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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5ed484 | algebra_quadratic_discriminant_v1_1915831931_2487 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $m = 4$. Define $D = (-2)^n - 4 \cdot 1 \cdot 1$. Let $a_1$ be the number of positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 q = 12$, ... | 1 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.01 | 2026-02-08T16:52:01.754026Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:52:01.763592Z"
} | 68efb8 | 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": 1063
},
"timestamp": "2026-02-17T15:19:48.985Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
579982 | comb_count_permutations_fixed_v1_655260480_3930 | Let $n = 8$. Define $k = \sum_{k_1=0}^{1} (-1)^{k_1} \binom{1}{k_1}$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 14,833 | graphs = [
Graph(
let={
"n": Const(8),
"k": Summation(var="k1", start=Const(0), end=Const(1), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Const(1), k=Var("k1")))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k'))))... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T17:37:40.438061Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T17:37:40.440232Z"
} | ccd442 | 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": 1186
},
"timestamp": "2026-02-18T05:09:57.556Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
639c0b | nt_sum_divisors_compute_v1_1742523217_3301 | Let $n = 29584$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 3063$ and there exist positive integers $a \leq 215$ and $b \leq 94$ with $t = 9a + 12b$. Let $c$ be the number of elements in $T$. Compute the remainder when
$$
\sigma(n)... | 75,053 | graphs = [
Graph(
let={
"_n": Const(84021),
"n": Const(29584),
"result": SumDivisors(n=Ref("n")),
"_c": 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'), ri... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | d6c893 | nt_sum_divisors_compute_v1 | two_moduli | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:46:23.903620Z | {
"verified": true,
"answer": 75053,
"timestamp": "2026-02-08T05:46:23.905627Z"
} | 131f09 | 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": 5267
},
"timestamp": "2026-02-12T13:45:18.894Z",
"answer": 75053
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
695f6a | antilemma_k3_v1_1440796553_106 | Let $n = 16560$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Let $Q$ be the remainder when $44121 \cdot x$ is divided by $89345$. Find the value of $Q$. | 69,695 | graphs = [
Graph(
let={
"_n": Const(16560),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(89345)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T11:35:02.426879Z | {
"verified": true,
"answer": 69695,
"timestamp": "2026-02-08T11:35:02.427336Z"
} | 06adc7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1025
},
"timestamp": "2026-02-14T15:52:23.685Z",
"answer": 69695
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6e36b0 | algebra_quadratic_discriminant_v1_1742523217_3609 | Let $a = 2$, $m = 12$, and $n = 4$. Define $b$ as the result of dividing $6$ times the sum of all $k$ over the ordered pairs $(k, j)$ with $1 \leq k \leq 3$ and $1 \leq j \leq 2$ by $m$. Let $c = -20$. Compute $b^2 - nac$. | 196 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(4),
"a": Const(2),
"b": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), e... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 0.022 | 2026-02-08T05:58:50.310225Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-08T05:58:50.332341Z"
} | e97cb4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 325
},
"timestamp": "2026-02-11T23:25:56.231Z",
"answer": -124
},
{
"id": 11,... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a9ba3f | antilemma_k3_v1_1742523217_3075 | Let $n = 83711$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 83,711 | graphs = [
Graph(
let={
"_n": Const(83711),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T05:31:15.481103Z | {
"verified": true,
"answer": 83711,
"timestamp": "2026-02-08T05:31:15.481478Z"
} | 0d6530 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 599
},
"timestamp": "2026-02-11T22:55:31.873Z",
"answer": 92971
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
9e2d50 | comb_binomial_compute_v1_1431428450_1078 | Let $N$ be the sum of $\phi(d)$ over all positive divisors $d$ of $49$, where $\phi$ denotes Euler's totient function. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = N$. Compute $\binom{n}{6}$. | 3,003 | graphs = [
Graph(
let={
"_n": SumOverDivisors(n=Const(value=49), var='d', expr=EulerPhi(n=Var(name='d'))),
"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(... | NT | null | COMPUTE | sympy | K3 | [
"K3/B3"
] | f0a0b3 | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3",
"K3"
] | 2 | 0.002 | 2026-02-08T13:53:09.675374Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T13:53:09.677193Z"
} | 5e52d6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 367
},
"timestamp": "2026-02-16T05:09:12.203Z",
"answer": 3003
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
5395b3 | diophantine_fbi2_count_v1_865884756_4595 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $k$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all positive integers $d$ such that $5 \le d \le 85$, $d$ divides $k$, $k/d \ge 6$, and $$ \frac{k}{d} \le \min\{x_1 + y_1 : x_1, y_1 \in \mat... | 16 | graphs = [
