843),
"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")), CountOverSet(set=SolutionsSet(var=Var("t"), co... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T13:32:41.941667Z | {
"verified": true,
"answer": 32487,
"timestamp": "2026-02-08T13:32:41.944802Z"
} | e1750c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 2572
},
"timestamp": "2026-02-09T14:50:44.317Z",
"answer": 32487
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||
616506 | antilemma_k2_v1_677425708_3258 | Compute $$\sum_{k=1}^{78} \phi(k) \cdot \left\lfloor \frac{1}{k} \sum_{k=1}^{12} \phi(k) \cdot \left\lfloor \frac{12}{k} \right\rfloor \right\rfloor.$$ | 3,081 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(78),
"x": Summation(var="k", start=Div(Const(74), Const(74)), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(12),... | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K2/K2",
"K2"
] | 4813e0 | antilemma_k2_v1 | null | 7 | 0 | [
"IDENTITY_DIV_SELF",
"K2"
] | 2 | 0.001 | 2026-02-08T05:35:21.962185Z | {
"verified": true,
"answer": 3081,
"timestamp": "2026-02-08T05:35:21.963294Z"
} | 87921b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1287
},
"timestamp": "2026-02-12T11:34:40.563Z",
"answer": 3081
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bb3c3f | diophantine_fbi2_count_v1_809748730_310 | Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 522$, $n$ is divisible by 3, and $\gcd(n, 35) = 1$.
Let $S$ be the set of all integers $d$ such that $5 \leq d \leq 68$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 67$.
Let $Q$ be the remainder when $44121$ times the number of elements in $S$ ... | 13,181 | graphs = [
Graph(
let={
"_n": Const(54844),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(522)), Divides(divisor=Const(3), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"result": CountOverS... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.012 | 2026-02-08T11:26:52.360543Z | {
"verified": true,
"answer": 13181,
"timestamp": "2026-02-08T11:26:52.372076Z"
} | 27f76e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1247
},
"timestamp": "2026-02-14T14:05:10.944Z",
"answer": 13181
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
92c87a | nt_count_divisible_and_v1_48377204_1223 | Let $d_1 = 6$ and $d_2 = \sum_{k=1}^{4} k$. Compute the number of positive integers $n$ such that $1 \leq n \leq 126810$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 4,227 | graphs = [
Graph(
let={
"upper": Const(126810),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 4.233 | 2026-02-08T15:58:27.708260Z | {
"verified": true,
"answer": 4227,
"timestamp": "2026-02-08T15:58:31.941369Z"
} | 20b6be | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 365
},
"timestamp": "2026-02-16T06:50:02.806Z",
"answer": 4227
},
{
"id": 11,
... | 2 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
2db6b4 | alg_poly_orbit_legendre_v1_601307018_9324 | Let $a$ be an integer with $0 \le a \le 29970$. Define the sequence:
\[
N = a^{20} \bmod 41,\quad M = (a^5 + 3a^3 - 2a^2 - 2a + 4) \bmod 41,
\]
\[
R = M^{20} \bmod 41,\quad S = (M^5 + 3M^3 - 2M^2 - 2M + 4) \bmod 41,
\]
\[
T = S^{20} \bmod 41,\quad K = (N + R + T) \bmod 41,
\]
\[
L = (S^5 + 3S^3 - 2S^2 - 2S + 4) \bmod 4... | 2,193 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(5)), Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(-2), Pow(Var("a"), Const(2))), Mul(Const(-2), Var("a")), Const(4)), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(5)), Mul(Const(3), Pow(Ref("p1"), Co... | NT | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 7 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.042 | 2026-03-10T09:44:35.658570Z | {
"verified": true,
"answer": 2193,
"timestamp": "2026-03-10T09:44:35.701017Z"
} | 869f67 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 350,
"completion_tokens": 8365
},
"timestamp": "2026-04-19T11:06:41.286Z",
"answer": 2193
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"st... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
454d4e | comb_binomial_compute_v1_153355830_2174 | Let $n$ be the largest prime number less than or equal to 13. Let $r = \binom{n}{5}$. Let $d_{\text{min}}$ be the smallest divisor of 17303 that is at least 2. Compute the Bell number $B_{|r| \bmod d_{\text{min}}}$. | 1 | graphs = [
Graph(
let={
"_n": Const(17303),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(13)), IsPrime(Var("n"))))),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Bell(Mod(... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | d2be59 | comb_binomial_compute_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T06:57:19.854406Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T06:57:19.856268Z"
