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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
961a27 | comb_catalan_compute_v1_1520064083_264 | Let $n$ be the number of integers $t$ with $7 \leq t \leq 20$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Compute the $n$-th Catalan number. | 16,796 | 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=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T03:09:04.881816Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:09:04.886161Z"
} | 9c1394 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1153
},
"timestamp": "2026-02-10T13:35:33.129Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
082270 | algebra_quadratic_discriminant_v1_124444284_5524 | Let $a = -7$ and $b = -7$. Let $c$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 840$, $\gcd(p, q) = 1$, and $p < q$. Compute $b^2 - 4ac$. | 273 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-7),
"b": Const(-7),
"c": 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... | NT | null | COMPUTE | sympy | B3 | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.005 | 2026-02-08T06:40:07.477055Z | {
"verified": true,
"answer": 273,
"timestamp": "2026-02-08T06:40:07.481844Z"
} | d98ec6 | 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": 1645
},
"timestamp": "2026-02-13T03:31:53.953Z",
"answer": 273
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e3ac5c | nt_lcm_compute_v1_1978505735_3594 | Let $a = 2985$. Let $b$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 35$ and $1 \leq j \leq 59$. Compute the least common multiple of $a$ and $b$. Let $Q$ be the remainder when $44121$ times this least common multiple is divided by $50959$. Find the value of $Q$. | 22,944 | graphs = [
Graph(
let={
"a": Const(2985),
"b": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(59)))),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(Const(44121), Ref(... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_lcm_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T17:43:35.620749Z | {
"verified": true,
"answer": 22944,
"timestamp": "2026-02-08T17:43:35.622766Z"
} | afdacf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1828
},
"timestamp": "2026-02-18T07:27:37.654Z",
"answer": 22944
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
25842b | antilemma_count_primes_v1_548369836_417 | Let $x$ be the number of prime numbers $n$ such that $2 \leq n \leq d$, where $d$ is the smallest divisor of 2053087811 that is at least 2. Compute the value of
$$
\sum_{i=0}^{\text{NumDigits}(x)-1} \left( \text{digit}_i(x) \cdot (i+1)^2 \right) + 43264,
$$
where $\text{digit}_i(x)$ denotes the $i$th digit of $x$ (star... | 43,287 | graphs = [
Graph(
let={
"_n": Const(2),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2053087811)))))), I... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_PRIMES",
"COUNT_PRIMES"
] | 7deaba | antilemma_count_primes_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T02:54:15.633915Z | {
"verified": true,
"answer": 43287,
"timestamp": "2026-02-08T02:54:15.635924Z"
} | 320453 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 458
},
"timestamp": "2026-02-09T05:57:25.798Z",
"answer": 43284
},... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"stat... | {
"lo": -1.8,
"mid": 3.87,
"hi": 9.6
} | ||
c7d7cf | modular_sum_quadratic_residues_v1_1520064083_880 | Let $p$ be the number of integers $t$ such that $8 \leq t \leq 404$ and there exist positive integers $a \leq 46$ and $b \leq 58$ satisfying $t = 5a + 3b$. Define $r = \frac{p(p-1)}{4}$. Find the remainder when $44121 \cdot r$ is divided by $87616$. | 26,077 | graphs = [
Graph(
let={
"_n": Const(87616),
"p": 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=46)), Geq(left=V... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:38:57.098546Z | {
"verified": true,
"answer": 26077,
"timestamp": "2026-02-08T03:38:57.100306Z"
} | f09845 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 5906
},
"timestamp": "2026-02-10T14:01:16.146Z",
"answer": 51490
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
0654ea | comb_binomial_compute_v1_784195855_5338 | Let $n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $43681 - \binom{n}{8}$. | 37,246 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sub(Const(43681), Ref("result")),
},
goa... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T07:49:48.056085Z | {
"verified": true,
"answer": 37246,
"timestamp": "2026-02-08T07:49:48.057087Z"
} | 02a854 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 537
},
"timestamp": "2026-02-15T19:05:13.436Z",
"answer": 37246
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
033e39 | antilemma_k2_v1_1874849503_402 | Compute the value of
$$
\sum_{k=1}^{306} \phi(k) \left\lfloor \frac{306}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 46,971 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(306), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(306), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:01:21.800502Z | {
"verified": true,
"answer": 46971,
"timestamp": "2026-02-08T13:01:21.801132Z"
} | f7971c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2885
},
"timestamp": "2026-02-09T16:29:26.313Z",
"answer": 46971
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
f23651 | nt_count_digit_sum_v1_784195855_9973 | Let $\text{upper}$ be the number of positive integers $t$ such that $56 \leq t \leq 30122$ and there exist positive integers $a \leq 857$ and $b \leq 807$ satisfying $t = 21a + 15b + 20$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and the sum of the decimal digits ... | 1,274 | graphs = [
Graph(
let={
"upper": 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=857)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.376 | 2026-02-08T17:21:03.058169Z | {
"verified": true,
"answer": 1274,
"timestamp": "2026-02-08T17:21:03.434431Z"
} | ccfc5e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 5250
},
"timestamp": "2026-02-18T00:45:53.303Z",
"answer": 1274
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cc88ba | comb_sum_binomial_row_v1_677425708_1898 | Compute $2^n$, where $$n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$$ and $\phi(k)$ denotes Euler's totient function. | 32,768 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | K2 | [
"K2"
] | 6897ab | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T04:37:55.042011Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T04:37:55.042772Z"
} | 35816e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 507
},
"timestamp": "2026-02-10T02:44:32.291Z",
"answer": 32768
},
{
"i... | 2 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
66a7ec | lte_diff_endings_v1_1520064083_3042 | Let $a = 13$ and $b = 5$. Define $d = a - b$. Let $v$ be the largest integer $k$ such that $2^k$ divides $d$. Let $T = 14$ and define $e = T - v$. Compute $2^e$. | 2,048 | graphs = [
Graph(
let={
"a_val": Const(13),
"b_val": Const(5),
"p_val": Const(2),
"T_val": Const(14),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0 | 2026-02-08T05:25:50.445619Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T05:25:50.445941Z"
} | f57ad5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 162
},
"timestamp": "2026-02-18T16:21:12.959Z",
"answer": 2048
}
] | 2 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
aee9da | comb_factorial_compute_v1_1470522791_721 | Let $j$ be a nonnegative integer such that $0 \le j \le 8706$. Determine the number of values of $j$ for which the binomial coefficient $\binom{8706}{j}$ is odd.
Let $n$ be this number. Define $r = n!$. Compute the remainder when $78933 \cdot r$ is divided by $57074$. | 18,172 | graphs = [
Graph(
let={
"_n": Const(8706),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8706)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T13:12:26.370459Z | {
"verified": true,
"answer": 18172,
"timestamp": "2026-02-08T13:12:26.371921Z"
} | a8b258 | 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": 1697
},
"timestamp": "2026-02-24T17:25:01.860Z",
"answer": 18172
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
3beec0 | alg_poly_preperiod_count_v1_601307018_3720 | Let $N = a^2 + 13 \bmod 79$, $M = N^2 + 13 \bmod 79$, $R = M^2 + 13 \bmod 79$, $S = R^2 + 13 \bmod 79$, and $T = S^2 + 13 \bmod 79$. Find the number of non-negative integers $a$ with $0 \leq a \leq 111073$ such that $T = M$, $R \neq M$, and $S \neq M$. | 11,248 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(13)), modulus=Const(79)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(13)), modulus=Const(79)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(13)), modulus=Const(79)),
"p4... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.022 | 2026-03-10T04:18:41.751156Z | {
"verified": true,
"answer": 11248,
"timestamp": "2026-03-10T04:18:41.773215Z"
} | 806e88 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:50:33.920Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
34d078 | antilemma_sum_equals_v1_1520064083_2644 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 5$, $1 \leq j \leq 6$, and $i + j = 7$. Let $Q$ be the remainder when $32537 \cdot x$ is divided by $50046$. Compute $Q$. | 12,547 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(6))))),
"_c": Co... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.047 | 2026-02-08T04:54:07.125586Z | {
"verified": true,
"answer": 12547,
"timestamp": "2026-02-08T04:54:07.172360Z"
} | b38ab5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 497
},
"timestamp": "2026-02-11T22:25:29.401Z",
"answer": 12447
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
18efb2 | nt_gcd_compute_v1_548369836_17 | Let $p = 83$. Define $c$ to be the number of prime factors of $p$ counted with multiplicity. Let $a_1 = 82$ and $b_1 = 79$. Define $t$ to be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(a_1, b_1)$, where $\mu$ denotes the M\"obius function. Let $a = 275755c$ and $b = 606661t$. Compute $\gcd(a, b)$. | 55,151 | graphs = [
Graph(
let={
"p": Const(83),
"c": BigOmega(n=Ref(name='p')),
"a1": Const(82),
"b1": Const(79),
"t": SumOverDivisors(n=GCD(a=Ref(name='a1'), b=Ref(name='b1')), var='d', expr=MoebiusMu(n=Var(name='d'))),
"a": Mul(Const(275755),... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"BIG_OMEGA_ONE"
] | b31cc9 | nt_gcd_compute_v1 | null | 3 | 2 | [
"BIG_OMEGA_ONE",
"MOBIUS_COPRIME"
] | 2 | 0.003 | 2026-02-08T02:42:48.938330Z | {
"verified": true,
"answer": 55151,
"timestamp": "2026-02-08T02:42:48.941269Z"
} | ed8672 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 4555
},
"timestamp": "2026-02-08T19:43:05.053Z",
"answer": 55151
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -4.84,
"mid": -1.65,
"hi": 1.93
} | ||
7cea01 | antilemma_sum_factor_cartesian_v1_1918700295_2245 | Let $x$ be the sum of $i \cdot j$ over all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 24$ and $1 \leq j \leq 24$. Let $p$ be the largest prime number less than or equal to $11$. Define $m = |x| \bmod p$.