Graph(
let={
"_n": Const(5),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T18:00:00.404899Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T18:00:00.414062Z"
} | f32b96 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1759
},
"timestamp": "2026-02-18T11:50:20.634Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
94ce06 | nt_sum_divisors_mod_v1_2051736721_1086 | Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 13$ and $1 \leq j \leq 21$ such that $\gcd(i, j) = 1$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by $10477$. | 546 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(21))))),
"M... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.003 | 2026-02-08T15:49:58.844402Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T15:49:58.847668Z"
} | 274f18 | 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": 1513
},
"timestamp": "2026-02-16T14:34:02.475Z",
"answer": 546
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a45768 | comb_factorial_compute_v1_971394319_1770 | Let $c = 24881$ and $N = 89660$. Define $n$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 16$. Let $r = n!$. Compute the remainder when $c \cdot r$ is divided by $N$. | 85,840 | graphs = [
Graph(
let={
"_n": Const(89660),
"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(16)))), expr=Sum(Var("x"), Var("y")))),
... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_factorial_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T13:54:17.190069Z | {
"verified": true,
"answer": 85840,
"timestamp": "2026-02-08T13:54:17.191336Z"
} | bb5509 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 10638
},
"timestamp": "2026-02-24T19:19:53.606Z",
"answer": 85840
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
a6259b | nt_min_coprime_above_v1_898971024_90 | Let $n$ be the number of integers $t$ with $49 \leq t \leq 1501$ for which there exist positive integers $a \leq 125$ and $b \leq 17$ such that $t = 9a + 21b + 19$. Let $\phi$ denote Euler's totient function, and define $m = \sum_{d \mid n} \phi(d)$. Let $r$ be the smallest integer $n$ such that $73984 < n \leq 74467$ ... | 34,474 | 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=125)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/K3"
] | c7df50 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.051 | 2026-02-08T15:10:53.698472Z | {
"verified": true,
"answer": 34474,
"timestamp": "2026-02-08T15:10:53.749120Z"
} | a82318 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 6481
},
"timestamp": "2026-02-16T01:04:34.947Z",
"answer": 34474
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fbfc49 | nt_max_prime_below_v1_1520064083_8127 | Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq 24964$. Let $r$ be the largest element of $P$. Let $J$ be the set of all positive integers $j$ such that $1 \leq j \leq 1111$ and $j^2 \leq 1234321$. Let $c$ be the number of elements in $J$. Compute the value of $c - r$, and find the remainder when t... | 60,436 | graphs = [
Graph(
let={
"upper": Const(24964),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"_c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | a45c54 | nt_max_prime_below_v1 | negation_mod | 4 | 0 | [
"C3"
] | 1 | 1.715 | 2026-02-08T10:01:38.208595Z | {
"verified": true,
"answer": 60436,
"timestamp": "2026-02-08T10:01:39.923682Z"
} | a29260 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 2485
},
"timestamp": "2026-02-14T06:08:40.015Z",
"answer": 60436
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f89177 | antilemma_k2_v1_1978505735_619 | Compute
$$
\sum_{k=1}^{189} \varphi(k) \left\lfloor \frac{189}{k} \right\rfloor,
$$
where $\varphi(k)$ denotes Euler's totient function. | 17,955 | graphs = [
Graph(
let={
"_n": Const(189),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(189), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T15:29:44.127120Z | {
"verified": true,
"answer": 17955,
"timestamp": "2026-02-08T15:29:44.127714Z"
} | 25bdae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 517
},
"timestamp": "2026-02-16T06:51:24.985Z",
"answer": 17955
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ec384a | sequence_fibonacci_compute_v1_458359167_5570 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 9$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Let $m$ be the minimum element of $T$. Define $n = \sum_{k=1}^{m} k$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ fo... | 34,634 | graphs = [
Graph(
let={
"_n": Const(57119),
"n": Summation(var="k", start=Const(1), end=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(9... | NT | null | COMPUTE | sympy | B3 | [
"B3/SUM_ARITHMETIC"
] | b6a880 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.001 | 2026-02-08T12:36:20.834193Z | {
"verified": true,
"answer": 34634,
"timestamp": "2026-02-08T12:36:20.835686Z"
} | b1872c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1279
},
"timestamp": "2026-02-15T02:35:00.139Z",
"answer": 34634
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V1",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9c8f8b | modular_sum_quadratic_residues_v1_601307018_4511 | Let $ a $ be an integer. Define the following values modulo $ 79 $: $ R = a^{39} \bmod 79 $, $ S = (a^3 - 3a) \bmod 79 $, $ T = S^{39} \bmod 79 $, $ K = (S^3 - 3S) \bmod 79 $, $ L = K^{39} \bmod 79 $, $ P = (K^3 - 3K) \bmod 79 $, $ Q = P^{39} \bmod 79 $, and $ W = R + T + L + Q $. Let $ U = (P^3 - 3P) \bmod m $, where ... | 8,147 | graphs = [
