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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
443f3a | antilemma_k2_v1_397696148_2334 | Let $N = 369$. Compute
$$
x = \sum_{k=1}^{N} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 369} \phi(d) \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Find the remainder when $67549 \cdot x$ is divided by $60248$. | 31,309 | graphs = [
Graph(
let={
"_n": Const(369),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=369), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
"Q": Mod(value=Mul(Const(67549), Ref("x"))... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T13:07:00.766302Z | {
"verified": true,
"answer": 31309,
"timestamp": "2026-02-08T13:07:00.767576Z"
} | c4d227 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1898
},
"timestamp": "2026-02-15T09:20:53.891Z",
"answer": 31309
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
07b765 | modular_min_modexp_v1_1520064083_4747 | Let $a = 7$, $b = 120$, and $m = 233$. Find the smallest positive integer $x$ such that $1 \leq x \leq 116$ and $a^x \equiv b \pmod{m}$. Compute this value of $x$. | 101 | graphs = [
Graph(
let={
"a": Const(7),
"b": Const(120),
"m": Const(233),
"upper": Const(116),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(ModExp(base=Ref("a"), exp=Var("... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_min_modexp_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.043 | 2026-02-08T06:25:13.316383Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T06:25:13.359435Z"
} | 04219b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 4336
},
"timestamp": "2026-02-12T23:36:02.969Z",
"answer": 101
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
1b3c7e | comb_sum_binomial_row_v1_1520064083_1565 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the smallest positive divisor of 79781 that is at least the number of elements in $P$. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_m": Const(79781),
"_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=108)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T04:07:32.758884Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T04:07:32.760524Z"
} | 857369 | 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": 940
},
"timestamp": "2026-02-10T15:25:44.748Z",
"answer": 8192
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7c7b16 | antilemma_k2_v1_1978505735_4130 | Compute the value of
$$
\sum_{k=1}^{132} \phi(k) \left\lfloor \frac{132}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 8,778 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(132), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(132), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T18:01:36.505730Z | {
"verified": true,
"answer": 8778,
"timestamp": "2026-02-08T18:01:36.506429Z"
} | dab435 | 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": 1239
},
"timestamp": "2026-02-18T12:32:36.353Z",
"answer": 8778
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
626373 | nt_count_gcd_equals_v1_1978505735_3378 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 28224$ and $\gcd(n, 95) = 1$.
Let $B$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10006$.
Compute the value of
$$
(A \bmod 251) + \left(B \cdot (A \bmod 397)\right) \bmod 91295.
$$ | 21,505 | graphs = [
Graph(
let={
"upper": Const(28224),
"k": Const(95),
"d": Const(1),
"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 | COMB1 | [
"COMB1"
] | cc201f | nt_count_gcd_equals_v1 | two_moduli | 4 | 0 | [
"COMB1"
] | 1 | 2.783 | 2026-02-08T17:35:52.117083Z | {
"verified": true,
"answer": 21505,
"timestamp": "2026-02-08T17:35:54.899585Z"
} | 5fca25 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1173
},
"timestamp": "2026-02-18T04:49:59.460Z",
"answer": 21505
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9f3802 | alg_poly4_min_v1_1218484723_1045 | Let $Q$ be the minimum value of
$$
3710610a^4 - 19789920a^3b + 39579840a^2b^2 - 35182080ab^3 + 11773170b^4
$$
over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 240$ and $1 \leq b \leq N$, where
$$
N = \left|\left\{ (a_1, b_1) : \begin{array}{c} 1 \leq a_1, b_1 \leq 20 \\ 13a_1^2 - 2a_1b_1 + 2b_... | 91,620 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(240)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/QF_PSD_COUNT_LEQ"
] | bbcc84 | alg_poly4_min_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.152 | 2026-02-25T02:45:53.820000Z | {
"verified": true,
"answer": 91620,
"timestamp": "2026-02-25T02:45:53.972180Z"
} | 00c8e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 22256
},
"timestamp": "2026-03-10T05:00:12.668Z",
"answer": 91620
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma":... | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
584d0e | alg_sum_powers_v1_1419126231_285 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3059001$. Let $R = \left( \sum_{k=1}^{465} k^3 \right) \bmod 1207$. Find the remainder when $N \cdot R$ is divided by $82127$. | 13,383 | graphs = [
Graph(
let={
"_n": Const(465),
"result": Mod(value=Summation(var="k", start=Const(1), end=Ref("_n"), expr=Pow(Var("k"), Const(3))), modulus=Const(1207)),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(Is... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | e0298c | alg_sum_powers_v1 | affine_mod | 4 | 0 | [
"B3"
] | 1 | 0.021 | 2026-02-25T09:49:13.639409Z | {
"verified": true,
"answer": 13383,
"timestamp": "2026-02-25T09:49:13.660495Z"
} | 3cdb1c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1430
},
"timestamp": "2026-03-30T07:53:15.154Z",
"answer": 13383
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
c793cb | comb_bell_compute_v1_798873815_285 | Let $n = \sum_{d \mid 9} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the Bell number $B_n$, which counts the number of partitions of a set of size $n$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(9),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Bell(Ref("n")),
},
goal=Ref("result"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | comb_bell_compute_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T02:32:17.159709Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T02:32:17.160280Z"
} | 816ca4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 308
},
"timestamp": "2026-02-08T19:19:53.998Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.71,
"mid": -2.85,
"hi": -0.88
} | ||
b90544 | nt_num_divisors_compute_v1_971394319_1315 | Let $n$ be the number of integers $t$ such that $17 \leq t \leq 127$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 33$, $1 \leq b \leq 3$, and $t = 3a + 7b + 7$. Compute the number of positive divisors of $n$. | 6 | 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=33)), 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 | 0.003 | 2026-02-08T13:36:06.872898Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T13:36:06.876368Z"
} | 915f1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2061
},
"timestamp": "2026-02-15T18:52:02.069Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7fc662 | modular_min_modexp_v1_717093673_1533 | Let $a = 11$ and $b = 121$. Let $m$ be the largest prime number less than or equal to 693. Define $S$ as the set of all integers $x$ such that $1 \leq x \leq 138$ and
$$
11^x \equiv 121 \pmod{m}.
$$
Let $r$ be the smallest element of $S$. Compute $r$. | 2 | graphs = [
Graph(
let={
"a": Const(11),
"b": Const(121),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(693)), IsPrime(Var("n"))))),
"upper": Const(138),
"result": MinOverSet(set=SolutionsS... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_min_modexp_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.01 | 2026-02-08T16:09:16.080990Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:09:16.090722Z"
} | a5c532 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1971
},
"timestamp": "2026-02-16T21:59:10.044Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
72cb5a | antilemma_k2_v1_1125832087_644 | Compute
$$
\sum_{k=1}^{216} \phi(k) \left\lfloor \frac{216}{k} \right\rfloor + \phi\left(\left| \sum_{k=1}^{216} \phi(k) \left\lfloor \frac{216}{k} \right\rfloor \right| + 1\right) + \tau\left(\left| \sum_{k=1}^{216} \phi(k) \left\lfloor \frac{216}{k} \right\rfloor \right| + 1\right),
$$
where $\phi(n)$ denotes Euler's... | 45,836 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(216), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(216), Var("k"))))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))),
},
... | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2"
] | 2 | 0.003 | 2026-02-08T03:10:56.689271Z | {
"verified": true,
"answer": 45836,
"timestamp": "2026-02-08T03:10:56.692709Z"
} | 28bca1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 1270
},
"timestamp": "2026-02-10T13:02:23.508Z",
"answer": 45836
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
fb45cf | alg_sum_ap_v1_1419126231_941 | Let $S$ be the set of integers $t$ such that $t = 4a + 6b + 10$ for some integers $a, b$ with $1 \leq a \leq 255$, $1 \leq b \leq 27$, and $20 \leq t \leq 1192$. Let $M = \sum_{k=0}^{|S|} (8k + 18) \bmod 7559$. Compute $27225 - M$. | 21,175 | graphs = [
Graph(
let={
"_n": Const(18),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(lef... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sum_ap_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-25T10:27:05.990630Z | {
"verified": true,
"answer": 21175,
"timestamp": "2026-02-25T10:27:05.999017Z"
} | c47c3d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 18431
},
"timestamp": "2026-03-30T10:46:45.124Z",
"answer": 21175
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
4298b0 | comb_count_derangements_v1_655260480_3694 | Let $c=96475$ and $m=44121$.
Let $T$ be the set of all integers $t$ such that $15\le t\le 42$ and there exist integers $a$ and $b$ with $1\le a\le 2$ and $1\le b\le 4$ satisfying
\[
t = 9a + 6b.
\]
Let $N$ be the number of elements of $T$.