} | 33715a | 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": 1043
},
"timestamp": "2026-02-13T06:40:56.431Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9fad29 | nt_count_gcd_equals_v1_865884756_6435 | Let $m = 34338$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of nonnegative integers $j \leq 34338$ such that $\binom{m}{j} \equiv 1 \pmod{n}$. Determine the value of the number of positive integer... | 17,672 | graphs = [
Graph(
let={
"_m": Const(34338),
"_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=36)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8"
] | 93b9b8 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 2.559 | 2026-02-08T19:12:10.631952Z | {
"verified": true,
"answer": 17672,
"timestamp": "2026-02-08T19:12:13.190955Z"
} | 2a013f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 3988
},
"timestamp": "2026-02-18T21:37:15.330Z",
"answer": 17672
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5857f3_n | comb_count_surjections_v1_1218484723_4596 | A puzzle designer creates $S(7,5)$ distinct ways to group 7 unique tokens into 5 non-empty indistinguishable boxes, then assigns $5!$ different labels to the boxes. The total number of labeled configurations is $M$. If the designer subtracts $M$ from 2584, what is the remainder when this difference is divided by 98467? | 84,251 | COMB | null | COUNT | sympy | K3 | [
"COUNT_CARTESIAN/STARS_BARS"
] | c8e63c | comb_count_surjections_v1 | negation_mod | 3 | null | [
"COUNT_CARTESIAN",
"K3",
"STARS_BARS"
] | 3 | 0.047 | 2026-02-25T06:16:13.584819Z | null | 6e999f | 5857f3 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 995
},
"timestamp": "2026-03-30T21:57:08.066Z",
"answer": 84251
},
{
"i... | 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": "STARS_BARS",
"status": "ok_later"
},
{
"... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
2149a1 | antilemma_sum_equals_v1_1978505735_7361 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 61$, $1 \leq j \leq 62$, and $i + j = 63$. Let $Q$ be the remainder when $\left(\text{the number of integers } t \text{ with } 5 \leq t \leq 14 \text{ for which there exist integers } a, b \text{ such that } 1 \leq a \leq 4, 1 \leq b \... | 66,482 | graphs = [
Graph(
let={
"_m": Const(66535),
"_n": Const(63),
"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(61)), right=Inte... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | 8ec7d9 | antilemma_sum_equals_v1 | negation_mod | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T20:13:13.509123Z | {
"verified": true,
"answer": 66482,
"timestamp": "2026-02-08T20:13:13.515087Z"
} | 656d91 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1519
},
"timestamp": "2026-02-25T01:52:55.396Z",
"answer": 66482
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
1cfdd1_n | comb_count_derangements_v1_1218484723_6818 | A robot moves on a grid with points labeled by coordinates $(x, y)$, where $x$ is from $\{1, 2\}$ and $y$ is from $\{1, 2, 3, 4\}$. There are $n$ such points. A technician programs the robot to visit each point exactly once, but in a scrambled order such that no point is visited in its 'natural' sequence position. The ... | 19,373 | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_derangements_v1 | null | 3 | null | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-25T08:17:29.868963Z | null | a8b488 | 1cfdd1 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1720
},
"timestamp": "2026-03-31T01:48:28.245Z",
"answer": 19373
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
d37208 | geo_visible_lattice_v1_1218484723_2023 | Let $n = \sum_{k=1}^{11} \varphi(k) \left\lfloor \frac{11}{k} \right\rfloor$, and let $R$ be the number of lattice points $(x,y)$ with $1 \leq x, y \leq n$ such that $\gcd(x,y) = 1$. Find the remainder when $30659 \cdot R$ is divided by $57044$. | 54,901 | graphs = [
Graph(
let={
"_n": Const(11),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(11), Var("k"))))),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(30659),
"Q": Mod(value=Mu... | GEOM | GEOM | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_visible_lattice_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.188 | 2026-02-25T03:43:36.417028Z | {
"verified": true,
"answer": 54901,
"timestamp": "2026-02-25T03:43:36.604698Z"
} | fa09bd | 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": 7956
},
"timestamp": "2026-03-29T02:35:33.854Z",
"answer": 54901
},
{
"... | 1 | [
{
"lemma": "K2",
"status": "ok"
}
] | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
77e85b | nt_count_intersection_v1_898971024_2107 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Define $N$ to be the minimum value of $x + y$ over all such pairs.