Graph(
let={
"_m": Const(79),
"_n": Const(79),
"p": Const(181),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Sum(Ref("result"), Mod(value=Pow(Const(2), Mod(value=Ref("result"), modulus=CountOverSet(set=SolutionsS... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/POLY_ORBIT_LEGENDRE"
] | 5862f9 | modular_sum_quadratic_residues_v1 | mod_exp | 8 | 0 | [
"MIN_PRIME_FACTOR",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.007 | 2026-03-10T05:08:45.402157Z | {
"verified": true,
"answer": 8147,
"timestamp": "2026-03-10T05:08:45.409042Z"
} | a335e4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 395,
"completion_tokens": 15270
},
"timestamp": "2026-04-19T00:06:40.630Z",
"answer": 8146
},
{
... | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
1d359e | nt_euler_phi_compute_v1_1874849503_109 | Let $p$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq=12$, $\gcd(p,q)=1$, and $p<q$.
Let
\[
e \equiv (p-1)!+1 \pmod{p}, \qquad 0 \le e < p.
\]
Let $N$ be the number of integers $n$ with $1 \le n \le 11395$ such that
\[
n \equiv \left\lfloor \frac{n}{2} \right\rflo... | 64,909 | graphs = [
Graph(
let={
"_n": Const(84874),
"p": 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=12)), Eq(left=GCD(a=Var(name='p'), b=Var(name... | NT | null | COMPUTE | sympy | L3C | [
"L3C/WILSON",
"COPRIME_PAIRS/WILSON",
"BIG_OMEGA_ZERO"
] | 5bbeb3 | nt_euler_phi_compute_v1 | negation_mod | 7 | 2 | [
"BIG_OMEGA_ZERO",
"COPRIME_PAIRS",
"L3C",
"WILSON"
] | 4 | 0.006 | 2026-02-08T12:48:43.626870Z | {
"verified": true,
"answer": 64909,
"timestamp": "2026-02-08T12:48:43.633271Z"
} | 5640f7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 2079
},
"timestamp": "2026-02-09T13:52:23.949Z",
"answer": 64908
},
{
... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": 1.42,
"mid": 4.59,
"hi": 7.07
} | ||
efa765 | antilemma_k3_v1_1470522791_488 | Let $x$ be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $17477$. Compute the remainder when $95174 \cdot x$ is divided by $92015$. | 843 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=17477), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(95174),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(92015)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:02:26.505722Z | {
"verified": true,
"answer": 843,
"timestamp": "2026-02-08T13:02:26.506629Z"
} | 1b5d03 | 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": 2316
},
"timestamp": "2026-02-15T08:43:31.698Z",
"answer": 843
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d34f37 | nt_sum_over_divisible_v1_784195855_7907 | Let $d$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 200$. Let $U = 11175$. Define $R$ to be the sum of all positive integers $n \leq U$ such that $$n \equiv \sum_{k=0}^{8} (-1)^k \binom{8}{k} \pmod{d}.$$ Find the remainder when $44121 \cdot R$ is divided by $87469$. | 58,526 | graphs = [
Graph(
let={
"_n": Const(87469),
"upper": Const(11175),
"divisor": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(n... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | e741ba | nt_sum_over_divisible_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.351 | 2026-02-08T09:36:49.970339Z | {
"verified": true,
"answer": 58526,
"timestamp": "2026-02-08T09:36:50.320960Z"
} | 1ad23b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2417
},
"timestamp": "2026-02-24T11:34:58.478Z",
"answer": 58526
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6d05e5 | modular_count_residue_v1_124444284_9700 | Let $m = \sum_{k=1}^{4} k$. Let $r$ be the number of integers $t$ such that $5 \leq t \leq 15$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Compute the number of positive integers $n$ such that $1 \leq n \leq 73984$ and $n \equiv r \pmod{m}$. | 7,398 | graphs = [
Graph(
let={
"upper": Const(73984),
"m": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"r": 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... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | modular_count_residue_v1 | null | 4 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 2.915 | 2026-02-08T12:37:44.488311Z | {
"verified": true,
"answer": 7398,
"timestamp": "2026-02-08T12:37:47.403054Z"
} | a2ae23 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1055
},
"timestamp": "2026-02-15T02:45:20.076Z",
"answer": 7398
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c28e6e | comb_binomial_compute_v1_1918700295_1490 | Let $ n $ be the smallest divisor of $ 221 $ that is at least $ 2 $. Let $ k = 7 $. Define $ \binom{n}{k} $ as the binomial coefficient. Let $ Q $ be the remainder when $ 65552 \cdot \binom{n}{k} $ is divided by $ 95295 $. Compute $ Q $. | 39,132 | graphs = [
Graph(
let={
"_n": Const(95295),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(221))))),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T05:52:01.952979Z | {
"verified": true,
"answer": 39132,
"timestamp": "2026-02-08T05:52:01.955023Z"
} | 37ed19 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1396
},
"timestamp": "2026-02-12T15:21:30.764Z",
"answer": 39132
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d86864 | comb_sum_binomial_row_v1_1915831931_2923 | Let $m = 2$ and $n = 2$. Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 28$ and there exist positive integers $a \in [1,7]$, $b \in [1,2]$ satisfying
$$
t = 2a + 7b.