Compute the $m$-th Bell number, where the Bell number $B_m$ is the number of partitions of a set of $m$ ... | 21,147 | graphs = [
Graph(
let={
"_n": Const(11),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(24)), right=IntegerRange(start=Const(1), end=Const(24)))), expr=M... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"SUM_FACTOR_CARTESIAN"
] | d5a4fd | antilemma_sum_factor_cartesian_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T07:46:19.934773Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T07:46:19.936729Z"
} | 15ea94 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 489
},
"timestamp": "2026-02-20T05:33:24.246Z",
"answer": 137638
}
] | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
196aa9 | algebra_vieta_sum_v1_458359167_1564 | Let $C$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying
\begin{itemize}
\item $1\le a\le 145$,
\item $1\le b\le 128$,
\item $9\le t\le 1220$,
\item $t = 4a + 5b$.
\end{itemize}
Consider the quartic polynomial
$$P(x) = x^{4} + 3x^{3} - 84x^{2} - 20x + C.$$
Let $R$ be the pro... | 62,276 | graphs = [
Graph(
let={
"_n": Const(81721),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=4)), Mul(Const(value=3), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=-84), Pow(base=Var(name='x'), ... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_vieta_sum_v1 | null | 8 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T04:45:26.155696Z | {
"verified": true,
"answer": 62276,
"timestamp": "2026-02-08T04:45:26.165356Z"
} | 20cc82 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 316,
"completion_tokens": 7602
},
"timestamp": "2026-02-11T21:52:40.576Z",
"answer": 57529
},
{
... | 0 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": 3.78,
"mid": 6.08,
"hi": 9.16
} | ||
482fcf | antilemma_k3_v1_898971024_409 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $80686$. Let $Q$ be the remainder when $x^2 + 16x + 5041$ is divided by $86490$. Compute $Q$. | 40,473 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=80686), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(5041),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(16), Ref("x")), Ref("_c")), modulus=Const(86490)),
},
goal=Ref("Q"),
)... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:26:49.312119Z | {
"verified": true,
"answer": 40473,
"timestamp": "2026-02-08T15:26:49.312722Z"
} | 5b395f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 3600
},
"timestamp": "2026-02-16T06:09:54.076Z",
"answer": 40473
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c14141 | nt_max_prime_below_v1_1440796553_1209 | Let $n = 200$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$, and let $M$ be the maximum value of $xy$ over all such pairs. Let $Q$ be the set of all prime numbers $p$ such that $2 \leq p \leq M$. Determine the value of the largest element in $Q$. | 9,973 | graphs = [
Graph(
let={
"_n": Const(200),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_max_prime_below_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.288 | 2026-02-08T12:14:23.067060Z | {
"verified": true,
"answer": 9973,
"timestamp": "2026-02-08T12:14:23.355218Z"
} | 11c308 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1743
},
"timestamp": "2026-02-15T18:25:03.480Z",
"answer": 9973
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
4bd12d | alg_poly_preperiod_count_v1_1218484723_5609 | For a non-negative integer $a$, define $N = (2a^3 - a^2 - 3a + 5) \bmod 61$, $M = (2N^3 - N^2 - 3N + 5) \bmod 61$, and $R = (2M^3 - M^2 - 3M + 5) \bmod 61$. Find the number of integers $a$ with $0 \leq a \leq 52215$ such that $R = N$ and $M \neq N$. | 6,848 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-1), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(5)), modulus=Const(61)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-1), Pow(Ref("p1"), Const(2))),... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.024 | 2026-02-25T07:08:06.710170Z | {
"verified": true,
"answer": 6848,
"timestamp": "2026-02-25T07:08:06.734142Z"
} | 2b3313 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 18823
},
"timestamp": "2026-03-29T21:56:49.873Z",
"answer": 9416
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
02cbf5 | nt_count_intersection_v1_2051736721_2775 | Let $N = 20000$. Let $a = 9$. Let $t$ range over all integers from 11 to 149, inclusive, such that $t = 4a + 7b$ for some integers $a$, $b$ with $1 \le a \le 18$ and $1 \le b \le 11$. Let $n$ be the number of such values of $t$. Let $S$ be the set of all pairs of positive integers $(x, y)$ such that $xy = n$. Let $b$ b... | 1,010 | graphs = [
Graph(
let={
"N": Const(20000),
"a": Const(9),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=Sol... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | nt_count_intersection_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.896 | 2026-02-08T16:54:35.254191Z | {
"verified": true,
"answer": 1010,
"timestamp": "2026-02-08T16:54:36.149924Z"
} | 003571 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 4855
},
"timestamp": "2026-02-17T14:49:47.854Z",
"answer": 1010
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
84b2bb | sequence_lucas_compute_v1_1439011603_1214 | Let $m = 12$ and let $p$ be the largest prime number at most $m$. Let $T$ be the set of integers $t$ with $19 \leq t \leq 200$ that can be expressed as $3a + 2b + 14$ for positive integers $a \leq 28$ and $b \leq 51$. Let $n$ be the number of positive integers $k$ at most $|T|$ such that the Fibonacci number $F_k$ is d... | 5,778 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_m")), IsPrime(Var("n1"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(1)), Le... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_FIB_DIVISIBLE",
"LIN_FORM/COUNT_FIB_DIVISIBLE"
] | 14e870 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.006 | 2026-02-08T15:58:46.104869Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T15:58:46.110672Z"
} | 0efc0b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 2351
},
"timestamp": "2026-02-16T18:34:09.421Z",
"answer": 5778
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
285d1e | sequence_count_fib_divisible_v1_349078426_1985 | Let $A$ be the number of integers $t$ with $9 \leq t \leq 932$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 32$, $1 \leq b \leq 354$, and $t = 7a + 2b$. Let $d$ be the number of positive integers $n$ with $1 \leq n \leq 9$ such that the sum of the decimal digits of $n$ is even. Determine... | 153 | graphs = [
Graph(
let={
"_n": Const(9),
"upper": 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=32)), Geq(left=V... | NT | null | COUNT | sympy | C4 | [
"LIN_FORM",
"L3B"
] | f85b0e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"C4",
"L3B",
"LIN_FORM"
] | 3 | 0.159 | 2026-02-08T14:02:33.115357Z | {
"verified": true,
"answer": 153,
"timestamp": "2026-02-08T14:02:33.274551Z"
} | 596222 | 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": 5646
},
"timestamp": "2026-02-15T23:17:52.937Z",
"answer": 153
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
49d4bf | algebra_poly_eval_v1_458359167_4012 | Let $t = 8$. Let $k$ be the number of positive integers $j$ such that $1 \le j \le 2$ and $j^2 \le 4$. Compute the value of
$$
\frac{25t^3 + 15t^k - 38t - 14}{47}.