Consider all ordered pairs $(x,y)$ of positive integers such that $x+y$ equals... | 86,009 | graphs = [
Graph(
let={
"_c": Const(96475),
"_m": Const(44121),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), r... | NT | COMB | COUNT | sympy | V8 | [
"V8/B1/MAX_VAL/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | f0715f | comb_count_derangements_v1 | null | 8 | 0 | [
"B1",
"LIN_FORM",
"MAX_PRIME_BELOW",
"MAX_VAL",
"V8"
] | 5 | 0.013 | 2026-02-08T17:29:42.634212Z | {
"verified": true,
"answer": 86009,
"timestamp": "2026-02-08T17:29:42.647400Z"
} | 7a8fb5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 340,
"completion_tokens": 2386
},
"timestamp": "2026-02-18T03:25:25.987Z",
"answer": 86009
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
45c3c7 | nt_count_coprime_and_v1_784195855_9936 | Let $n = 2$ and $\text{upper} = 14630$. Let $k_1 = 3$. Let $k_2$ be the smallest integer $d \geq n$ that divides the number of prime numbers between $2$ and $149$, inclusive. Compute the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 7,803 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(14630),
"k1": Const(3),
"k2": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MIN_PRIME_FACTOR"
] | b226d2 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 2 | 1.792 | 2026-02-08T17:19:15.979762Z | {
"verified": true,
"answer": 7803,
"timestamp": "2026-02-08T17:19:17.771777Z"
} | c4b63d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1311
},
"timestamp": "2026-02-18T00:15:34.349Z",
"answer": 7803
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ec693 | modular_sum_quadratic_residues_v1_458359167_752 | Let $n = 44121$. Let $p$ be the smallest integer greater than or equal to 2 that divides 3995370059. Define $\text{result} = \frac{p(p-1)}{4}$. Let $Q$ be the remainder when $n \cdot \text{result}$ is divided by 79546. Compute $Q$. | 30,740 | graphs = [
Graph(
let={
"_n": Const(44121),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3995370059))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mo... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:32:06.422399Z | {
"verified": true,
"answer": 30740,
"timestamp": "2026-02-08T03:32:06.423591Z"
} | 2335ea | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 8080
},
"timestamp": "2026-02-23T20:19:52.253Z",
"answer": 30740
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3bd5a2 | nt_count_coprime_v1_1918700295_1157 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 17161$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. Find the remainder when this number is divided by $65586$. | 5,721 | graphs = [
Graph(
let={
"upper": Const(17161),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(144)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 2.529 | 2026-02-08T05:36:29.004207Z | {
"verified": true,
"answer": 5721,
"timestamp": "2026-02-08T05:36:31.532903Z"
} | be472a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 875
},
"timestamp": "2026-02-12T11:01:53.364Z",
"answer": 5721
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c09f1f | comb_bell_compute_v1_48377204_2205 | Let $n = 8$. Let $B_n$ be the number of partitions of a set of $n$ elements. Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 8649$. For each such pair, compute $x_1 + y_1$, and let $s_{\min}$ be the smallest such sum. Now let $T$ be the set of all ordered pairs $(x, y)$ of... | 4,509 | graphs = [
Graph(
let={
"_n": Const(8649),
"n": Const(8),
"result": Bell(Ref("n")),
"Q": Sub(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... | COMB | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 6cdf3d | comb_bell_compute_v1 | negation_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T16:38:31.225509Z | {
"verified": true,
"answer": 4509,
"timestamp": "2026-02-08T16:38:31.229398Z"
} | b5d2f0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1348
},
"timestamp": "2026-02-17T09:14:01.506Z",
"answer": 4509
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"st... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
5e1df6 | lin_form_endings_v1_397696148_2665 | Let $a = 60$ and $b = 84$. Define $g = \gcd(a, b)$, and let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 47$ and $B = 17$. Compute the value of $(a' \cdot A + b' \cdot B - a' \cdot b')$, multiply this result by 12440, and then take the remainder when divided ... | 33,128 | graphs = [
Graph(
let={
"a_coeff": Const(60),
"b_coeff": Const(84),
"A_val": Const(47),
"B_val": Const(17),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:28:50.033405Z | {
"verified": true,
"answer": 33128,
"timestamp": "2026-02-08T13:28:50.034565Z"
} | 4c73d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 780
},
"timestamp": "2026-02-15T16:41:43.129Z",
"answer": 33128
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
404fe7 | nt_num_divisors_compute_v1_124444284_648 | Let $n$ be the number of integers $t$ such that $36 \leq t \leq 4437$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 57$, $1 \leq b \leq 216$, and
$$
t = 21a + 15b.
$$
Compute the number of positive divisors of $n$. | 9 | 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=57)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T03:25:57.422558Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T03:25:57.426141Z"
} | d2b971 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 3957
},
"timestamp": "2026-02-23T19:07:12.773Z",
"answer": 9
},
{
"id"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
006c60 | comb_sum_binomial_row_v1_1915831931_3741 | Let $a$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 5$. Let $n_2 = \binom{14}{14} - 1$. Define $e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $b = 2e$, and let $n_1 = a + b$. Define $f = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}$. Compute $(2 + f)^{15... | 32,768 | graphs = [
Graph(
let={
"_n": Const(2),
"n2": Sub(Binom(n=Const(14), k=Const(14)), Const(1)),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": CountOverSet(set=SolutionsSet(var=Tup... | COMB | null | SUM | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | fcdf3f | comb_sum_binomial_row_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"ZERO_BINOM_N"
] | 3 | 0.006 | 2026-02-08T17:52:14.001226Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T17:52:14.007580Z"
} | 427ca8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 875
},
"timestamp": "2026-02-24T23:08:14.643Z",
"answer": 32768
},
{... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
e1c2c3 | nt_num_divisors_compute_v1_784195855_5723 | Let $m = 9801$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = m$. For each such pair, compute $x + y$. Let $s$ be the minimum value of $x + y$ over all such pairs.
Now consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = s$. For each such pair, comp... | 28 | graphs = [
Graph(
let={
"_m": Const(9801),
"_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 | MOBIUS_SUM | [
"B3/B1"
] | 7f76f7 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B1",
"B3",
"MOBIUS_SUM"
] | 3 | 0.04 | 2026-02-08T08:05:16.163007Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T08:05:16.203280Z"
} | 85c421 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1038
},
"timestamp": "2026-02-13T14:27:35.130Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
014c50 | comb_sum_binomial_row_v1_1915831931_2446 | Let $a = 2^{14}$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16777216$. Let $c$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when $c - a$ is divided by $59397$. | 51,205 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(14),
"result": Pow(Ref("_n"), Ref("n")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), E... | NT | null | SUM | sympy | B3 | [
"B3"
] | fc629c | comb_sum_binomial_row_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:49:51.252927Z | {
"verified": true,
"answer": 51205,
"timestamp": "2026-02-08T16:49:51.255334Z"
} | ed60ec | 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": 873
},
"timestamp": "2026-02-17T15:14:24.373Z",
"answer": 51205
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
877f11 | nt_min_coprime_above_v1_48377204_1002 | Let $A = 11664$ and $B = 11933$. Let $M$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 7$ and $1 \leq j \leq 37$. Consider the set of integers $n$ such that $A < n \leq B$ and $\gcd(n, M) = 1$. Let $R$ be the smallest such integer $n$. Determine the value of $R$. | 11,665 | graphs = [
Graph(
let={
"start": Const(11664),
"upper": Const(11933),
"modulus": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(37)))),
"result": MinOverSet(set=SolutionsSet(var=V... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_min_coprime_above_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.043 | 2026-02-08T15:51:47.891700Z | {
"verified": true,
"answer": 11665,
"timestamp": "2026-02-08T15:51:47.934778Z"
} | 9f9e36 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 750
},
"timestamp": "2026-02-16T14:58:07.545Z",
"answer": 11665
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e1098a | nt_sum_totient_over_divisors_v1_1440796553_96 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 4491$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 819$, $1 \leq b \leq 243$, and $t = 4a + 5b$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. | 4,471 | 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=819)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T11:34:48.789172Z | {
"verified": true,
"answer": 4471,
"timestamp": "2026-02-08T11:34:48.798791Z"
} | e30b4e | 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": 6157
},
"timestamp": "2026-02-14T15:57:02.870Z",
"answer": 4471
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
479e7f | antilemma_sum_equals_v1_1978505735_7121 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 57$, $1 \leq i \leq 56$, and $1 \leq j \leq 57$. Let $Q = 50000 - x$. Determine the value of $Q$. | 49,944 | graphs = [
Graph(
let={
"_n": Const(57),
"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(56)), 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 | 0.008 | 2026-02-08T20:03:53.980767Z | {
"verified": true,
"answer": 49944,
"timestamp": "2026-02-08T20:03:53.988284Z"
} | 2c3a5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 518
},
"timestamp": "2026-02-25T01:51:51.959Z",
"answer": 49944
},
{... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||
36dc9c | sequence_fibonacci_compute_v1_655260480_1430 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 24$, $1 \le j \le 25$, and $i + j = 26$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \ge 3$. | 46,368 | graphs = [