$$
Let $N$ be the largest prime number $n_1$ such that $n \leq n_1 \leq |T|$. Compute $m^N$. | 8,192 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T17:14:23.810676Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T17:14:23.814166Z"
} | 8c3d2f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1023
},
"timestamp": "2026-02-16T09:14:34.862Z",
"answer": 8192
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
9a3a9a | antilemma_k3_v1_865884756_837 | Compute the sum $$\sum_{d\mid 62936} \varphi(d),$$ where $\varphi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $62936$. | 62,936 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=62936), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:37:24.521250Z | {
"verified": true,
"answer": 62936,
"timestamp": "2026-02-08T15:37:24.521873Z"
} | 6fc2b5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 475
},
"timestamp": "2026-02-16T06:10:20.151Z",
"answer": 129024
},
{
"id": 11... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
976333 | modular_inverse_v1_153355830_1384 | Let $m$ be the largest prime number between $2$ and $860$, inclusive. Find the smallest positive integer $x$ such that $1 \leq x \leq 858$ and $38x \equiv 1 \pmod{m}$. | 746 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(38),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(860)), IsPrime(Var("n"))))),
"upper": Const(858),
"result": MinOverSet(set=SolutionsS... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.035 | 2026-02-08T06:22:25.886989Z | {
"verified": true,
"answer": 746,
"timestamp": "2026-02-08T06:22:25.922365Z"
} | dc760e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1353
},
"timestamp": "2026-02-12T23:07:35.079Z",
"answer": 746
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cd794e | comb_binomial_compute_v1_458359167_5724 | Let $n = \sum_{d \mid 13} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute $\binom{n}{6}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(13),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | comb_binomial_compute_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:40:00.842876Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T12:40:00.843752Z"
} | 84df0c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 824
},
"timestamp": "2026-02-16T04:01:41.520Z",
"answer": 1716
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
5babe3 | nt_count_divisible_v1_717093673_3266 | Let $n = 100$. 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.
Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 80656$ and $k$ is divisible by $d$. Comput... | 77,646 | graphs = [
Graph(
let={
"_n": Const(100),
"upper": Const(80656),
"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 | 2.521 | 2026-02-08T17:28:14.498434Z | {
"verified": true,
"answer": 77646,
"timestamp": "2026-02-08T17:28:17.019741Z"
} | 25d0cb | 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": 1163
},
"timestamp": "2026-02-18T02:02:58.059Z",
"answer": 77646
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca756b | nt_sum_over_divisible_v1_1742523217_2896 | Let $N = 5031$. Define $p_{\text{max}}$ to be the largest prime number $p$ such that $2 \leq p \leq N$. Compute the sum of all positive integers $n$ such that $1 \leq n \leq p_{\text{max}}$ and $n$ is divisible by $136$. | 90,576 | graphs = [
Graph(
let={
"_n": Const(5031),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"divisor": Const(136),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | SUM | sympy | COMB1 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"COMB1",
"MAX_PRIME_BELOW"
] | 2 | 2.757 | 2026-02-08T05:26:06.326728Z | {
"verified": true,
"answer": 90576,
"timestamp": "2026-02-08T05:26:09.083527Z"
} | bdceb3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 2091
},
"timestamp": "2026-02-12T08:59:36.632Z",
"answer": 90576
},
... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
12d036 | diophantine_fbi2_count_v1_2051736721_933 | Let $k = 1260$. Compute the number of integers $d$ such that $2 \leq d \leq 112$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 115$. | 18 | graphs = [
Graph(
let={
"k": Const(1260),
"a": Const(1),
"b": Const(4),
"upper": Const(111),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(112)), Divides(divisor=Var("d"), dividend=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.069 | 2026-02-08T15:45:49.837909Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T15:45:49.906901Z"