$$Then let $Q$ be the remainder when $13999$ times this value is divided by $57266$. Find $Q$. | 52,360 | graphs = [
Graph(
let={
"_n": Const(47),
"t": Const(8),
"result": Div(Sum(Mul(Const(25), Pow(Ref("t"), Const(3))), Mul(Const(15), Pow(Ref("t"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2)), Leq(Pow(Var("j"), Co... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | algebra_poly_eval_v1 | null | 2 | 0 | [
"C3"
] | 1 | 0.004 | 2026-02-08T11:28:32.008918Z | {
"verified": true,
"answer": 52360,
"timestamp": "2026-02-08T11:28:32.012911Z"
} | fc6bb3 | 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": 1010
},
"timestamp": "2026-02-14T14:29:59.458Z",
"answer": 52360
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8961c5 | nt_count_gcd_equals_v1_397696148_2091 | Let $S$ be the set of all integers $t$ such that $7 \leq t \leq 217$ and there exist integers $a$ and $b$ with $1 \leq a \leq 13$, $1 \leq b \leq 76$, and $t = 5a + 2b$. Let $k$ be the number of elements in $S$. Define $\mathcal{N}$ as the set of all positive integers $n$ such that $1 \leq n \leq 32768$ and $\gcd(n, k)... | 950 | graphs = [
Graph(
let={
"upper": Const(32768),
"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=13)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 4.735 | 2026-02-08T12:57:09.685809Z | {
"verified": true,
"answer": 950,
"timestamp": "2026-02-08T12:57:14.421247Z"
} | 185149 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 4064
},
"timestamp": "2026-02-15T07:43:12.069Z",
"answer": 950
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
eaf13f | modular_count_residue_v1_784195855_4663 | Let $m$ be the number of positive integers $k$ such that $1 \leq k \leq 154$ and $7$ divides $k$. Let $r$ be the number of integers $t$ with $8 \leq t \leq 36$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 3$, $1 \leq b \leq 7$, and $t = 5a + 3b$. Let $N$ be the number of positive integers $n$ su... | 29,990 | graphs = [
Graph(
let={
"_m": Const(154),
"_n": Const(44121),
"upper": Const(63504),
"m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_m")), Divides(divisor=Const(7), dividend=Var("k"))), domain='positi... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"C2"
] | c556ae | modular_count_residue_v1 | null | 5 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 4.571 | 2026-02-08T07:14:47.087897Z | {
"verified": true,
"answer": 29990,
"timestamp": "2026-02-08T07:14:51.658545Z"
} | 17bd53 | 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": 2738
},
"timestamp": "2026-02-13T09:29:15.210Z",
"answer": 29990
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIA... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a285f1 | antilemma_product_of_sums_v1_1742523217_167 | Let $S_1 = \sum_{k=1}^{15} k$. Let $S_2$ be the sum of all values $k$ where $(k, j)$ ranges over all ordered pairs of positive integers with $1 \leq k \leq 14$ and $1 \leq j \leq 4$. Define $x = S_1 \cdot S_2$. Compute the remainder when $35955 \times x$ is divided by $73727$. | 69,794 | graphs = [
Graph(
let={
"S1": Summation(var="k", start=Const(1), end=Const(15), expr=Var("k")),
"S2": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(14)), ri... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 2 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T02:54:38.586605Z | {
"verified": true,
"answer": 69794,
"timestamp": "2026-02-08T02:54:38.587123Z"
} | c1ab14 | 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": 2652
},
"timestamp": "2026-02-09T14:26:42.194Z",
"answer": 69794
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
0a2493 | nt_count_coprime_v1_677425708_547 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 18412681$. For each such pair, compute $x + y$, and let $n$ be the minimum value of $x + y$ over all such pairs. Let $k$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 8582$ and the binomial coefficient $\binom{n}{... | 5,202 | 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(18412681)))), expr=Sum(Var("x"), Var("y")))),
"upper": Cons... | NT | null | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | nt_count_coprime_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.783 | 2026-02-08T03:35:51.940761Z | {
"verified": true,
"answer": 5202,
"timestamp": "2026-02-08T03:35:52.723785Z"
} | 02198a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 4053
},
"timestamp": "2026-02-08T20:45:02.188Z",
"answer": 5202
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
},
{
"lemma": "V8_S... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
9b4f5a | comb_count_permutations_fixed_v1_809748730_1019 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 8$. Compute $\binom{n}{3} \cdot !(n-3)$, where $!k$ denotes the number of derangements of $k$ elements. | 315 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"k": Const(3),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=... | NT | COMB | COUNT | sympy | BINOMIAL_ALTERNATING | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"MAX_PRIME_BELOW"
] | 2 | 0.009 | 2026-02-08T12:00:15.207635Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T12:00:15.216564Z"
} | 75615f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 979
},
"timestamp": "2026-02-16T03:29:20.760Z",
"answer": 315
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
da2bda_n | alg_sum_powers_v1_1218484723_6011 | A contractor is designing two different rectangular areas.
First, they must build a rectangular lot of area $5067001$ square units, with integer side lengths. Among all such rectangles, let $M$ be the smallest possible perimeter divided by $2$ (that is, the minimum of $x + y$ over integer sides $x,y$ with $xy = 506700... | 4,679 | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN/B1",
"B3/POLY3_MIN"
] | 3f8feb | alg_sum_powers_v1 | negation_mod | 6 | null | [
"B1",
"B3",
"POLY3_MIN"
] | 3 | 0.019 | 2026-02-25T07:36:53.017253Z | null | 8e92ec | da2bda | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 357,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T00:32:18.661Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
6e7505 | nt_num_divisors_compute_v1_124444284_3698 | Let $n$ be the number of integers $t$ such that $24 \leq t \leq 4112$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 213$, $1 \leq b \leq 113$, and $t = 14a + 10b$. Let $\text{result}$ be the number of positive divisors of $n$. Find the remainder when $44121 \cdot \text{result}$ is divided by $84895$... | 6,694 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=213)), Geq(left=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T05:32:52.276158Z | {
"verified": true,
"answer": 6694,
"timestamp": "2026-02-08T05:32:52.279117Z"
} | ec7497 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 6882
},
"timestamp": "2026-02-12T10:34:02.059Z",
"answer": 6694
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a43792 | nt_count_phi_equals_v1_717093673_3674 | Let $\text{upper} = 3249$ and $k = 1304$. Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq 3249$ and $\phi(n) = 1304$, where $\phi$ denotes Euler's totient function. Let $P$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 198$... | 9,799 | graphs = [
Graph(
let={
"upper": Const(3249),
"k": Const(1304),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Sub(MaxOverSet(set=MapOverSet(... | NT | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | nt_count_phi_equals_v1 | negation_mod | 7 | 0 | [
"B1"
] | 1 | 0.239 | 2026-02-08T17:45:43.282084Z | {
"verified": true,
"answer": 9799,
"timestamp": "2026-02-08T17:45:43.521519Z"
} | fe3748 | 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": 2107
},
"timestamp": "2026-02-18T07:15:55.489Z",
"answer": 9799
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9f2b3f | comb_catalan_compute_v1_1218484723_2345 | Let $n = \sum_{k=1}^{4} k$. Compute the $n$-th Catalan number $C_n$. | 16,796 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Catalan(Ref("n")),
},
goal=Ref("result"),
)
] | COMB | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_catalan_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-25T04:09:47.502536Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-25T04:09:47.503222Z"
} | fe6438 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 224
},
"timestamp": "2026-03-29T04:14:02.561Z",
"answer": 16796
},
{
"i... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
547c69 | comb_binomial_compute_v1_1125832087_602 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 441000$, $\gcd(p, q) = 1$, and $p < q$. Compute $\binom{16}{k}$. | 12,870 | graphs = [
Graph(
let={
"n": Const(16),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=441000)), Eq(left=GCD(a=Var(name='p'), b=Var(name... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_binomial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T03:10:03.124420Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-02-08T03:10:03.125583Z"
} | b319d3 | 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": 2850
},
"timestamp": "2026-02-10T13:15:41.259Z",
"answer": 12870
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0e2a40 | sequence_lucas_compute_v1_677425708_460 | Let $c = 4$. Define $\mathcal{T}$ as the set of all ordered pairs $(i,j)$ with $1 \leq i \leq 2$, $1 \leq j \leq 3$, and $i + j = c$. Let $n_0$ be the number of elements in $\mathcal{T}$. Let $m_0 = \sum_{k=1}^{7} k$. Define $n$ to be the largest prime number satisfying $n_0 \leq n \leq m_0$. Compute the $n$-th Lucas n... | 64,079 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Summation(var="k", start=Const(1), end=Const(7), expr=Var("k")),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_c")), domain=CartesianProduct(left=Inte... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/COUNT_SUM_EQUALS/MAX_PRIME_BELOW"
] | c64e9b | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.012 | 2026-02-08T03:33:15.451082Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T03:33:15.462986Z"
} | 53c38d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1128
},
"timestamp": "2026-02-08T20:35:58.106Z",
"answer": 64079
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POL... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
bc5514 | modular_inverse_v1_2051736721_1551 | Let $n = 2$. Define $a$ to be the smallest divisor $d$ of $5605027$ such that $d \geq n$. Let $m = 179$. Define $\text{upper}$ to be the number of integers $t$ with $10 \leq t \leq 199$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 22$, $1 \leq b \leq 19$, and $t = 3a + 7b$. Determine the valu... | 149 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(5605027))))),
"m": Const(179),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), conditio... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | modular_inverse_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.027 | 2026-02-08T16:05:45.480516Z | {
"verified": true,
"answer": 149,
"timestamp": "2026-02-08T16:05:45.507747Z"
} | c26773 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 7504
},
"timestamp": "2026-02-16T20:54:17.247Z",
"answer": 149
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c190cc | antilemma_k2_v1_124444284_6108 | Compute $\sum_{k=1}^{307} \phi(k) \left\lfloor \frac{307}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. | 47,278 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(307), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(307), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T08:08:33.535765Z | {