Graph(
let={
"_n": Const(26),
"n": 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(24)), right=IntegerRange(start=Const(1), end=Con... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T16:08:24.527399Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T16:08:24.540312Z"
} | 2fd588 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 659
},
"timestamp": "2026-02-16T06:57:09.587Z",
"answer": 46368
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
269d0e | nt_sum_totient_over_divisors_v1_1520064083_6004 | Let $m = 2$, and let $n$ be the largest prime number at most $12$. Define $N = 73270$. Let $R$ be the sum of $\phi(d)$ over all positive divisors $d$ of $N$, where $\phi$ is Euler's totient function. Let $p_{\min}$ be the smallest positive integer $d \geq 2$ that divides $30$, and let $p_{\max}$ be the largest prime nu... | 41,866 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"n": Const(73270),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 661aa6 | nt_sum_totient_over_divisors_v1 | bell_mod | 7 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.006 | 2026-02-08T07:46:13.190014Z | {
"verified": true,
"answer": 41866,
"timestamp": "2026-02-08T07:46:13.195609Z"
} | a579c1 | 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": 888
},
"timestamp": "2026-02-13T12:20:09.208Z",
"answer": 41866
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cf76de | nt_num_divisors_compute_v1_124444284_1822 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 37$ and $1 \leq j \leq 37$. Let $d$ be the number of positive divisors of $n$. Compute the remainder when $44121 \cdot d$ is divided by $79504$. | 52,859 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(37)), right=IntegerRange(start=Const(1), end=Const(37)))),
"result": NumDivisors(n=Ref("n")),
"Q": Mod(value=Mul(Ref("_n"), Ref("resu... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:09:54.079325Z | {
"verified": true,
"answer": 52859,
"timestamp": "2026-02-08T04:09:54.080280Z"
} | 1dc7d9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 454
},
"timestamp": "2026-02-10T15:34:10.705Z",
"answer": 52859
},
{
"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
bd87a9 | nt_count_gcd_equals_v1_865884756_1690 | Let $k = 229$ and let $U = 43264$. Let $d$ be the smallest divisor of $2971291259$ that is at least $2$. Determine the number of positive integers $n$ such that $1 \le n \le 43264$ and $\gcd(n, k) = d$. | 188 | graphs = [
Graph(
let={
"upper": Const(43264),
"k": Const(229),
"d": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(2)), Divides(divisor=Var("d1"), dividend=Const(2971291259))))),
"result": CountOverSet(set=SolutionsSet(var=Var("... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.515 | 2026-02-08T16:13:43.085028Z | {
"verified": true,
"answer": 188,
"timestamp": "2026-02-08T16:13:46.600378Z"
} | 397cb6 | 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": 2538
},
"timestamp": "2026-02-16T23:09:36.496Z",
"answer": 188
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
842696 | algebra_quadratic_discriminant_v1_1520064083_4480 | Let $a = -2$, $b = 16$, and $c = 0$. Compute $b^2 - 4ac$. | 256 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(16),
"c": Const(0),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.01 | 2026-02-08T06:17:44.535495Z | {
"verified": true,
"answer": 256,
"timestamp": "2026-02-08T06:17:44.545465Z"
} | f1887c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 116
},
"timestamp": "2026-02-15T17:21:44.538Z",
"answer": 256
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
60e703 | comb_binomial_compute_v1_2051736721_5559 | Let $f = \sum_{k_1=0}^{0} (-1)^{k_1} \binom{0}{k_1}$ and $e = \sum_{k_2=0}^{7} (-1)^{k_2} \binom{7}{k_2}$. Let $t$ be the number of integers $t$ such that $7 \le t \le 24$ and there exist integers $a$ and $b$ with $1 \le a \le 3$, $1 \le b \le 4$, and $t = 4a + 3b$. Define $n = t \cdot f + e$. Compute $\binom{n}{5}$. | 792 | graphs = [
Graph(
let={
"n2": Const(0),
"f": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"a": Const(4),
"b": Const(3),
"n1": Sum(Ref("a"), Ref("b")),
"e": Sum... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T18:40:02.174722Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T18:40:02.176835Z"
} | 2f8381 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1160
},
"timestamp": "2026-02-18T18:35:40.314Z",
"answer": 792
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
32ac74 | antilemma_product_of_sums_v1_1918700295_924 | Let $m = 2$ and $n = 31$. Define $S_1$ to be the sum of $k$ over all ordered pairs $(k, j)$ where $k$ ranges from $1$ to $6$ and $j$ ranges from $1$ to $4$. Let $D$ be the set of all integers $d \geq m$ that divide $47027$, and let $d_{\min}$ be the smallest element of $D$. Define $S_2$ to be the sum over all integers ... | 41,664 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(31),
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=EulerPhi(n=Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"PRODUCT_OF_SUMS",
"ONE_PHI_1"
] | 2f7d27 | antilemma_product_of_sums_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"ONE_PHI_1",
"PRODUCT_OF_SUMS"
] | 3 | 0.003 | 2026-02-08T05:24:05.839685Z | {
"verified": true,
"answer": 41664,
"timestamp": "2026-02-08T05:24:05.842967Z"
} | 25dff5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 454
},
"timestamp": "2026-02-18T16:07:55.922Z",
"answer": 480
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
8147bb | geo_count_lattice_triangle_v1_601307018_3387 | Let $M$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 2664$. Let $R = |333 \cdot 105 + 91 \cdot (-190)|$. Define $$S = \gcd(333, 190) + \gcd\left(\left|91 - \left|\left\{ (a, b) : a \geq 1,\ a \leq M,\ b \geq 1,\ b \leq 35,\ -2ab + 13a^2 + 2b^2 \leq \max \{ d : d \geq... | 8,834 | graphs = [
Graph(
let={
"_m": Const(2000),
"_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(2664)))), expr=Abs(arg=Sub(left=Var(name... | GEOM | NT | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/QF_PSD_COUNT_LEQ",
"B3_DIFF/QF_PSD_COUNT_LEQ"
] | e2e5df | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3_DIFF",
"MAX_DIVISOR",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.033 | 2026-03-10T03:57:29.032390Z | {
"verified": true,
"answer": 8834,
"timestamp": "2026-03-10T03:57:29.065141Z"
} | 89903b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 327,
"completion_tokens": 9194
},
"timestamp": "2026-03-29T08:31:15.998Z",
"answer": 8834
},
{
"i... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
02429c | modular_modexp_compute_v1_1520064083_3612 | Let $a = 19$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 153664$. Let $e$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $m = 29241$. Compute the value of $a^e \bmod m$, that is, the remainder when $a^e$ is divided by $m$. | 23,104 | graphs = [
Graph(
let={
"a": Const(19),
"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(153664)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T05:46:50.081206Z | {
"verified": true,
"answer": 23104,
"timestamp": "2026-02-08T05:46:50.083098Z"
} | 8e85ba | 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": 2532
},
"timestamp": "2026-02-12T14:30:15.566Z",
"answer": 23104
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
9b4569 | antilemma_product_of_sums_v1_1742523217_5651 | Let $S_1$ be the sum of all integers $j$ such that $0 \leq j \leq 7$ and $\binom{7}{j}$ is odd, where the lower bound is determined by the sum of the M\"obius function over the positive divisors of $\gcd(60, 20)$. Let $S_2$ be the sum of $ij$ over all ordered pairs $(i, j)$ with $1 \leq i \leq 7$ and $1 \leq j \leq 5$.... | 11,760 | graphs = [
Graph(
let={
"S1": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=GCD(a=Const(value=60), b=Const(value=20)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("j"), Const(7)), Eq(Mod(value=Binom(n=Const(7), k=Var("j")), modulus=Const(2)), Con... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"PRODUCT_OF_SUMS"
] | 17cc0f | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"PRODUCT_OF_SUMS"
] | 2 | 0.001 | 2026-02-08T11:08:39.510288Z | {
"verified": true,
"answer": 11760,
"timestamp": "2026-02-08T11:08:39.511649Z"
} | 1116af | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 569
},
"timestamp": "2026-02-21T13:23:42.889Z",
"answer": 2940
}
] | 0 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
d39d26 | comb_count_derangements_v1_260342960_54 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 7$. Define $r = !n$, the number of derangements of $n$ elements. Compute the remainder when $18183 \cdot r$ is divided by 89365. | 20,677 | graphs = [
Graph(
let={
"_n": Const(18183),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("resul... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T11:12:03.148021Z | {
"verified": true,
"answer": 20677,
"timestamp": "2026-02-08T11:12:03.149248Z"
} | 055838 | 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": 1727
},
"timestamp": "2026-02-08T20:28:11.817Z",
"answer": 20677
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"sta... | {
"lo": 0.62,
"mid": 2.54,
"hi": 4.29
} | ||
60bd97 | modular_mod_compute_v1_458359167_5196 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1562500$. Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive inte... | 100 | 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(1562500)))), expr=Sum(Var("x"), Var("y")))),
"a": MinOverSe... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | modular_mod_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T12:20:30.250621Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T12:20:30.256385Z"
} | 85f0ca | 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": 1446
},
"timestamp": "2026-02-15T00:35:37.074Z",
"answer": 100
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
776d46 | algebra_poly_eval_v1_1520064083_4142 | Let $a$ and $b$ be positive integers such that $ab = 61740$ and $\gcd(a, b) = 1$, with $a < b$. Let $S$ be the set of all such integers $a$. Compute the number of elements in $S$. Let $T$ be the set of integers $t$ such that $5 \leq t \leq 15$ and $t = 3a + 2b$ for some positive integers $a, b \leq 3$. Compute the numb... | 649 | graphs = [
Graph(
let={
"_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=61740)), Eq(left=GCD(a=Var(name='p'), b=Var(name... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_ARITHMETIC",
"LIN_FORM"