Let $a = 11$ and $b = 6$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $\gcd(n, 6) = 1$.
Find the value... | 151 | 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(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(11),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.388 | 2026-02-08T16:33:28.735532Z | {
"verified": true,
"answer": 151,
"timestamp": "2026-02-08T16:33:29.123082Z"
} | 96b6a4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1883
},
"timestamp": "2026-02-17T06:44:24.500Z",
"answer": 151
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
008e2e | antilemma_sum_equals_v1_1820931509_599 | Let $n = 97$. Define $x$ to be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 97$ and $1 \le j \le 97$ such that $i + j = 97$. Compute the value of $4900 - x$. | 4,804 | graphs = [
Graph(
let={
"_n": Const(97),
"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(97)), 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 | 0.003 | 2026-02-08T11:46:55.760488Z | {
"verified": true,
"answer": 4804,
"timestamp": "2026-02-08T11:46:55.763443Z"
} | 313375 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 590
},
"timestamp": "2026-02-24T14:43:23.187Z",
"answer": 4804
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
ccd3aa | nt_count_digit_sum_v1_784195855_4336 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 71$ and $\gcd(n, 20) = 1$. Let $T$ be the set of all prime numbers $n$ such that $2 \leq n \leq |S|$. Define $s$ to be the maximum element of $T$. Let $U$ be the set of all integers $n$ such that $1 \leq n \leq 99999$ and the sum of the decimal digits of $... | 6,087 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(71)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"upper": Const(99999),
"target_sum": MaxOverSet(set=SolutionsSet(var=Var("n"), conditi... | NT | null | COUNT | sympy | C4 | [
"C4/MAX_PRIME_BELOW"
] | 757853 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 7.473 | 2026-02-08T07:02:16.521186Z | {
"verified": true,
"answer": 6087,
"timestamp": "2026-02-08T07:02:23.994104Z"
} | 8544f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2152
},
"timestamp": "2026-02-13T07:20:36.908Z",
"answer": 6087
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"l... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
51f0cb | diophantine_fbi2_count_v1_717093673_3036 | Let $k = 60$. Determine the number of positive integers $d$ such that $5 \leq d \leq 59$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 58$. | 5 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(59)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(Re... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | diophantine_fbi2_count_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.018 | 2026-02-08T17:20:44.408247Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T17:20:44.425857Z"
} | 93803e | 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": 870
},
"timestamp": "2026-02-18T00:21:24.563Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b5efc1 | comb_factorial_compute_v1_1918700295_4049 | Let $j$ be a nonnegative integer. Define $n$ as the number of integers $j$ with $0 \leq j \leq 18433$ such that the binomial coefficient $\binom{18433}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(18433),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(18433)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T09:06:14.834286Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T09:06:14.835710Z"
} | 6e9f80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 839
},
"timestamp": "2026-02-24T10:34:25.538Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
f3a670 | nt_min_coprime_above_v1_1520064083_10324 | Let $A$ be the number of positive integers $n$ between $1$ and $16578$ inclusive such that the sum of the digits of $n$ is even. Let $B = 8128$. Let $C$ be the smallest integer $n$ such that $n > B$, $n \leq A$, and $\gcd(n, 151) = 1$. Compute the remainder when $3617 \cdot C$ is divided by $75794$. | 70,315 | graphs = [
Graph(
let={
"start": Const(8128),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(16578)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"modulus": Const(151),
"res... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | nt_min_coprime_above_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.017 | 2026-02-08T11:21:16.518526Z | {
"verified": true,
"answer": 70315,
"timestamp": "2026-02-08T11:21:16.535066Z"