"verified": true,
"answer": 47278,
"timestamp": "2026-02-08T08:08:33.536066Z"
} | 4eccb5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 712
},
"timestamp": "2026-02-13T14:51:24.711Z",
"answer": 47278
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
6774a1 | diophantine_product_count_v1_458359167_4589 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 44100$. Let $m$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $k$ be the number of positive integers $n \leq m$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Find the number of positive int... | 12 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("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(Va... | NT | null | COUNT | sympy | B3 | [
"B3/L3C"
] | 345f3b | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 0.007 | 2026-02-08T11:54:53.079205Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T11:54:53.086001Z"
} | 598854 | 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": 1470
},
"timestamp": "2026-02-14T21:09:50.257Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
870171 | lin_form_endings_v1_784195855_4546 | Let $a = 18$ and $b = 24$. Compute $\left\lfloor \frac{24}{\gcd(a, b)} \right\rfloor$, multiply the result by $13473$, and then find the remainder when this product is divided by $84739$. | 53,892 | graphs = [
Graph(
let={
"a_coeff": Const(18),
"b_coeff": Const(24),
"_inner_result": Floor(Div(Const(24), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(13473),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T07:09:53.414163Z | {
"verified": true,
"answer": 53892,
"timestamp": "2026-02-08T07:09:53.414963Z"
} | 398950 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 310
},
"timestamp": "2026-02-15T18:54:12.744Z",
"answer": 53892
},
{
"id": 11,
... | 2 | [
{
"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": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
488cb9 | diophantine_fbi2_count_v1_677425708_2350 | Let $d$ be a positive integer. Consider the set of all integers $d$ such that $4 \le d \le 84$, $d$ divides $240$, and $4 \le \frac{240}{d} \le 84$. Let $r$ be the number of elements in this set. Compute the remainder when $76268 \cdot r$ is divided by $58517$. | 14,446 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(84)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(R... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.015 | 2026-02-08T05:00:48.299699Z | {
"verified": true,
"answer": 14446,
"timestamp": "2026-02-08T05:00:48.315153Z"
} | f34cc2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1148
},
"timestamp": "2026-02-11T22:44:29.284Z",
"answer": 14446
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9c0aa3 | diophantine_product_count_v1_1874849503_794 | Let $k = 360$. Define $u$ to be the number of integers $t$ with $10 \leq t \leq 378$ for which there exist positive integers $a \leq 49$ and $b \leq 33$ such that $t = 3a + 7b$. Determine the number of positive integers $x$ such that $x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Compute this number. | 22 | graphs = [
Graph(
let={
"k": Const(360),
"upper": 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=49)), Geq(left=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.013 | 2026-02-08T13:18:48.597952Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T13:18:48.611445Z"
} | d10a62 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 3755
},
"timestamp": "2026-02-11T07:42:29.781Z",
"answer": 24
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.07,
"hi": 5.68
} | ||
7c2145 | comb_count_derangements_v1_601307018_1755 | Let $D_n$ denote the number of derangements of $n$ elements. For each integer $a$ with $0 \leq a \leq 29790$, define $M = (a^5 + a^4 + a^3 + 3a^2 + 4a) \bmod 29791$ and $R = (M^5 + M^4 + M^3 + 3M^2 + 4M) \bmod 29791$. Let $S$ be the number of such $a$ for which $R = a$ and $M \ne a$. Let $n = \sum_{k=0}^{2} S^k$. Compu... | 1,854 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(29790)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"n": Summation(var="k", start=Const(0), end=Const(2)... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/SUM_GEOM"
] | 8a1734 | comb_count_derangements_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 2 | 0.003 | 2026-03-10T02:28:57.960858Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-03-10T02:28:57.963703Z"
} | 836bd4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 31796
},
"timestamp": "2026-03-29T03:20:41.554Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
358130 | nt_count_divisible_and_v1_1125832087_87 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 163116$, $n$ is divisible by 9, and $n$ is divisible by 12. Compute the remainder when $44121$ times the number of elements in $S$ is divided by $97913$. | 71,818 | graphs = [
Graph(
let={
"upper": Const(163116),
"d1": Const(9),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Co... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 6.949 | 2026-02-08T02:51:29.811194Z | {
"verified": true,
"answer": 71818,
"timestamp": "2026-02-08T02:51:36.759801Z"
} | cb677f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 476
},
"timestamp": "2026-02-17T14:52:18.794Z",
"answer": 1
}
] | 0 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
3c5b3b | geo_count_lattice_rect_v1_1520064083_5231 | Let $a = 333$ and $b = 90$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let this number be $N$. Find the remainder when $62993 \cdot N$ is divided by $53236$. | 29,738 | graphs = [
Graph(
let={
"a": Const(333),
"b": Const(90),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(62993),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(53236)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T06:41:25.945740Z | {
"verified": true,
"answer": 29738,
"timestamp": "2026-02-08T06:41:25.948513Z"
} | 60647a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 3472
},
"timestamp": "2026-02-24T06:49:03.033Z",
"answer": 29738
},
{
"... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
8406a4 | alg_poly_orbit_hensel_v1_1419126231_60 | For each non-negative integer $a$ with $0 \le a \le 10574534$, define $$N = (3a^3 - a^2 - a + 4) \bmod 7921,$$ $$M = (3N^3 - N^2 - N + 4) \bmod 7921,$$ $$R = (3M^3 - M^2 - M + 4) \bmod 7921.$$ Find the number of such $a$ for which $R = a$, but $N \ne a$ and $M \ne a$. | 4,005 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(-1), Pow(Var("a"), Const(2))), Mul(Const(-1), Var("a")), Const(4)), modulus=Const(7921)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(3))), Mul(Const(-1), Pow(Ref("p1"), Const(2))... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.067 | 2026-02-25T09:36:54.866462Z | {
"verified": true,
"answer": 4005,
"timestamp": "2026-02-25T09:36:54.933170Z"
} | 006aac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 28898
},
"timestamp": "2026-03-30T06:48:16.721Z",
"answer": 4005
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
6dcf55 | comb_count_derangements_v1_1526740231_88 | Let $d$ be a positive integer divisor of $847$ with $d \geq 2$. Let $n$ be the smallest such $d$. Define $Q$ to be the remainder when $57029 \cdot !n$ is divided by $98222$, where $!n$ denotes the number of derangements of $n$ objects. Compute $Q$. | 44,894 | graphs = [
Graph(
let={
"_n": Const(98222),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(847))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(57029),
"Q":... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:20:45.407527Z | {
"verified": true,
"answer": 44894,
"timestamp": "2026-02-08T11:20:45.408409Z"
} | f165bb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1103
},
"timestamp": "2026-02-14T11:55:02.470Z",
"answer": 44894
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
32d9b8 | sequence_count_fib_divisible_v1_1248542787_311 | Let $n = 44121$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 179776$. Define $u$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $d = 11$. Determine the number of positive integers $n'$ such that $1 \le n' \le u$ and $d$ divides the $n'$-th Fibonacci number.... | 17,819 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(179776)))), expr=Sum(Var("x"), Var("... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.031 | 2026-02-08T03:03:23.914337Z | {
"verified": true,
"answer": 17819,
"timestamp": "2026-02-08T03:03:23.945671Z"
} | 19cd0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1829
},
"timestamp": "2026-02-09T02:37:48.482Z",
"answer": 17819
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -0.18,
"mid": 2.14,
"hi": 4.09
} | ||
943c2b | nt_max_prime_below_v1_1520064083_2764 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Consider the set of all prime numbers $n$ such that $m \leq n \leq 70225$. Determine the value of the largest such prime $n$. | 70,223 | graphs = [
Graph(
let={
"upper": Const(70225),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.172 | 2026-02-08T04:59:48.613983Z | {
"verified": true,
"answer": 70223,
"timestamp": "2026-02-08T04:59:50.786354Z"
} | 5b912f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 3556
},
"timestamp": "2026-02-11T22:39:42.413Z",
"answer": 70223
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
3ca06d | nt_count_divisible_and_v1_124444284_852 | Let $S$ be the set of positive integers $n$ such that $1 \le n \le 28020$, $n$ is divisible by 6, and the remainder when $n$ is divided by 10 equals the sum of the Möbius function $\mu(d)$ over all positive divisors $d$ of the smallest integer greater than or equal to 2 that divides 3757. Let $r$ be the number of eleme... | 72,607 | graphs = [
Graph(
let={
"upper": Const(28020),
"d1": Const(6),
"d2": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(M... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_SUM"
] | 615574 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_SUM"
] | 2 | 0.977 | 2026-02-08T03:32:57.016110Z | {
"verified": true,
"answer": 72607,
"timestamp": "2026-02-08T03:32:57.993159Z"
} | 9ead75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 2110
},
"timestamp": "2026-02-09T23:00:13.684Z",
"answer": 72607
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok_l... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
290675 | nt_count_intersection_v1_1125832087_131 | Let $N = 50000$. Define $r$ as the number of positive integers $n$ such that $1 \leq n \leq N$, $9$ divides $n$, and $\gcd(n, 10) = 1$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = 4000000$. Compute $s - r$. | 1,778 | graphs = [
Graph(
let={
"N": Const(50000),
"a": Const(9),
"b": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=R... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_intersection_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 1.606 | 2026-02-08T02:52:42.157740Z | {
"verified": true,
"answer": 1778,
"timestamp": "2026-02-08T02:52:43.764164Z"
} | b7f88a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 3896
},
"timestamp": "2026-02-23T18:28:16.980Z",
"answer": 1778
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -1,
"mid": 0.94,
"hi": 2.59
} | ||
b016c1 | comb_catalan_compute_v1_397696148_2051 | Let $n$ be the number of elements in the Cartesian product $\{1, 2\} \times \{1, 2, 3, 4, 5\}$. Let $C_n$ denote the $n$th Catalan number, defined by
$$
C_n = \frac{1}{n+1} \binom{2n}{n}.