] | a15c58 | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T06:06:35.527535Z | {
"verified": true,
"answer": 649,
"timestamp": "2026-02-08T06:06:35.530768Z"
} | 9965b9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 2769
},
"timestamp": "2026-02-12T20:09:58.903Z",
"answer": 649
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMET... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b9b16c | sequence_lucas_compute_v1_601307018_4572 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ satisfying $10ab + 5a^2 + 5b^2 = 2880$. Let $R = L_n$, where $L_n$ denotes the $n$-th Lucas number. Find the remainder when $32761 - R$ is divided by $88916$. | 57,598 | graphs = [
Graph(
let={
"_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(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(10), Var("a"), Var("b")), Mul(Cons... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.004 | 2026-03-10T05:12:56.433398Z | {
"verified": true,
"answer": 57598,
"timestamp": "2026-03-10T05:12:56.437025Z"
} | 277946 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1141
},
"timestamp": "2026-03-29T12:43:59.360Z",
"answer": 57598
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
a1f5a8 | nt_lcm_compute_v1_865884756_1510 | Let $a = 782$ and let $b = \sum_{k=1}^{45} k$. Let $L$ be the least common multiple of $a$ and $b$. Compute the remainder when $25600 - L$ is divided by $54159$. | 44,569 | graphs = [
Graph(
let={
"_n": Const(54159),
"a": Const(782),
"b": Summation(var="k", start=Const(1), end=Summation(var="k1", start=Const(1), end=Const(9), expr=Var("k1")), expr=Var("k")),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(Co... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 2a57af | nt_lcm_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.005 | 2026-02-08T16:05:28.970371Z | {
"verified": true,
"answer": 44569,
"timestamp": "2026-02-08T16:05:28.974874Z"
} | f9c9da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 867
},
"timestamp": "2026-02-16T21:37:04.380Z",
"answer": 44569
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
676229 | sequence_count_fib_divisible_v1_1918700295_4564 | Let $m$ be the number of integers $t$ with $10 \le t \le 14462$ such that there exist positive integers $a \le 1839$ and $b \le 857$ satisfying $t = 6a + 4b$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $c = 29410$ and let $u$ be the largest positive divi... | 42 | graphs = [
Graph(
let={
"_c": Const(29410),
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1839)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3/MAX_DIVISOR"
] | ea3355 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"MAX_DIVISOR"
] | 3 | 0.101 | 2026-02-08T09:27:54.823063Z | {
"verified": true,
"answer": 42,
"timestamp": "2026-02-08T09:27:54.923733Z"
} | 392c62 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 4342
},
"timestamp": "2026-02-14T04:26:58.603Z",
"answer": 42
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_la... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5f6aa0 | comb_binomial_compute_v1_1248542787_30 | Let $n = \sum_{k=1}^{5} k$ and let $k = 6$. Compute $\binom{n}{k}$. | 5,005 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | LTE_DIFF | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"LTE_DIFF",
"SUM_ARITHMETIC"
] | 2 | 0.004 | 2026-02-08T02:55:13.635020Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T02:55:13.639241Z"
} | 6b18cf | 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": 507
},
"timestamp": "2026-02-08T23:17:14.249Z",
"answer": 5005
},
{
"id... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -10,
"mid": -7.78,
"hi": -5.56
} | ||
4fadf5 | antilemma_k3_v1_1520064083_21 | Let $n = 78074$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 78,074 | graphs = [
Graph(
let={
"_n": Const(78074),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T02:57:32.723818Z | {
"verified": true,
"answer": 78074,
"timestamp": "2026-02-08T02:57:32.724252Z"
} | a54279 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1189
},
"timestamp": "2026-02-08T20:05:50.325Z",
"answer": 78074
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
4a9ff4 | antilemma_v1_legendre_1742523217_559 | Let $m = 11011$ and $n = 26852$. Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 36$, and $\gcd(p, q) = 1$. Let $a$ be the number of elements in $S$. Let $D$ be the set of all positive divisors $d$ of $m$ such that $d \geq a$. Let $b$ be the smallest ele... | 4,474 | graphs = [
Graph(
let={
"_m": Const(11011),
"_n": Const(26852),
"x": MaxKDivides(target=Factorial(Ref("_n")), base=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p'))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/V1",
"V1"
] | 08fea4 | antilemma_v1_legendre | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"V1"
] | 3 | 0.003 | 2026-02-08T03:07:18.771555Z | {
"verified": true,
"answer": 4474,
"timestamp": "2026-02-08T03:07:18.774268Z"
} | 923a43 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 2066
},
"timestamp": "2026-02-09T04:27:54.300Z",
"answer": 4474
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PA... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
2c309c | comb_sum_binomial_row_v1_151522320_1529 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 22$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 5a + 2b + 2$. Let $n$ be the number of elements in $T$. Compute $2^n$. | 1,024 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:04:54.979693Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T04:04:54.981439Z"
} | 763244 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 582
},
"timestamp": "2026-02-10T15:19:23.132Z",
"answer": 1024
},
{
"i... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
34fdb2 | alg_poly4_min_v1_1218484723_7745 | Find the minimum value of
$$
-861900a b^{3} - 596700 a^{3} b + 1014390 a^{2} b^{2} + 179010 a^{4} + 283985 b^{\min\{ x + y : x > 0,\, y > 0,\, x y = 4 \}}
$$
over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 149$ and $1 \leq b \leq \max \{ n : n \geq 2,\, n \leq 150,\, n \text{ is prime} \}$. | 18,785 | graphs = [
Graph(
let={
"_m": Const(150),
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(149)), Geq(Var("b"), Const(1)), Leq(Var("b"), MaxOverSet(set... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | alg_poly4_min_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.065 | 2026-02-25T09:18:57.235840Z | {
"verified": true,
"answer": 18785,
"timestamp": "2026-02-25T09:18:57.301319Z"
} | 24b241 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 16191
},
"timestamp": "2026-03-30T06:13:26.860Z",
"answer": 18785
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
4b1a4e | modular_sum_quadratic_residues_v1_717093673_3535 | Let $p = 233$. Let $T$ be the set of all positive integers $p_1$ for which there exists an integer $q$ such that $p_1 q = 90$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Compute $\frac{p(p-1)}{|T|}$. | 13,514 | graphs = [
Graph(
let={
"p": Const(233),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), CountOverSet(set=SolutionsSet(var=Var("p1"), condition=And(IsPositive(arg=Var(name='p1')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p1'), Var(name='q')), right=Const(va... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.005 | 2026-02-08T17:40:30.769522Z | {
"verified": true,
"answer": 13514,
"timestamp": "2026-02-08T17:40:30.774345Z"
} | 6e1297 | 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": 1642
},
"timestamp": "2026-02-18T06:21:52.746Z",
"answer": 13514
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c314b6 | nt_sum_divisors_compute_v1_809748730_340 | Let $n = 22500$ and $m = 76747$. Let $S$ be the sum of all positive divisors of $n$. Let $C$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $D$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 2$ and $1 \leq j \leq 10$ such that $\gcd(i, j... | 71,073 | graphs = [
Graph(
let={
"_n": Const(76747),
"n": Const(22500),
"result": SumDivisors(n=Ref("n")),
"Q": Sum(Ref("result"), Mod(value=Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"COPRIME_PAIRS"
] | 3c4e9d | nt_sum_divisors_compute_v1 | mod_exp | 5 | 0 | [
"COPRIME_PAIRS",
"COUNT_COPRIME_GRID"
] | 2 | 0.003 | 2026-02-08T11:28:44.435165Z | {
"verified": true,
"answer": 71073,
"timestamp": "2026-02-08T11:28:44.437821Z"
} | 23f454 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1574
},
"timestamp": "2026-02-14T14:54:16.838Z",
"answer": 71073
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
90f0c9 | modular_count_residue_v1_153355830_1523 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 2002$. Let $r$ be the smallest divisor of $n$ that is greater than or equal to 2. Compute the number of positive integers $n$ less than or equal to 53361 such that $n \equiv r \pmod{17}$. | 3,139 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(2002))))),
"... | NT | null | COUNT | sympy | COMB1 | [
"COMB1/MIN_PRIME_FACTOR"
] | ace0d3 | modular_count_residue_v1 | null | 5 | 0 | [
"COMB1",
"MIN_PRIME_FACTOR"
] | 2 | 4.691 | 2026-02-08T06:28:44.347002Z | {
"verified": true,
"answer": 3139,
"timestamp": "2026-02-08T06:28:49.037883Z"
} | 1914c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 996
},
"timestamp": "2026-02-13T00:46:04.939Z",
"answer": 3139
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
982d57 | algebra_vieta_sum_v1_1918700295_254 | Let $f(x) = -x^3 + 12x^2 - 35x + k$, where $k$ is the number of integers $t$ such that $25 \le t \le 54$ and there exist positive integers $a \le 12$ and $b \le 2$ satisfying
$$
t = 2a + 7b + 16.
$$
Compute the product of all real roots of the equation $f(x) = 0$. | 24 | graphs = [
Graph(
let={
"_n": Const(3),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=-1), Pow(base=Var(name='x'), exp=Ref(name='_n'))), Mul(Const(value=12), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=-35), Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 7b2633 | algebra_vieta_sum_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.055 | 2026-02-08T03:06:47.091382Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T03:06:47.146535Z"
} | 3dbf36 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1635
},
"timestamp": "2026-02-10T13:11:01.383Z",
"answer": 24
},
{
"id"... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
405d27 | alg_poly_orbit_count_v1_1218484723_3554 | For an integer $a$, define
\[
N = a^{2} + a - 4 \bmod 73,\quad M = N^{2} + N - 4 \bmod 73,\quad R = M^{2} + M - 4 \bmod 73,
\]
\[
S = R^{2} + R - 4 \bmod 73,\quad T = S^{2} + S - 4 \bmod 73,\quad K = T^{2} + T - 4 \bmod 73.