} | ba1a08 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2761
},
"timestamp": "2026-02-14T12:06:37.009Z",
"answer": 70315
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e6d617 | modular_sum_quadratic_residues_v1_1742523217_5038 | Let $ p = 433 $. Consider the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 4 $. For each such pair, compute $ x + y $, and let $ m $ be the minimum value of $ x + y $ over all such pairs. Define $ r = \frac{p(p-1)}{m} $. Find the remainder when $ 44121 \cdot r $ is divided by $ 66571 $. | 39,441 | graphs = [
Graph(
let={
"_n": Const(66571),
"p": Const(433),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y'... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T10:45:44.455852Z | {
"verified": true,
"answer": 39441,
"timestamp": "2026-02-08T10:45:44.457703Z"
} | e3e785 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1606
},
"timestamp": "2026-02-14T08:39:13.273Z",
"answer": 39441
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1e04b2 | comb_count_derangements_v1_1915831931_1321 | Let $m = 14$ and $n_0 = 33800$. Define $S$ as the set of all nonnegative integers $j$ such that $0 \le j \le 33800$ and
$$
\binom{33800}{j} \equiv 1 \pmod{d},
$$
where $d$ is the number of positive integers $n_1$ satisfying $1 \le n_1 \le 27$, $9 \mid n_1$, and $\gcd(n_1, 14) = 1$.
Let $n$ be the number of elements in... | 32,965 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": Const(33800),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(33800)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("n1... | NT | COMB | COUNT | sympy | C5 | [
"C5/V8"
] | ead758 | comb_count_derangements_v1 | null | 7 | 0 | [
"C5",
"V8"
] | 2 | 0.003 | 2026-02-08T15:59:59.433330Z | {
"verified": true,
"answer": 32965,
"timestamp": "2026-02-08T15:59:59.436717Z"
} | 4fab47 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2952
},
"timestamp": "2026-02-16T19:32:22.745Z",
"answer": 32965
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "ok... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fc9725 | nt_num_divisors_compute_v1_151522320_1630 | Let $n$ be the minimum possible value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 90000$. Let $Q$ be the remainder when $44121$ times the number of positive divisors of $n$ is divided by $78488$. Compute $Q$. | 38,560 | graphs = [
Graph(
let={
"_n": Const(90000),
"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")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T04:08:50.329412Z | {
"verified": true,
"answer": 38560,
"timestamp": "2026-02-08T04:08:50.332746Z"
} | 79761d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1583
},
"timestamp": "2026-02-10T15:37:38.594Z",
"answer": 38560
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a7803c | nt_count_divisible_and_v1_784195855_7042 | Let $d_2 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq 34380$, $n$ is divisible by $4$, and $n$ is divisible by $d_2$. Compute the remainder when the absolute value of this count is divid... | 2,865 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(34380),
"d1": Const(4),
"d2": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 5 | 0 | [
"K2"
] | 1 | 1.205 | 2026-02-08T09:03:46.115812Z | {
"verified": true,
"answer": 2865,
"timestamp": "2026-02-08T09:03:47.320685Z"
} | ac7ddf | 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": 699
},
"timestamp": "2026-02-13T23:55:07.086Z",
"answer": 2865
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
d65a06 | modular_count_residue_v1_1978505735_2197 | Let $A$ be the set of positive integers $n$ such that $1 \leq n \leq 85849$ and $n \equiv 13 \pmod{27}$. Let $r = |A|$. Now, let $T$ be the set of integers $t$ with $7 \leq t \leq 24$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 7$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Let $m = |T|$. Compute $r ... | 3,184 | graphs = [
Graph(
let={
"upper": Const(85849),
"m": Const(27),
"r": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 812dee | modular_count_residue_v1 | mod_exp | 5 | 0 | [
"LIN_FORM"
] | 1 | 2.945 | 2026-02-08T16:45:44.529957Z | {
"verified": true,
"answer": 3184,
"timestamp": "2026-02-08T16:45:47.475220Z"
} | 38f205 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1168
},
"timestamp": "2026-02-17T11:14:28.989Z",
"answer": 3184
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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