$$
Compute the remainder when $1 - C_n$ is divided by $84865$. | 68,070 | graphs = [
Graph(
let={
"_n": Const(84865),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"_c": Const(1),
"Q": Mod(value=Sub(... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T12:55:48.733961Z | {
"verified": true,
"answer": 68070,
"timestamp": "2026-02-08T12:55:48.735868Z"
} | e1a56f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 429
},
"timestamp": "2026-02-24T16:41:34.162Z",
"answer": 68070
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
39a8a7 | modular_mod_compute_v1_601307018_4188 | Let $m$ be the largest positive integer $d$ such that $d^2 \leq 4618185$ and $d$ divides $4618185$. Find the remainder when $-63504$ is divided by $m$. | 846 | graphs = [
Graph(
let={
"a": Const(-63504),
"m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(4618185)), Leq(Mul(Var("d"), Var("d")), Const(4618185))))),
"result": Mod(value=Ref("a"), modulus=Ref... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | modular_mod_compute_v1 | null | 3 | 0 | [
"B3_CLOSEST"
] | 1 | 0.003 | 2026-03-10T04:48:59.387290Z | {
"verified": true,
"answer": 846,
"timestamp": "2026-03-10T04:48:59.390363Z"
} | ae8e2e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 3120
},
"timestamp": "2026-03-29T11:19:05.445Z",
"answer": 846
},
{
"id... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
14f48e | geo_count_lattice_rect_v1_784195855_2377 | Let $a = 128$ and $b = 76$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $c = 46897$ and define $Q$ to be the remainder when $c \cdot \text{result}$ is divided by $93525$. Compute $Q$. | 73,401 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(76),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(46897),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(93525)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T05:42:04.043634Z | {
"verified": true,
"answer": 73401,
"timestamp": "2026-02-08T05:42:04.045216Z"
} | 287389 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1284
},
"timestamp": "2026-02-24T04:21:24.475Z",
"answer": 73401
},
{
"... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
9ee25c | nt_count_coprime_v1_784195855_3316 | Let $\text{upper} = 11197$ and $k = 35$. Define $\mathcal{S}$ as the set of all integers $n$ such that $\phi(2) \leq n \leq \text{upper}$ and $\gcd(n, k) = \phi(2)$, where $\phi$ denotes Euler's totient function. Compute the number of elements in $\mathcal{S}$. | 7,678 | graphs = [
Graph(
let={
"upper": Const(11197),
"k": Const(35),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), EulerPhi(n=Const(2)))))),
},
... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_coprime_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 0.88 | 2026-02-08T06:20:04.035990Z | {
"verified": true,
"answer": 7678,
"timestamp": "2026-02-08T06:20:04.915494Z"
} | 20ea6a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 571
},
"timestamp": "2026-02-19T05:14:47.701Z",
"answer": 7678
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
529150 | antilemma_k2_v1_784195855_5374 | Let $m = 2130$ and $n = 101$. Let $T$ be the set of all positive integers $x$ such that $x^2 - 101x + 2130 = 0$. Let $s$ be the sum of all elements in $T$. Define $x$ as:
$$
x = \sum_{k=1}^{s} \varphi(k) \left\lfloor \frac{1}{k} \sum_{d \mid n} \varphi(d) \right\rfloor.
$$
Find the value of $x$. | 5,151 | graphs = [
Graph(
let={
"_m": Const(2130),
"_n": Const(101),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-101), Var("x")), Ref("_m")), Const(0)))), expr=Mul(EulerPhi(n=Var("k")),... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K3/K2",
"K2"
] | 4108ea | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2",
"K3",
"VIETA_SUM"
] | 4 | 0.002 | 2026-02-08T07:51:03.986651Z | {
"verified": true,
"answer": 5151,
"timestamp": "2026-02-08T07:51:03.988386Z"
} | 7b3069 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1331
},
"timestamp": "2026-02-13T12:36:42.638Z",
"answer": 5151
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"l... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cfd325 | nt_min_crt_v1_1915831931_1563 | Let $m = 5$ and $k = 8$. Let $a = 4$ and $b = 1$. Define $S$ as the set of all real solutions $x$ to the equation $x^2 - 40x + 351 = 0$. Let $\text{upper}$ be the sum of all elements in $S$. Now, let $T$ be the set of all integers $n$ such that $1 \leq n \leq \text{upper}$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{... | 9 | graphs = [
Graph(
let={
"m": Const(5),
"k": Const(8),
"a": Const(4),
"b": Const(1),
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-40), Var("x")), Const(351)), Const(0)))),
"resul... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_min_crt_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.01 | 2026-02-08T16:15:41.881653Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T16:15:41.891645Z"
} | 529d57 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 558
},
"timestamp": "2026-02-16T07:15:08.828Z",
"answer": 9
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"statu... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
97c267 | nt_count_divisible_and_v1_1978505735_1516 | Let $m = 95730$ and $n = 2144$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1149184$. Let $s$ be the minimum value of $x + y$ over all such pairs.\\
Let $j$ be a nonnegative integer such that $0 \leq j \leq s$ and $\binom{2144}{j}$ is odd. Let $d_2$ be the number of such integer... | 6,417 | graphs = [
Graph(
let={
"_m": Const(95730),
"_n": Const(2144),
"upper": Const(71064),
"d1": Const(6),
"d2": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), MinOverSet(set=MapOverSet(set=SolutionsSet(... | ALG | COMB | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 3.233 | 2026-02-08T16:14:23.416406Z | {
"verified": true,
"answer": 6417,
"timestamp": "2026-02-08T16:14:26.649780Z"
} | 23bf82 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 303,
"completion_tokens": 2480
},
"timestamp": "2026-02-24T20:19:31.602Z",
"answer": 6417
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
220bf5 | antilemma_k3_v1_655260480_4745 | Let $x = \sum_{d \mid 92100} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $53115 \cdot x$ is divided by $87532$. | 78,148 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=92100), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(53115), Ref("x")), modulus=Const(87532)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T18:05:41.167177Z | {
"verified": true,
"answer": 78148,
"timestamp": "2026-02-08T18:05:41.168326Z"
} | f1ddde | 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": 2337
},
"timestamp": "2026-02-18T14:02:05.095Z",
"answer": 78148
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e09f2a | modular_count_residue_v1_784195855_10081 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 169$. Compute the number of positive integers $n$ such that $1 \le n \le 32400$ and $n \equiv 14 \pmod{m}$. Let this count be $r$. Find the remainder when the Bell number $B_r$ is divided by $11$, and then comput... | 5 | graphs = [
Graph(
let={
"_n": Const(169),
"upper": Const(32400),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))),... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 5 | 0 | [
"B3"
] | 1 | 2.424 | 2026-02-08T17:25:17.302355Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T17:25:19.726136Z"
} | 63a2dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1926
},
"timestamp": "2026-02-18T01:46:08.380Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c02553 | nt_count_phi_equals_v1_458359167_5058 | Let $A$ be the set of positive integers $k$ such that $1 \leq k \leq 291744$ and $144$ divides $k$. Define $\alpha = |A|$. Let $B$ be the set of positive integers $n$ such that $1 \leq n \leq \alpha$ and $\phi(n) = 1006$. Define $\beta = |B|$. Let $\gamma$ be the number of positive integers $j$ such that $1 \leq j \leq... | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(291744)), Divides(divisor=Const(144), dividend=Var("k"))), domain='positive_integers')),
"k": Const(1006),
"... | NT | COMB | COUNT | sympy | B3 | [
"C3",
"C2"
] | ba075c | nt_count_phi_equals_v1 | bell_mod | 6 | 0 | [
"B3",
"C2",
"C3"
] | 3 | 1.872 | 2026-02-08T12:16:00.352203Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T12:16:02.224381Z"
} | b3ac73 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 4008
},
"timestamp": "2026-02-14T23:17:40.904Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FA... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
cf3b80 | nt_count_digit_sum_v1_677425708_234 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 22$ and $n$ is divisible by $22$. Compute the sum of the elements in $S$, and denote this sum by $T$. Let $R$ be the number of positive integers $n$ such that $1 \leq n \leq 99999$ and the sum of the decimal digits of $n$ is equal to $T$. Compute ... | 75 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(22)), Eq(Mod(value=Var("n"), modulus=Const(22)), Const(0))))),
"result": CountOverSet(set=SolutionsSet(var=Var... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 3.839 | 2026-02-08T03:10:23.488266Z | {
"verified": true,
"answer": 75,
"timestamp": "2026-02-08T03:10:27.327701Z"
} | 77dff8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 8560
},
"timestamp": "2026-02-23T17:19:22.920Z",
"answer": 75
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
15048a | antilemma_sum_equals_v1_124444284_3662 | Let $n = 26$. Determine the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 26$ and $1 \leq j \leq 26$ such that $i + j = 26$. | 25 | graphs = [
Graph(
let={
"_n": Const(26),
"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(26)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.022 | 2026-02-08T05:32:36.070817Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T05:32:36.092363Z"
} | 20ed36 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 233
},
"timestamp": "2026-02-24T03:55:49.683Z",
"answer": 25
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
c7f438 | nt_sum_gcd_range_mod_v1_153355830_2590 | Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 7370977967106434130450$, $\gcd(p, q) = 1$, and $p < q$. Let $k = 72$ and $M = 10957$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 953 | 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=7370977967106434130450)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), righ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.159 | 2026-02-08T07:14:12.118588Z | {
"verified": true,
"answer": 953,
"timestamp": "2026-02-08T07:14:12.277219Z"
} | e27c94 | 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": 4933
},
"timestamp": "2026-02-13T09:11:22.895Z",
"answer": 953
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a8831a | algebra_poly_eval_v1_1520064083_2161 | Let $a=27$. Let $M$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy=461041$. Let $N$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy=64009$.