\]
Let $Q$ be the number of integers $a$ with $0 \le a \le 100958$ such that $K = a$ and $N, M, ... | 8,298 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-4)), modulus=Const(73)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-4)), modulus=Const(73)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-4)), mod... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.041 | 2026-02-25T05:11:04.090986Z | {
"verified": true,
"answer": 8298,
"timestamp": "2026-02-25T05:11:04.132156Z"
} | 496152 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T10:59:15.682Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
0db57a | comb_bell_compute_v1_655260480_1448 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 9$, $1 \leq j \leq 10$, and $i + j = 11$. Let $c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $w = \sum_{k1=0}^{0} (-1)^{k1} \binom{0}{k1}$. Define $n = |S| \cdot c \cdot w$. Let $B_n$ denote the $n$th Bell number, the number of partitio... | 22,534 | graphs = [
Graph(
let={
"_n": Const(43681),
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"w": Summation(var="k1", start=Const(0), end=Ref... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_bell_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.019 | 2026-02-08T16:08:49.976652Z | {
"verified": true,
"answer": 22534,
"timestamp": "2026-02-08T16:08:49.996053Z"
} | 0d2efe | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 648
},
"timestamp": "2026-02-24T19:56:33.255Z",
"answer": 22534
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"s... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
c31cca | nt_min_coprime_above_v1_971394319_1900 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 130$. Let $P$ be the set of all values of $xy$ as $(x,y)$ ranges over $S$. Let $M$ be the maximum value in $P$. Let $d_0$ be the smallest divisor of $13044194633$ that is at least $2$. Find the smallest integer $n$ such that $n > M$... | 4,226 | graphs = [
Graph(
let={
"_n": Const(2),
"start": 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(130)))), expr=Mul(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B1"
] | e7724f | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.031 | 2026-02-08T14:00:00.031291Z | {
"verified": true,
"answer": 4226,
"timestamp": "2026-02-08T14:00:00.062157Z"
} | d96bb5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2652
},
"timestamp": "2026-02-15T22:38:16.456Z",
"answer": 4226
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
fd4dd9 | sequence_count_fib_divisible_v1_717093673_536 | Let $\text{upper}$ be the sum of $\phi(d)$ over all positive divisors $d$ of $472$.
Compute the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $8$ divides the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 78 | graphs = [
Graph(
let={
"upper": SumOverDivisors(n=Const(value=472), var='d1', expr=EulerPhi(n=Var(name='d1'))),
"d": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d... | NT | null | COUNT | sympy | VIETA_SUM | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.276 | 2026-02-08T15:30:02.905786Z | {
"verified": true,
"answer": 78,
"timestamp": "2026-02-08T15:30:03.181628Z"
} | 0fa81c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1180
},
"timestamp": "2026-02-16T08:18:43.124Z",
"answer": 78
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
08128f | sequence_fibonacci_compute_v1_124444284_7253 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 26$ and $1 \leq i, j \leq 24$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 28,657 | graphs = [
Graph(
let={
"_n": Const(26),
"n": 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(24)), right=IntegerRange(start=Const(1), end=Con... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.009 | 2026-02-08T08:58:25.943726Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T08:58:25.952566Z"
} | 337358 | 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": 570
},
"timestamp": "2026-02-13T23:40:54.357Z",
"answer": 28657
},
{... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
863341 | comb_catalan_compute_v1_677425708_3802 | Let $m = 26$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 11$, $1 \leq j \leq 11$, and $i + j = k$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"_m": Const(26),
"_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 | null | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS"
] | 4d9cac | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.01 | 2026-02-08T05:56:37.910998Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T05:56:37.920969Z"
} | ce346e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1047
},
"timestamp": "2026-02-24T04:56:10.623Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
a325f1_n | sequence_lucas_compute_v1_601307018_8808 | A botanist studies a plant species that follows the Lucas sequence: the number of leaves on the $k$-th stem is $L_k$, where $L_0 = 2$, $L_1 = 1$, and each subsequent count is the sum of the two previous. If the plant has a stem numbered $n$, where $n = 4^0 + 4^1 + 4^2$, how many leaves are on that stem? | 24,476 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(0), end=Ref("_n"), expr=Pow(Const(4), Var("k"))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | sequence_lucas_compute_v1 | null | 2 | null | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-03-10T09:16:14.721772Z | null | 5fb0cf | a325f1 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 987
},
"timestamp": "2026-04-23T13:41:15.419Z",
"answer": 24476
}
] | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
e71c28 | nt_count_with_divisor_count_v1_1742523217_2911 | Let $n$ be a positive integer. Let $d$ be the number of prime numbers $n$ such that $2 \leq n \leq 41$. Compute the number of positive integers $n$ such that $1 \leq n \leq 10404$ and the number of positive divisors of $n$ is equal to $d$. Multiply this count by $44121$ and report the result. | 44,121 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(10404),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(41)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n")... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.428 | 2026-02-08T05:27:31.109119Z | {
"verified": true,
"answer": 44121,
"timestamp": "2026-02-08T05:27:31.536772Z"
} | 2bd481 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 948
},
"timestamp": "2026-02-11T22:49:07.313Z",
"answer": 2809344
},
{
"id": 1... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a3407e | antilemma_product_of_sums_v1_677425708_3747 | Let $m = 21$. Let $d$ be the largest positive divisor of $609$ that is at most $m$. Define $$s = \sum_{k=1}^{d} k.$$ Let $T$ be the set of all ordered pairs $(i, j)$ such that $1 \leq i \leq 3$ and $1 \leq j \leq 10$. Define $x = s \cdot \sum_{(i,j) \in T} i \cdot j$. Let $Q = x + 2^{x \bmod 14} \bmod 91303$. Compute t... | 76,231 | graphs = [
Graph(
let={
"_m": Const(21),
"_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(609))))),
"x": Mul(Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/PRODUCT_OF_SUMS/SUM_ARITHMETIC"
] | d5c254 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"MAX_DIVISOR",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T05:55:11.369015Z | {
"verified": true,
"answer": 76231,
"timestamp": "2026-02-08T05:55:11.372107Z"
} | bbb3ce | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 513
},
"timestamp": "2026-02-18T21:22:14.876Z",
"answer": 6090
}
] | 0 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
a45cbb | alg_linear_system_2x2_v1_601307018_5498 | Let $N$ be the number of elements in the Cartesian product $\{1, 2, \ldots, 35\} \times \{1, 2, \ldots, 36\}$. Let $R$ be the minimum value of $6ab^2 + b^3 + 12a^2b$ over all positive integers $a, b$ with $1 \le a, b \le 11$. Define $\det = -17R + 28$, $S = -236529 \cdot 19 + 92709 \cdot 4$, and $T = -17 \cdot (-92709)... | 51,411 | graphs = [
Graph(
let={
"_m": Const(64398),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(11)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(11)))), expr=Sum(Mul(Const(6), Var("a")... | ALG | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"POLY3_MIN/COUNT_CARTESIAN"
] | 8a8533 | alg_linear_system_2x2_v1 | negation_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"POLY3_MIN"
] | 2 | 0.01 | 2026-03-10T06:06:36.071544Z | {
"verified": true,
"answer": 51411,
"timestamp": "2026-03-10T06:06:36.081887Z"
} | 750a3f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 1542
},
"timestamp": "2026-04-19T02:14:34.662Z",
"answer": 51411
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
c081d2 | nt_sum_divisors_compute_v1_1520064083_4485 | Let $n = 55696$. Compute the sum of all positive divisors of $n$. Let $s$ denote this sum. Let $p_{\text{max}}$ be the largest prime number at most $2003$. Compute the remainder when
$$
(s \bmod 317) + p_{\text{max}} \cdot (s \bmod 313)
$$
is divided by $59111$. | 28,975 | graphs = [
Graph(
let={
"_n": Const(2003),
"n": Const(55696),
"result": SumDivisors(n=Ref("n")),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Const(317)), Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"),... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_sum_divisors_compute_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T06:17:53.506951Z | {
"verified": true,
"answer": 28975,
"timestamp": "2026-02-08T06:17:53.508540Z"
} | 1ec837 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1356
},
"timestamp": "2026-02-12T22:14:33.467Z",
"answer": 28975
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
977a7b | alg_poly4_min_v1_1218484723_6062 | Find the minimum value of $8282b^4 + 6464a^3b + 21008ab^3 + 3232a^4 + 24240a^2b^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 410$. | 63,226 | graphs = [
Graph(
let={
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(410)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(410)))), expr=Sum(Mul(Const(8282), Pow(Var("b"), Const(4))), Mul(C... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/QF_PSD_COUNT_LEQ",
"VIETA_SUM"
] | a2550c | alg_poly4_min_v1 | null | 4 | null | [
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ",
"VIETA_SUM"
] | 3 | 1.518 | 2026-02-25T07:41:48.251087Z | {
"verified": true,
"answer": 63226,
"timestamp": "2026-02-25T07:41:49.769150Z"
} | bcfffc | 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": 4437
},
"timestamp": "2026-03-30T00:02:16.455Z",
"answer": 63226
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