Define
$$S = 90a^5 + 682a^4 + Ma^3 + Na^2 - 572a - 336.$$
Let $Q = \dfrac{S}{6950... | 24,186 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(90),
"a": Const(27),
"result": Div(Sum(Mul(Ref("_n"), Pow(Ref("a"), Const(5))), Mul(Const(682), Pow(Ref("a"), Const(4))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 8 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T04:32:19.823425Z | {
"verified": true,
"answer": 24186,
"timestamp": "2026-02-08T04:32:19.828194Z"
} | 2183fc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2597
},
"timestamp": "2026-02-10T17:07:41.737Z",
"answer": 24186
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -0.04,
"mid": 2.43,
"hi": 4.79
} | ||
2f70de | antilemma_cartesian_v1_1918700295_3315 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 21$ and $1 \leq j \leq 25$. Compute the value of $$
\sum_{n=\binom{19}{0}}^{x} \tau(n),
$$ where $\tau(n)$ denotes the number of positive divisors of $n$. | 3,374 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(25)))),
"Q": Summation(var="n", start=Binom(n=Const(19), k=Const(0)), end=Abs(arg=Ref(name='x')), expr=NumDivisors(n=Var("n"))... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_BINOM_0"
] | 674433 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_0"
] | 2 | 0.001 | 2026-02-08T08:30:52.030629Z | {
"verified": true,
"answer": 3374,
"timestamp": "2026-02-08T08:30:52.031627Z"
} | c9ce06 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 22285
},
"timestamp": "2026-02-24T09:43:10.537Z",
"answer": 3374
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
9441dd | nt_min_crt_v1_349078426_1836 | Let $n = 1296$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1296$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all such pairs. Determine the smallest positive integer $n$ such that $1 \leq n \leq s_{\text{min}}$, $n \equiv 2 \pmod{8}$, and $n \equiv 0 \pmod{9}$. Fin... | 18 | graphs = [
Graph(
let={
"_n": Const(1296),
"m": Const(8),
"k": Const(9),
"a": Const(2),
"b": Const(0),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_crt_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T13:57:02.699820Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T13:57:02.712567Z"
} | b00c35 | 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": 1170
},
"timestamp": "2026-02-15T22:41:20.530Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
734706 | algebra_quadratic_discriminant_v1_458359167_1454 | Let $m = 2$. Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq 4$ and $j^m \leq 16$. Let $a = 2$, $b = 8$, and $c = -42$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of eleme... | 400 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(4)), Leq(Pow(Var("j"), Ref("_m")), Const(16))), domain='positive_integers')),
"a": Const(2),
"b": Const(8),
... | NT | null | COMPUTE | sympy | C3 | [
"C3/COPRIME_PAIRS"
] | 6c678f | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"C3",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T04:37:11.867323Z | {
"verified": true,
"answer": 400,
"timestamp": "2026-02-08T04:37:11.870038Z"
} | 5b94bb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 1018
},
"timestamp": "2026-02-10T17:21:03.199Z",
"answer": 400
},
{
"i... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
e61959 | nt_sum_phi_v1_458359167_2815 | Let $ m = 44 $ and $ n = 98014 $. Define $ S $ as the set of all positive integers $ k $ such that $ k $ is a multiple of 44 and $ 1 \leq k \leq m $. Let $ T $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ x + y = \sum_{k \in S} k $. Define $ P $ as the set of all values $ xy $ where $ (x,... | 59,250 | graphs = [
Graph(
let={
"_m": Const(44),
"_n": Const(98014),
"upper": 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")), SumOverSet(se... | NT | null | SUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B1"
] | f6d1e2 | nt_sum_phi_v1 | null | 6 | 0 | [
"B1",
"SUM_DIVISIBLE"
] | 2 | 0.102 | 2026-02-08T06:47:53.733644Z | {
"verified": true,
"answer": 59250,
"timestamp": "2026-02-08T06:47:53.835722Z"
} | 98643b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2563
},
"timestamp": "2026-02-13T04:46:05.195Z",
"answer": 59250
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5e2a53 | comb_count_surjections_v1_717093673_1804 | Let $k$ be the number of ordered pairs $(i, j)$ with $i, j \in \{1, 2\}$ such that $i + j = 3$. Compute $k! \cdot S(7, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 126 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(7),
"k": 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(2)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.019 | 2026-02-08T16:19:34.962735Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T16:19:34.981419Z"
} | d761cd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 412
},
"timestamp": "2026-02-24T20:41:44.556Z",
"answer": 126
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
9fdc15 | comb_factorial_compute_v1_124444284_3312 | Let $n$ be the smallest divisor of $1002001$ that is at least $2$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1002001))))),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T05:21:05.649205Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T05:21:05.650785Z"
} | 042cff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 404
},
"timestamp": "2026-02-12T06:44:38.483Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
ecf271 | nt_count_divisible_v1_168721529_994 | Let $n = 49$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. For each such pair, compute $x + y$, and let $d$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive integers $k$ such that $1 \leq k \leq 35344$ and $k$ is divisible by $d$. Compute th... | 2,524 | graphs = [
Graph(
let={
"_n": Const(49),
"upper": Const(35344),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 3 | 0 | [
"B3"
] | 1 | 1.451 | 2026-02-08T13:23:25.641848Z | {
"verified": true,
"answer": 2524,
"timestamp": "2026-02-08T13:23:27.093197Z"
} | 5db1ec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 758
},
"timestamp": "2026-02-09T11:46:33.230Z",
"answer": 2524
},
{
"id... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -10,
"mid": -7.3,
"hi": -4.6
} | ||
ce80d6 | antilemma_k2_v1_865884756_4083 | Let $n = 16160$. Define $S$ to be the set of all positive integers $x$ such that $x^2 - 282x + n = 0$. Let $m$ be the sum of all elements in $S$. Compute $$\sum_{k=1}^{m} \phi(k) \left\lfloor \frac{282}{k} \right\rfloor.$$ | 39,903 | graphs = [
Graph(
let={
"_n": Const(16160),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-282), Var("x1")), Ref("_n")), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(282), Var... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T17:43:55.909127Z | {
"verified": true,
"answer": 39903,
"timestamp": "2026-02-08T17:43:55.910807Z"
} | ad648a | 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": 1083
},
"timestamp": "2026-02-18T06:54:03.214Z",
"answer": 39903
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0fda2d | comb_count_derangements_v1_1520064083_5364 | Let $n$ be the largest prime number such that $$ n \leq \left| \left\{ p \in \mathbb{Z}^+ \mid \text{there exists an integer } q \text{ with } p < q,\ pq = 330750,\ \gcd(p, q) = 1 \right\} \right|. $$ Let $Q$ be the remainder when $68633 \cdot !n$ is divided by $62791$, where $!n$ denotes the number of derangements of... | 31,016 | graphs = [
Graph(
let={
"_n": Const(62791),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_derangements_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T06:45:28.490007Z | {
"verified": true,
"answer": 31016,
"timestamp": "2026-02-08T06:45:28.494044Z"
} | dd5e43 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 3190
},
"timestamp": "2026-02-13T04:14:33.121Z",
"answer": 31016
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
77e4a3 | nt_count_divisible_v1_1742523217_863 | Let $T$ be the set of all integers $t$ such that $43 \le t \le 145$ and there exist integers $a$ and $b$ with $1 \le a \le 9$, $1 \le b \le 3$, and $t = 9a + 15b + 19$. Let $d$ be the number of elements in $T$. Determine the number of positive integers $n$ such that $2 \le n \le 35344$ and $n$ is divisible by $d$. | 1,309 | graphs = [
Graph(
let={
"upper": Const(35344),
"divisor": 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=9)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_2"
] | 9858be | nt_count_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_2"
] | 2 | 2.865 | 2026-02-08T03:18:19.926885Z | {
"verified": true,
"answer": 1309,
"timestamp": "2026-02-08T03:18:22.792169Z"
} | 5d4129 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1689
},
"timestamp": "2026-02-09T23:45:09.382Z",
"answer": 1309
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
98baf5 | alg_poly_orbit_count_v1_601307018_6242 | Let $a$ be a non-negative integer with $0 \le a \le 24388$. Define the sequence $N = (2a^3) \bmod 29$, $M = (2N^3) \bmod 29$, $R = (2M^3) \bmod 29$, $S = (2R^3) \bmod 29$, $T = (2S^3) \bmod 29$, and $K = (2T^3) \bmod 29$. Find the number of values of $a$ such that $K = a$, but $N \ne a$, $M \ne a$, $R \ne a$, $S \ne a$... | 20,184 | graphs = [
Graph(
let={
"p1": Mod(value=Mul(Const(2), Pow(Var("a"), Const(3))), modulus=Const(29)),
"p2": Mod(value=Mul(Const(2), Pow(Ref("p1"), Const(3))), modulus=Const(29)),
"p3": Mod(value=Mul(Const(2), Pow(Ref("p2"), Const(3))), modulus=Const(29)),
"p4": ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.022 | 2026-03-10T06:50:38.170716Z | {
"verified": true,
"answer": 20184,
"timestamp": "2026-03-10T06:50:38.193089Z"