b1c355 | comb_factorial_compute_v1_865884756_6820 | Let $n$ be the largest prime number such that $2 \leq n \leq 8$. Compute the remainder when $57171 \cdot n!$ is divided by $63853$. | 37,104 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(8)), IsPrime(Var("n1"))))),
"result": Factorial(Ref("n")),
"_c": Const(57171),
"Q": Mod(value=Mul(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T19:24:35.956568Z | {
"verified": true,
"answer": 37104,
"timestamp": "2026-02-08T19:24:35.957727Z"
} | 9b91cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 1243
},
"timestamp": "2026-02-18T22:17:58.602Z",
"answer": 37104
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
143d7f | lin_form_endings_v1_1978505735_7158 | Let $a = 45$ and $b = 36$. Compute the remainder when $6299 \left\lfloor \frac{36}{\gcd(a,b)} \right\rfloor$ is divided by $71614$. | 25,196 | graphs = [
Graph(
let={
"a_coeff": Const(45),
"b_coeff": Const(36),
"_inner_result": Floor(Div(Const(36), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(6299),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T20:05:40.049710Z | {
"verified": true,
"answer": 25196,
"timestamp": "2026-02-08T20:05:40.050425Z"
} | f1a437 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 273
},
"timestamp": "2026-02-16T18:47:48.338Z",
"answer": 25196
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d0510c | nt_max_prime_below_v1_784195855_2964 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq 18225$. Determine the value of the largest element in $T$. | 18,223 | graphs = [
Graph(
let={
"upper": Const(18225),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.533 | 2026-02-08T06:09:32.949264Z | {
"verified": true,
"answer": 18223,
"timestamp": "2026-02-08T06:09:33.482230Z"
} | 2a0fbc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 467
},
"timestamp": "2026-02-19T01:57:10.285Z",
"answer": 18223
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
ba27e4 | sequence_lucas_compute_v1_124444284_82 | Let $n$ be the number of positive integers $j$ such that $1 \le j \le 22$ and $j^4 \le 234256$. Compute the $n$-th Lucas number. | 39,603 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), EulerPhi(n=Const(1))), Leq(Var("j"), Const(22)), Leq(Pow(Var("j"), Ref("_n")), Const(234256))), domain='positive_integers')),
"result": Lucas(arg=Ref(name=... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"C3"
] | 5b9f33 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"C3",
"ONE_PHI_1"
] | 2 | 0.001 | 2026-02-08T02:57:10.067266Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T02:57:10.068640Z"
} | 2270b2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1110
},
"timestamp": "2026-02-09T13:38:15.702Z",
"answer": 39603
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
d775d2 | lin_form_endings_v1_1742523217_568 | Let $a = 105$, $b = 75$, $A = 45$, and $B = 16$. Let $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $T$ be a set whose size is given by $a'A + b'B - a'b'$. The total number of lattice points $(x, y)$ satisfying $1 \leq x \leq A$ and $1 \leq y \leq... | 5,386 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(75),
"A_val": Const(45),
"B_val": Const(16),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node":... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:07:31.739988Z | {
"verified": true,
"answer": 5386,
"timestamp": "2026-02-08T03:07:31.740870Z"
} | 116579 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 792
},
"timestamp": "2026-02-09T19:33:32.149Z",
"answer": 5386
},
{
"id... | 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": "V7",
"status... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
137c04 | antilemma_k2_v1_124444284_6398 | Let $N$ be the sum of $\varphi(d)$ over all positive divisors $d$ of $293$, where $\varphi$ denotes Euler's totient function. For each integer $k$ with $1 \le k \le N$, let $S_k$ be the sum of all integers $x$ that satisfy
$$x^2-293x-2718=0,$$
and define
$$T_k = \varphi(k) \left\lfloor \frac{S_k}{k} \right\rfloor.$$
Le... | 43,071 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=293), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n"... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K3/K2",
"K2"
] | 4108ea | antilemma_k2_v1 | null | 8 | 0 | [
"K2",
"K3",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T08:20:26.114560Z | {
"verified": true,
"answer": 43071,
"timestamp": "2026-02-08T08:20:26.117183Z"
} | deeb84 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1415
},
"timestamp": "2026-02-13T17:42:03.423Z",
"answer": 43071
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
9baabb | diophantine_fbi2_min_v1_2051736721_787 | Let $k$ be the number of integers $t$ with $33 \leq t \leq 305$ for which there exist positive integers $a \leq 21$ and $b \leq 10$ such that $t = 10a + 8b + 15$. Let $u$ be the number of positive integers $n$ with $1 \leq n \leq 337$ such that $\gcd(n, 20) = 1$. Let $d$ be the smallest integer with $4 \leq d \leq u$ s... | 8 | graphs = [
Graph(
let={
"_n": Const(6),
"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=21)), Geq(left=Var(n... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"LIN_FORM",
"C4"
] | 9ecaa2 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"C4",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 0.059 | 2026-02-08T15:40:16.855765Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T15:40:16.915125Z"
} | 780cb7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3402
},
"timestamp": "2026-02-16T11:14:03.632Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e9a079 | modular_sum_quadratic_residues_v1_1918700295_600 | Let $T$ be the set of all integers $t$ such that $18 \leq t \leq 874$ and $t = 10a + 8b$ for some positive integers $a \leq 57$ and $b \leq 38$. Let $N$ be the number of elements in $T$. Determine the largest prime number $p$ such that $2 \leq p \leq N$. Compute $\frac{p(p-1)}{4}$, multiply the result by $19385$, and f... | 51,270 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T03:20:47.431309Z | {
"verified": true,
"answer": 51270,
"timestamp": "2026-02-08T03:20:47.433580Z"
} | adff2e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 7510
},
"timestamp": "2026-02-10T13:16:46.093Z",
"answer": 29657
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
d9e6c6 | nt_count_intersection_v1_458359167_1236 | Let $N = 100000$. Let $a = 5$ and let
$$
b = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function.
Determine the number of positive integers $n \leq N$ such that $5$ divides $n$ and $\gcd(n, b) = 1$. | 6,667 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(5),
"b": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), ... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_intersection_v1 | null | 4 | 0 | [
"K2"
] | 1 | 5.731 | 2026-02-08T04:30:39.035312Z | {
"verified": true,
"answer": 6667,
"timestamp": "2026-02-08T04:30:44.765950Z"
} | 33d424 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1192
},
"timestamp": "2026-02-10T16:54:31.975Z",
"answer": 6667
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
3d35c3 | comb_count_partitions_v1_1470522791_1282 | Let $t$ be a positive integer such that $10 \leq t \leq 60$ and $t = 3a + 7b$ for some positive integers $a \leq 13$ and $b \leq 3$. Let $n$ be the number of such values of $t$. Compute the number of integer partitions of $n$. Then, find the remainder when 14943 times this number is divided by 72578. | 46,695 | graphs = [
Graph(
let={
"_n": Const(72578),
"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=13)), Geq(left=V... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:33:06.348796Z | {
"verified": true,
"answer": 46695,
"timestamp": "2026-02-08T13:33:06.351345Z"
} | 6a615b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2946
},
"timestamp": "2026-02-24T18:42:34.960Z",
"answer": 46695
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c8d017 | lin_form_endings_v1_124444284_2564 | Let $a_{\text{coeff}} = 15$, $b_{\text{coeff}} = 6$, $A_{\text{val}} = 27$, and $B_{\text{val}} = 36$. Let $g_{\text{step}} = \gcd(a_{\text{coeff}}, b_{\text{coeff}})$. Define
$$
a_p = \left\lfloor \frac{a_{\text{coeff}}}{g_{\text{step}}} \right\rfloor
\quad\text{and}\quad
b_p = \left\lfloor \frac{b_{\text{coeff}}}{g_{... | 64,554 | graphs = [
Graph(
let={
"a_coeff": Const(15),
"b_coeff": Const(6),
"A_val": Const(27),
"B_val": Const(36),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:45:43.714254Z | {
"verified": true,
"answer": 64554,
"timestamp": "2026-02-08T04:45:43.716432Z"
} | 25e52e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 379,
"completion_tokens": 617
},
"timestamp": "2026-02-11T22:03:01.074Z",
"answer": 64554
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
cad666_n | geo_count_lattice_triangle_v1_601307018_3250 | A game show awards points using the formula $44121T \bmod 90760$, where $T$ is computed from three challenges. First, a contestant calculates $R = |120 \cdot 100 - 31 \cdot 9|$. Next, they compute $S$ as the sum of three GCDs: the GCD of 9 and the minimal perimeter of a rectangle with area 3600 and positive integer sid... | 20,459 | GEOM | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"B3_DIFF",
"B3"
] | 69b567 | geo_count_lattice_triangle_v1 | null | 6 | null | [
"B3",
"B3_DIFF",
"BINOMIAL_ALTERNATING"
] | 3 | 0.07 | 2026-03-10T03:47:00.932880Z | null | 2245e3 | cad666 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 1749
},
"timestamp": "2026-03-29T17:16:59.298Z",
"answer": 20459
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
414b24 | comb_binomial_compute_v1_784195855_2315 | Let $n = 14$ and $k = 6$. Define $r = \binom{n}{k}$. Let $s$ be the sum of $\mu(d)$ over all positive divisors $d$ of 28. Compute the value of $$\sum_{i=s}^{\lfloor \log_{10} |r|
floor} \left( \text{the } i\text{-th digit of } |r| \right) \cdot (i+1)^2 + 65536.$$ | 65,587 | graphs = [
Graph(
let={
"n": Const(14),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(65536),
"Q": Sum(Summation(var="i", start=SumOverDivisors(n=Const(value=28), var='d', expr=MoebiusMu(n=Var(name='d'))), end=Sub(NumDigits(x=... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM"
] | 518e32 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MOBIUS_SUM"
] | 1 | 0.002 | 2026-02-08T05:40:00.794558Z | {
"verified": true,
"answer": 65587,
"timestamp": "2026-02-08T05:40:00.796148Z"
} | e69d61 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 535
},
"timestamp": "2026-02-18T18:18:02.500Z",
"answer": 65587
}
] | 2 | [
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
ba7563 | nt_min_with_divisor_count_v1_1978505735_4441 | Let $ m = 2 $. Define
$$
n = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor.