} | 2cccfc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 3483
},
"timestamp": "2026-04-19T04:00:16.035Z",
"answer": 20184
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
bc4a0b | geo_count_lattice_rect_v1_1470522791_950 | Let $a = 200$ and $b = 220$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$. | 44,421 | graphs = [
Graph(
let={
"a": Const(200),
"b": Const(220),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T13:21:03.774915Z | {
"verified": true,
"answer": 44421,
"timestamp": "2026-02-08T13:21:03.776081Z"
} | 4331ca | 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": 368
},
"timestamp": "2026-02-24T17:49:58.326Z",
"answer": 44421
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
d0a997 | lin_form_endings_v1_397696148_2553 | Let $a = 9$ and $b = 21$. Let $k = 10287$ and $M = 69683$. Compute the remainder when $k \cdot \mathrm{lcm}(a, b)$ is divided by $M$. | 20,934 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(21),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(10287),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(69683),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:24:49.804579Z | {
"verified": true,
"answer": 20934,
"timestamp": "2026-02-08T13:24:49.805178Z"
} | f15e80 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 594
},
"timestamp": "2026-02-15T15:22:13.668Z",
"answer": 20934
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
da01b7 | comb_count_partitions_v1_1978505735_5368 | Let $n$ be the smallest divisor of $167462081$ that is at least $2$. Define $p(n)$ to be the number of integer partitions of $n$. Compute the remainder when $50096 \cdot p(n)$ is divided by $60241$. | 55,134 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(167462081))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(50096), Ref... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_partitions_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T18:57:41.641350Z | {
"verified": true,
"answer": 55134,
"timestamp": "2026-02-08T18:57:41.644250Z"
} | 8711ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 5177
},
"timestamp": "2026-02-18T20:51:57.307Z",
"answer": 55134
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIA... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f7cd4 | nt_count_divisors_in_range_v1_153355830_309 | Let $n = 332640$. Define $b$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 8832784$. Compute the number of positive divisors $d$ of $n$ such that $1 \leq d \leq b$. | 158 | graphs = [
Graph(
let={
"n": Const(332640),
"a": Const(1),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(8832784)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.109 | 2026-02-08T03:02:21.552655Z | {
"verified": true,
"answer": 158,
"timestamp": "2026-02-08T03:02:21.661203Z"
} | c92989 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 5537
},
"timestamp": "2026-02-10T12:31:42.545Z",
"answer": 158
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
21c796 | antilemma_cartesian_v1_124444284_3867 | Let $x$ be the number of ordered pairs $(a, b)$ where $a$ is an integer with $1 \leq a \leq 7$ and $b$ is an integer with $1 \leq b \leq 10$. Compute the remainder when $63947x$ is divided by $60672$. | 47,234 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(10)))),
"Q": Mod(value=Mul(Const(63947), Ref("x")), modulus=Const(60672)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T05:38:54.921203Z | {
"verified": true,
"answer": 47234,
"timestamp": "2026-02-08T05:38:54.921899Z"
} | d3ff24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1084
},
"timestamp": "2026-02-24T04:09:26.174Z",
"answer": 47234
},
{
"... | 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": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
e6fb5f | alg_poly4_count_v1_1218484723_6942 | Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 188$ such that $$-388a^3b + mb^4 + 97a^4 - 388ab^3 + 582a^2b^2 = 1420177,$$ where $m = \max\left\{ d \ge 1 : d \le \min\{ d_1 \ge 2 \mid d_1 \mid 101918191 \},\ d \mid 9991 \right\}$. Find $Q$. | 354 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(9991),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(188)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(188)), Eq(Sum(Mul(Co... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_DIVISOR"
] | 03060e | alg_poly4_count_v1 | null | 6 | 0 | [
"MAX_DIVISOR",
"MIN_PRIME_FACTOR"
] | 2 | 0.256 | 2026-02-25T08:22:58.544692Z | {
"verified": true,
"answer": 354,
"timestamp": "2026-02-25T08:22:58.800618Z"
} | 7e70bf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T03:21:14.275Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
cf4b7c | sequence_count_fib_divisible_v1_1918700295_1112 | Let $d$ be the number of prime numbers $n$ such that $2 \leq n \leq 71$. Determine the number of positive integers $n \leq 123$ for which $d$ divides the $n$th Fibonacci number. Compute $32768$ minus this number. | 32,764 | graphs = [
Graph(
let={
"upper": Const(123),
"d": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(71)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1))... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.007 | 2026-02-08T05:36:08.970368Z | {
"verified": true,
"answer": 32764,
"timestamp": "2026-02-08T05:36:08.977384Z"
} | 3f75e4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 1661
},
"timestamp": "2026-02-12T10:59:35.533Z",
"answer": 32764
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
90e40f | comb_bell_compute_v1_124444284_1442 | Let $x$ and $y$ be positive integers such that $x + y = 6$. Consider the set of all possible values of $xy$. Let $n$ be the maximum value in this set. Define $Q$ to be the remainder when $91845$ multiplied by the Bell number $B_n$ is divided by $79909$. Compute $Q$. | 57,970 | graphs = [
Graph(
let={
"_n": Const(79909),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T03:52:45.850207Z | {
"verified": true,
"answer": 57970,
"timestamp": "2026-02-08T03:52:45.851511Z"
} | 18c2cb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2463
},
"timestamp": "2026-02-10T16:14:58.350Z",
"answer": 57970
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ede815 | antilemma_product_of_sums_v1_677425708_117 | Let $S_1$ be the sum of the first components $k$ over all ordered pairs $(k, j)$ where $k$ ranges from $1$ to $11$ and $j$ ranges from $1$ to $2$. Let $S_2 = \sum_{k = \phi(2)}^{6} k$. Compute the value of $S_1 \cdot S_2$. | 2,772 | graphs = [
Graph(
let={
"_n": Const(6),
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(2)))), expr=V... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS",
"ONE_PHI_2"
] | 5bd3e5 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"ONE_PHI_2",
"PRODUCT_OF_SUMS"
] | 2 | 0.001 | 2026-02-08T03:04:39.033217Z | {
"verified": true,
"answer": 2772,
"timestamp": "2026-02-08T03:04:39.034165Z"
} | 021678 | 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": 506
},
"timestamp": "2026-02-08T20:19:04.353Z",
"answer": 2772
},
{
"id... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
45f1a8 | lin_form_endings_v1_397696148_411 | Let $a = 18$, $b = 27$, $A = 19$, and $B = 33$. Let $g = \gcd(a, b)$. Define
$$
n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.
$$
Let $k = 13543$. Compute the value of $(k \cdot n) \bmod 68516$. | 19,803 | graphs = [
Graph(
let={
"a_coeff": Const(18),
"b_coeff": Const(27),
"A_val": Const(19),
"B_val": Const(33),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:28:08.792618Z | {
"verified": true,
"answer": 19803,
"timestamp": "2026-02-08T11:28:08.793216Z"
} | 7e6617 | 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": 839
},
"timestamp": "2026-02-14T14:19:17.745Z",
"answer": 19803
},
{... | 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": "V7",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
10cf55 | sequence_count_fib_divisible_v1_677425708_1881 | Let $d$ be the smallest divisor of $437$ that is at least $2$. Determine the number of positive integers $n \leq 285$ such that $d$ divides the $n$-th Fibonacci number. | 15 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(285),
"d": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(437))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditi... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.014 | 2026-02-08T04:35:29.360036Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T04:35:29.373614Z"
} | d3fd13 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1558
},
"timestamp": "2026-02-10T02:27:52.560Z",
"answer": 15
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
2a248e | alg_sym_quad_system_v1_601307018_430 | Let $R$ be the sum of $a^4 + b^4 + c^4$ over all positive integer triples $(a, b, c)$ satisfying $a^2 + b^2 + c^2 = ab + bc + ca$ and $4a + b + 3c = 1936$, taken modulo the largest positive divisor $d$ of $82537189$ such that $d^2 \leq 82537189$. Find the remainder when $55853 \cdot R$ is divided by $83711$. | 73,608 | graphs = [
Graph(
let={
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | alg_sym_quad_system_v1 | null | 8 | 0 | [
"B3_CLOSEST"
] | 1 | 0.021 | 2026-03-10T00:57:35.153716Z | {
"verified": true,
"answer": 73608,
"timestamp": "2026-03-10T00:57:35.174467Z"
} | e65616 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 10766
},
"timestamp": "2026-04-18T14:45:58.388Z",
"answer": 52625
},
{
... | 0 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": 3.49,
"mid": 5.82,
"hi": 8.5
} | ||
a96c75 | nt_min_phi_inverse_v1_153355830_2836 | Let $S_1$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2500$. Define $m$ to be the minimum value of $x + y$ over all pairs in $S_1$.
Let $S_2$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Define $u$ to be the minimum value of $x + y$ over all pairs ... | 31,113 | graphs = [
Graph(
let={
"_m": Const(63164),
"_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(2500)))), expr=Sum(Var("x"), Var("y")))... | NT | null | EXTREMUM | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T07:25:45.882356Z | {
"verified": true,
"answer": 31113,
"timestamp": "2026-02-08T07:25:45.887158Z"
} | 62eb8a | 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": 1691
},
"timestamp": "2026-02-13T10:09:20.754Z",
"answer": 31113
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
996ddb | nt_sum_over_divisible_v1_898971024_2523 | Let $S_1$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 11303044$. Let $s_{\min}$ be the minimum value of $x_1 + y_1$ over all such pairs. Let $S_2$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x y = s_{\min}$. Let $d$ be the minimum value of $x + y$ ... | 86,622 | graphs = [
Graph(
let={
"_n": Const(89778),
"upper": Const(17689),
"divisor": 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")), MinOv... | NT | null | SUM | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.59 | 2026-02-08T16:47:50.885839Z | {
"verified": true,
"answer": 86622,
"timestamp": "2026-02-08T16:47:51.476124Z"
} | dc638e | 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": 2198
},
"timestamp": "2026-02-17T13:01:09.081Z",
"answer": 86622
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fc069e | comb_count_surjections_v1_1218484723_7771 | Let $k = 7$ and $n = \sum_{k1=\sum_{k2=0}^{8} (-1)^{k2} \binom{8}{k2}}^{2} 2^{k1}$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling numbers of the second kind. | 5,040 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Summation(var="k2", start=Const(0), end=Const(8), expr=Mul(Pow(Const(-1), Var("k2")), Binom(n=Const(8), k=Var("k2")))), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(7),
"result": Mul(Factorial(Ref("k")), S... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"SUM_GEOM"
] | c3d408 | comb_count_surjections_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"SUM_GEOM"
] | 2 | 0.002 | 2026-02-25T09:20:04.862802Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T09:20:04.864427Z"
} | a96a2b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 684
},
"timestamp": "2026-03-30T06:19:35.819Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"s... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
f21353 | nt_min_coprime_above_v1_1915831931_2212 | Let $m$ be the number of positive integers $n$, not exceeding $9369$, that are divisible by $9$ and relatively prime to $14$. Let $r$ be the smallest integer greater than $30976$ and not exceeding $31433$ such that $\gcd(r, m) = 1$. Compute the remainder when $|r|$ is divided by $58583$. | 30,977 | graphs = [
Graph(
let={
"_n": Const(9369),
"start": Const(30976),
"upper": Const(31433),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(9), dividend=Var("n")), Eq(GC... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.076 | 2026-02-08T16:40:29.871959Z | {
"verified": true,
"answer": 30977,
"timestamp": "2026-02-08T16:40:29.948102Z"
} | 782f48 | 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": 1376
},
"timestamp": "2026-02-17T09:03:40.359Z",
"answer": 30977
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
94dfc4 | nt_lcm_compute_v1_124444284_1414 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 964324$. Let $a = 2635$ and let $b$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $L$ be the least common multiple of $a$ and $b$. Find the remainder when $44121 \cdot L$ is divided by 74590. | 54,590 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(2635),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(964324))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:52:33.478114Z | {
"verified": true,
"answer": 54590,
"timestamp": "2026-02-08T03:52:33.479410Z"
} | 33eaf6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 6820
},
"timestamp": "2026-02-10T16:14:35.728Z",
"answer": 54590
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
864a86 | nt_count_divisible_v1_1520064083_3085 | Let $k$ be the largest integer such that $2^k \leq 236773026$. Find the number of positive integers $n$ such that $1 \leq n \leq 45796$ and $n$ is divisible by $k$. Let this number be $N$. Compute the remainder when $44121 \cdot N$ is divided by 63230. | 28,126 | graphs = [
Graph(
let={
"upper": Const(45796),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Const(236773026)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_count_divisible_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 2.098 | 2026-02-08T05:27:18.561339Z | {
"verified": true,
"answer": 28126,
"timestamp": "2026-02-08T05:27:20.659468Z"
} | 0bc66c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1647
},
"timestamp": "2026-02-12T08:43:59.195Z",
"answer": 28126
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6186bd | antilemma_cartesian_v1_1520064083_8473 | Compute the remainder when $35201$ times the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 11$ and $1 \leq j \leq 49$ is divided by $83880$. | 16,459 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(49)))),
"Q": Mod(value=Mul(Const(35201), Ref("x")), modulus=Const(83880)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T10:12:03.125767Z | {
"verified": true,
"answer": 16459,
"timestamp": "2026-02-08T10:12:03.126593Z"
} | 36e67b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1094
},
"timestamp": "2026-02-24T11:52:41.521Z",
"answer": 16459
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
db6d0e | comb_factorial_compute_v1_601307018_5218 | Let $S = \{ v \mid 45 \le v \le 8820,\ \exists\ a,b \in \mathbb{Z}^+\ \text{with}\ 1 \le a,b \le 14\ \text{such that}\ 5a^2 + 20b^2 + 20ab = v \}$. Let $T = \{ j \mid 0 \le j \le 36223,\ \binom{36223}{j} \bmod 2 = 1 \}$. Let $n$ be the number of ordered pairs $(a,b)$ of positive integers with $1 \le a \le b \le |S|$ su... | 40,320 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=V... | COMB | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/QF_PSD_ORBIT",
"V8/QF_PSD_ORBIT"
] | 8f039f | comb_factorial_compute_v1 | null | 7 | 0 | [
"QF_PSD_DISTINCT",
"QF_PSD_ORBIT",
"V8"
] | 3 | 0.01 | 2026-03-10T05:54:31.627525Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-03-10T05:54:31.637607Z"
} | 63e6b9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 2811
},
"timestamp": "2026-04-19T01:34:58.438Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"statu... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
331893 | sequence_fibonacci_compute_v1_238844314_718 | Let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$. Compute $F_{23}$. Now, let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 625$, and let $s_{\min}$ be the minimum value of $x + y$ over all such pairs. Let $c$ be the number of positive integers $j \le s_{\min}$ such th... | 30,702 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Const(23),
"result": Fibonacci(arg=Ref(name='n')),
"_c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements... | NT | null | COMPUTE | sympy | B3 | [
"B3/C3"
] | b1fd51 | sequence_fibonacci_compute_v1 | negation_mod | 5 | 0 | [
"B3",
"C3"
] | 2 | 0.008 | 2026-02-08T13:33:07.615605Z | {
"verified": true,
"answer": 30702,
"timestamp": "2026-02-08T13:33:07.623338Z"
} | 5b6795 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 968
},
"timestamp": "2026-02-15T17:37:12.173Z",
"answer": 30702
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d3e4d1 | antilemma_k2_v1_1978505735_6176 | Let $x = \frac{5}{\sum_{d \mid 40} \phi(d)} \sum_{k=1}^{182} \sum_{j=1}^{8} \phi(k) \left\lfloor \frac{182}{k} \right\rfloor$. Compute the remainder when $\sum_{n=1}^{|x|} \phi(n)$ is divided by 81654. | 33,814 | graphs = [
Graph(
let={
"_c": Const(5),
"_m": Const(81654),
"_n": Const(182),
"x": Div(Mul(Ref("_c"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Cons... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/SUM_INDEPENDENT",
"K2"
] | bf3419 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3",
"SUM_INDEPENDENT"
] | 3 | 0.942 | 2026-02-08T19:27:39.750387Z | {
"verified": true,
"answer": 33814,
"timestamp": "2026-02-08T19:27:40.692244Z"
} | 76fd53 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 4778
},
"timestamp": "2026-02-18T22:30:32.172Z",
"answer": 0
},
{... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemm... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
893ecb | comb_factorial_compute_v1_1218484723_608 | Find the number $n$ of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $64a^3 + 144a^2b + 108ab^2 + 27b^3 = 1061208$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(144),
"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(Ref("_n"), Pow(Var("a"), Const(2)), Va... | COMB | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY3_COUNT"
] | 1 | 0.001 | 2026-02-25T02:17:13.697783Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T02:17:13.699011Z"
} | 024d0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1066
},
"timestamp": "2026-03-28T23:25:26.866Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -6.52,
"mid": -3.37,
"hi": -0.99
} | ||
4291e6_n | comb_count_permutations_fixed_v1_1218484723_5741 | A puzzle game has $n$ tiles labeled $1$ through $n$, where $n = \sum_{k_1=1}^{3} \varphi(k_1) \left\lfloor \frac{3}{k_1} \right\rfloor$. A valid configuration uses exactly $3$ fixed tiles and deranges the rest. The number of such configurations is $N = \binom{n}{3} D_{n-3}$. Compute the remainder when $37023N$ is divid... | 22,600 | COMB | null | COUNT | sympy | HALFPLANE_COUNT | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 3 | null | [
"HALFPLANE_COUNT",
"K2"
] | 2 | 0.072 | 2026-02-25T07:18:40.582033Z | null | 2261ed | 4291e6 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 797
},
"timestamp": "2026-03-31T00:03:25.678Z",
"answer": 22600
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
2672ee | lin_form_endings_v1_579913215_33 | Let $k = 12489$ and $M = 71189$. Define $T$ as the set of all integers $t$ such that $70 \leq t \leq 1573$ and there exist positive integers $a \leq 38$ and $b \leq 15$ satisfying
$$
t = 27a + 36b + 7.
$$
Let $c$ be the number of elements in $T$. Compute the remainder when $k \cdot c$ is divided by $M$. | 29,926 | graphs = [
Graph(
let={
"_inner_result": 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=38)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T12:47:26.084768Z | {
"verified": true,
"answer": 29926,
"timestamp": "2026-02-08T12:47:26.087481Z"
} | ee6429 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 16871
},
"timestamp": "2026-02-24T16:28:31.777Z",
"answer": 29926
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
c3e9f1 | modular_inverse_v1_124444284_7469 | Let $a = 4$ and $m = 103$. Define $x_0$ to be the smallest positive integer $x$ such that $1 \leq x \leq 102$ and $4x \equiv 1 \pmod{103}$.
Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 130$. Let $M$ be the maximum value of $xy$ as $(x, y)$ ranges over $P$. Let $D$ be the set... | 4,199 | graphs = [
Graph(
let={
"a": Const(4),
"m": Const(103),
"upper": Const(102),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Const(... | NT | null | EXTREMUM | sympy | B1 | [
"B1/MAX_DIVISOR"
] | cafde3 | modular_inverse_v1 | negation_mod | 7 | 0 | [
"B1",
"MAX_DIVISOR"
] | 2 | 0.027 | 2026-02-08T09:08:54.621505Z | {
"verified": true,
"answer": 4199,
"timestamp": "2026-02-08T09:08:54.648519Z"
} | 9d0eb2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 486
},
"timestamp": "2026-02-21T01:29:55.161Z",
"answer": 4199
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} |
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