$$
Let $ D = \displaystyle\sum_{k_1=1}^{3} \phi(k_1) \left\lfloor \frac{n}{k_1} \right\rfloor $, and let $ S $ be the set of all positive integers $ n $ such that $ 1 \le n \le 91809 $ and the number of positive divisors of ... | 24 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k"))))),
"upper": Const(91809),
"div_count": Summation(var="k1", start=Const(1), end=Const(3), expr=Mul(Eule... | NT | null | EXTREMUM | sympy | K2 | [
"K2/K2"
] | ddede2 | nt_min_with_divisor_count_v1 | null | 7 | 0 | [
"K2"
] | 1 | 4.534 | 2026-02-08T18:14:51.931434Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T18:14:56.465883Z"
} | 48e68a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 2176
},
"timestamp": "2026-02-18T15:34:52.761Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ac45eb | nt_count_phi_equals_v1_48377204_3143 | Define $u = \sum_{k=1}^{49} \phi(k) \left\lfloor \frac{49}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k = 285$. Compute the number of positive integers $n$ such that $1 \le n \le u$ and $\phi(n) = k$. | 0 | graphs = [
Graph(
let={
"upper": Summation(var="k1", start=Const(1), end=Const(49), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(49), Var("k1"))))),
"k": Const(285),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_phi_equals_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.072 | 2026-02-08T17:12:57.972523Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T17:12:58.044931Z"
} | 95c38f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1967
},
"timestamp": "2026-02-17T21:38:26.253Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8f00da | comb_bell_compute_v1_458359167_536 | Let $ n $ be the number of positive integers $ p $ for which there exists a positive integer $ q $ such that $ p \cdot q = 1260 $, $ \gcd(p, q) = 1 $, and $ p < q $.
Let $ r $ be the $ n $-th Bell number, which counts the number of partitions of a set of $ n $ elements.
Compute the remainder when $ 44121 \cdot r $ is... | 74,850 | graphs = [
Graph(
let={
"_n": Const(81694),
"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=1260)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T03:23:58.073140Z | {
"verified": true,
"answer": 74850,
"timestamp": "2026-02-08T03:23:58.074896Z"
} | c613fd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1721
},
"timestamp": "2026-02-10T14:19:26.752Z",
"answer": 74850
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
bb5c3a | modular_mod_compute_v1_865884756_2042 | Let $n = 14450$ and $a = 13456$. Define $P$ to be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let $m$ be the number of elements in $P$. Compute the remainder when $a$ is divided by $m$, and let $r$ be this remainder. Find the smallest positive integer $k$ such that the ... | 1,080 | graphs = [
Graph(
let={
"_n": Const(14450),
"a": Const(13456),
"m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2'))... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_mod_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T16:29:03.677844Z | {
"verified": true,
"answer": 1080,
"timestamp": "2026-02-08T16:29:03.681113Z"
} | b3b8ee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 2821
},
"timestamp": "2026-02-17T05:12:49.314Z",
"answer": 1080
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
db9bd6 | comb_count_partitions_v1_1218484723_2116 | Let $n$ be the number of elements in the Cartesian product $\{1, 2, \ldots, 6\} \times \{1, 2, \ldots, 7\}$. Let $M = p(n)$, where $p(n)$ denotes the number of integer partitions of $n$. Find the remainder when $76579M$ is divided by $62580$. | 56,306 | graphs = [
Graph(
let={
"_n": Const(62580),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(7)))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(76579), Ref... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_partitions_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-25T03:50:16.913857Z | {
"verified": true,
"answer": 56306,
"timestamp": "2026-02-25T03:50:16.914961Z"
} | bd8ae5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 3096
},
"timestamp": "2026-03-29T03:07:41.406Z",
"answer": 56306
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
8848f8 | nt_sum_divisors_mod_v1_784195855_6232 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 32400$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10589$. | 1,170 | 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(32400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10589)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T08:28:17.569620Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T08:28:17.571602Z"
} | de457b | 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": 1460
},
"timestamp": "2026-02-13T19:28:00.008Z",
"answer": 1170
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
7ff157 | lin_form_endings_v1_151522320_1180 | Let $a = 45$ and $b = 27$. Compute the least common multiple of $a$ and $b$, multiply it by $13503$, and then compute the remainder when this product is divided by $53640$. | 52,785 | graphs = [
Graph(
let={
"a_coeff": Const(45),
"b_coeff": Const(27),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(13503),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(53640),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:49:53.638263Z | {
"verified": true,
"answer": 52785,
"timestamp": "2026-02-08T03:49:53.639189Z"
} | 68d1cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 625
},
"timestamp": "2026-02-10T15:52:04.558Z",
"answer": 52785
},
{
"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": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
fe7ad2 | comb_count_partitions_v1_865884756_1095 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 293$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{7}$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $24541 \cdot p(n)$ is divided by $50385$. | 1,128 | graphs = [
Graph(
let={
"_n": Const(293),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | COMB | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | comb_count_partitions_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T15:47:16.937504Z | {
"verified": true,
"answer": 1128,
"timestamp": "2026-02-08T15:47:16.939471Z"
} | a3660a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2012
},
"timestamp": "2026-02-16T13:33:20.753Z",
"answer": 1128
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bf649a | comb_count_partitions_v1_1820931509_322 | Let $n$ be the number of ordered pairs $(a,b)$ such that $a$ is an integer with $1 \le a \le 2$ and $b$ is an integer with $1 \le b \le 19$. Compute the number of integer partitions of $n$. | 26,015 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(19)))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_partitions_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T11:29:21.517518Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T11:29:21.520549Z"
} | 99b0e6 | 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": 1022
},
"timestamp": "2026-02-24T13:58:24.938Z",
"answer": 26015
},
{
"... | 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": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
c04237 | sequence_lucas_compute_v1_865884756_5137 | Let $n$ be the sum of all positive integers $n_1$ such that $1 \leq n_1 \leq 22$ and $n_1$ is divisible by $22$. Compute the $n$-th Lucas number. | 39,603 | graphs = [
Graph(
let={
"_n": Const(22),
"n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(22)), Eq(Mod(value=Var("n1"), modulus=Ref("_n")), Const(0))))),
"result": Lucas(arg=Ref(name='n')),
},
goa... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T18:23:21.084021Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T18:23:21.085430Z"
} | c0b63d | 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": 813
},
"timestamp": "2026-02-18T16:39:26.499Z",
"answer": 39603
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f45084_n | comb_count_permutations_fixed_v1_601307018_4008 | A theater group has $n$ actors, where $n = 2^0 + 2^1 + 2^2$. They are rehearsing a scene where exactly $2$ actors will play their own roles, and the remaining $n-2$ actors must each play someone else's role (no one plays their own). In how many ways can the roles be assigned so that the $2$ fixed actors are correctly c... | 924 | COMB | null | COUNT | sympy | HALFPLANE_COUNT | [
"SUM_GEOM"
] | 04214c | comb_count_permutations_fixed_v1 | null | 3 | null | [
"HALFPLANE_COUNT",
"SUM_GEOM"
] | 2 | 0.238 | 2026-03-10T04:37:11.180140Z | null | d42e10 | f45084 | narrative | 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": 879
},
"timestamp": "2026-03-29T18:16:24.222Z",
"answer": 924
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
981841 | modular_min_linear_v1_677425708_896 | Let $a = 15757$, $b = 15181$, and $m = 32612$. Find the smallest integer $x$ such that $x \geq \phi(\phi(1))$, $x \leq m$, and
$$
a x \equiv b \pmod{m}.
$$ | 12,833 | graphs = [
Graph(
let={
"a": Const(15757),
"b": Const(15181),
"m": Const(32612),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=EulerPhi(n=Const(1)))), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), m... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | modular_min_linear_v1 | null | 6 | 0 | [
"ONE_PHI_1"
] | 1 | 1.311 | 2026-02-08T03:50:07.902862Z | {
"verified": true,
"answer": 12833,
"timestamp": "2026-02-08T03:50:09.214282Z"
} | e05d22 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1868
},
"timestamp": "2026-02-09T13:52:35.745Z",
"answer": 12833
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
991be2 | geo_count_lattice_triangle_v1_1218484723_3560 | Let $N = |200 \cdot 128 + 196 \cdot (0 - 128)|$, let $M = \gcd(200, 128) + \gcd(|196 - 200|, |128 - 128|) + \gcd(|0 - 196|, |0 - 128|)$, and let $R = \frac{N + 2 - M}{2}$. Find the remainder when $16002R$ is divided by $62057$. | 12,850 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=200), Const(value=128)), Mul(Const(value=196), Sub(left=Const(value=0), right=Const(value=128))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=200)), b=Abs(arg=Const(value=128))), GCD(a=Abs(arg=Sub(left=Const(value=196), r... | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 3 | 0 | null | null | 0.004 | 2026-02-25T05:11:07.331986Z | {
"verified": true,
"answer": 12850,
"timestamp": "2026-02-25T05:11:07.336127Z"
} | d587ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 999
},
"timestamp": "2026-03-29T11:00:22.443Z",
"answer": 12850
},
{
"i... | 1 | [] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||||
fc0b5c | modular_mod_compute_v1_1742523217_3112 | Let $a$ be the number of integers $t$ such that $7 \leq t \leq 3343$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 607$, $1 \leq b' \leq 154$, and $t = 5a' + 2b'$. Compute the remainder when $a$ is divided by $59049$. | 3,333 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=607)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:39:35.232729Z | {
"verified": true,
"answer": 3333,
"timestamp": "2026-02-08T05:39:35.235055Z"
} | a2e815 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 4841
},
"timestamp": "2026-02-12T12:29:06.370Z",
"answer": 3333
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c6b9ad | diophantine_fbi2_min_v1_1520064083_661 | Let $n = 121$ and $k = 12$. Consider all ordered pairs of positive integers $(x, y)$ such that $xy = 121$. Let $s$ be the sum $x + y$ for such a pair. Define $u$ to be the minimum value of $s$ over all such pairs. Find the smallest divisor $d$ of 12 such that $4 \leq d \leq u$ and $\frac{12}{d} \geq 2$. Let this value ... | 54,796 | graphs = [
Graph(
let={
"_n": Const(121),
"k": Const(12),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ex... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T03:31:41.885199Z | {
"verified": true,
"answer": 54796,
"timestamp": "2026-02-08T03:31:41.894176Z"
} | 46dcaf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 891
},
"timestamp": "2026-02-10T14:56:20.883Z",
"answer": 54896
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
d72217 | comb_factorial_compute_v1_124444284_1097 | Let $n$ be the largest prime number less than or equal to 9. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(9),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T03:41:05.686315Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T03:41:05.687328Z"
} | 9ceec2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 182
},
"timestamp": "2026-02-10T02:40:58.466Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status":... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
6600ed | comb_sum_binomial_row_v1_124444284_2207 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Let $b$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 2829750$, and $\gcd(p, q) = 1$. Compute $a^b$. | 65,536 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T04:31:28.420738Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T04:31:28.422982Z"
} | 06bc9f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1565
},
"timestamp": "2026-02-10T16:58:49.495Z",
"answer": 65536
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
c754ee | comb_binomial_compute_v1_655260480_5373 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 64$. Compute $\binom{n}{9}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(64),
"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")))),
... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T18:26:53.861048Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T18:26:53.862970Z"
} | c9a1c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 32768
},
"timestamp": "2026-02-25T00:05:25.510Z",
"answer": null
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||
f0c43c | modular_count_residue_v1_397696148_2801 | Let $m$ be the smallest divisor of $175$ that is at least $2$. Let $\text{upper} = 88804$. Determine the number of positive integers $n \leq \text{upper}$ such that $n \equiv 0 \pmod{m}$. Compute this number. | 17,760 | graphs = [
Graph(
let={
"upper": Const(88804),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(175))))),
"r": Const(0),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditi... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.56 | 2026-02-08T13:33:48.367481Z | {
"verified": true,
"answer": 17760,
"timestamp": "2026-02-08T13:33:51.926991Z"
} | 9e409b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 265
},
"timestamp": "2026-02-16T05:14:48.147Z",
"answer": 17760
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
51ce27 | nt_count_primes_v1_865884756_4907 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $P$. Let $N$ be the set of all prime numbers $n$ such that $L \leq n \leq 32768$. Compute the number of elements in $N$. Find the value o... | 3,512 | graphs = [
Graph(
let={
"upper": Const(32768),
"result": CountOverSet(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'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.747 | 2026-02-08T18:16:59.714411Z | {
"verified": true,
"answer": 3512,
"timestamp": "2026-02-08T18:17:00.461286Z"
} | c3aec6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1954
},
"timestamp": "2026-02-18T15:50:40.176Z",
"answer": 3512
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9f1948 | nt_count_digit_sum_v1_677425708_535 | Let $r$ be the number of positive integers $n$ with $1 \leq n \leq 54289$ such that the sum of the digits of $n$ is $27$. Let $c$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 2829124$. Compute the value of $$\sum_{i=0}^{d-1} d_i (i+1)^2 + c,$$ where $d$ is the number of d... | 3,484 | graphs = [
Graph(
let={
"upper": Const(54289),
"target_sum": Const(27),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
"_c": MinOverSet(set... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 8e300c | nt_count_digit_sum_v1 | digits_weighted_mod | 4 | 0 | [
"B3"
] | 1 | 1.951 | 2026-02-08T03:35:26.090948Z | {
"verified": true,
"answer": 3484,
"timestamp": "2026-02-08T03:35:28.042408Z"
} | 8ffee5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 4494
},
"timestamp": "2026-02-10T05:25:29.189Z",
"answer": 3484
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5ba97e | nt_min_crt_v1_677425708_3546 | Let $m = 4$ and $k = 9$. Define $a = \phi(2)$ and let $b$ be the largest prime number $n$ such that $2 \leq n \leq 9$. Let $\text{upper}$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 12$. Determine the smallest positive integer $n$ such that $1 \leq n \leq \text{up... | 25 | graphs = [
Graph(
let={
"m": Const(4),
"k": Const(9),
"a": EulerPhi(n=Const(2)),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"upper": MaxOverSet(set=MapOverSet... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"MAX_PRIME_BELOW",
"ONE_PHI_2",
"B1"
] | 38ea64 | nt_min_crt_v1 | null | 6 | 0 | [
"B1",
"COUNT_PRIMES",
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 4 | 0.083 | 2026-02-08T05:48:56.388884Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T05:48:56.471953Z"
} | c531a7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 589
},
"timestamp": "2026-02-18T19:59:35.797Z",
"answer": 25
}
] | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
6748ad | nt_lcm_compute_v1_677425708_2977 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1575025$. Let $a$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all integers $t$ with $5 \leq t \leq 1564$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 276$, $1 \leq b \leq 368$,... | 877 | graphs = [
Graph(
let={
"_n": Const(11),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1575025)))), expr=Sum(Var("x"), Var("y"))))... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_lcm_compute_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T05:24:46.692663Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T05:24:46.696326Z"
} | 3bfdee | 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": 5126
},
"timestamp": "2026-02-12T08:48:48.132Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1e5ef0 | nt_sum_totient_over_divisors_v1_238844314_832 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 29561$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $N$ be the number of elements in $S$. Define
$$
R = \sum_{d \mid N} \phi(d),
$$
where $\phi$ denotes Euler's totient function. Find the remainder when $44121 \cdot R$ is di... | 8,560 | graphs = [
Graph(
let={
"_n": Const(29561),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.004 | 2026-02-08T13:38:40.145011Z | {
"verified": true,
"answer": 8560,
"timestamp": "2026-02-08T13:38:40.149068Z"
} | a1a4c6 | 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": 1331
},
"timestamp": "2026-02-15T18:37:42.225Z",
"answer": 8560
},
{... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1f5280 | diophantine_product_count_v1_677425708_3003 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 396900$. For each such pair, compute $x + y$, and let $k$ be the smallest value among all such sums.
Now consider the number of positive integers $x$ such that $1 \le x \le 101$, $x$ divides $k$, and $\frac{k}{x} \le 101$. Compute thi... | 16 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(1... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 11.764 | 2026-02-08T05:25:46.627195Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T05:25:58.391469Z"
} | 4f6e30 | 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": 3259
},
"timestamp": "2026-02-12T08:51:20.270Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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