} | 54dc64 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 1681
},
"timestamp": "2026-02-16T12:33:53.595Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
13e5af | sequence_lucas_compute_v1_1520064083_6137 | Let $n = 22$. Define $L_n$ to be the $n$-th Lucas number. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 158$. Compute the remainder when $L_n^2 + 8L_n + M$ is divided by $71506$. | 22,046 | graphs = [
Graph(
let={
"_n": Const(158),
"n": Const(22),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(8), Ref("result")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | bf138c | sequence_lucas_compute_v1 | quadratic_mod | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T07:52:59.154563Z | {
"verified": true,
"answer": 22046,
"timestamp": "2026-02-08T07:52:59.156238Z"
} | c2ad1a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1674
},
"timestamp": "2026-02-13T13:23:26.487Z",
"answer": 22046
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fb3e2e | comb_sum_binomial_mod_v1_1918700295_3120 | Let $S = \sum_{k=9}^{367} \binom{442}{k}$, and let $r$ be the remainder when $S$ is divided by $10477$. Compute the Bell number $B_n$, where $n = |r| \bmod 11$.
Find the value of $B_n$. | 877 | graphs = [
Graph(
let={
"sum": Summation(var="k", start=Const(9), end=Const(367), expr=Binom(n=Const(442), k=Var("k"))),
"result": Mod(value=Ref("sum"), modulus=Const(10477)),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Re... | COMB | null | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT"
] | 477d5f | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"SUM_INDEPENDENT"
] | 1 | 0.098 | 2026-02-08T08:23:24.833542Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T08:23:24.931281Z"
} | e72301 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T09:33:54.610Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V8_SUM... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
c823fd | lte_diff_endings_v1_168721529_591 | Let $a = 259$, $b = 9$, $p = 5$, $K = 5$, and $N = 2936690$. Define $d = a - b$, and let $v$ be the largest integer such that $p^v$ divides $d$. Let $t = K - v$, and define $p^t$ and $p^{t+1}$ accordingly. Let $c_1 = \left\lfloor \frac{N}{p^t} \right\rfloor$ and $c_2 = \left\lfloor \frac{N}{p^{t+1}} \right\rfloor$.
C... | 93,974 | graphs = [
Graph(
let={
"a_val": Const(259),
"b_val": Const(9),
"p_val": Const(5),
"K_val": Const(5),
"N_val": Const(2936690),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("ab_diff"), base=Re... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T13:08:47.809609Z | {
"verified": true,
"answer": 93974,
"timestamp": "2026-02-08T13:08:47.810539Z"
} | 2edc68 | 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": 968
},
"timestamp": "2026-02-09T06:43:01.261Z",
"answer": 93974
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.5,
"hi": -3.01
} | ||
ab6294 | nt_max_prime_below_v1_1520064083_4929 | Let $n = 10$. Determine the set of all positive integers $d$ such that $\phi(2) \leq d \leq 2$ and $d$ divides $n$, and let $m$ be the maximum element of this set. Find the largest prime number $p$ such that $m \leq p \leq 77841$. Compute this prime number. | 77,839 | graphs = [
Graph(
let={
"_n": Const(10),
"upper": Const(77841),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), EulerPhi(n=Const(2))), Leq(Var("d"), Const(2)), Divides(di... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"ONE_PHI_2"
] | 62a6de | nt_max_prime_below_v1 | null | 3 | 0 | [
"MAX_DIVISOR",
"ONE_PHI_2"
] | 2 | 1.851 | 2026-02-08T06:31:12.479966Z | {
"verified": true,
"answer": 77839,
"timestamp": "2026-02-08T06:31:14.330864Z"
} | f5232a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 341
},
"timestamp": "2026-02-19T09:34:00.816Z",
"answer": 77839
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
29e868 | alg_poly_orbit_count_v1_1218484723_6878 | Let $f(x) = (x^2 + 7) \bmod 37$. For a non-negative integer $a$, define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$, $K = f(T)$. Find the number of integers $a$ with $0 \le a \le 13467$ such that $K = a$, but $a$ does not appear in the sequence $N, M, R, S, T$. | 2,184 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(7)), modulus=Const(37)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(7)), modulus=Const(37)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(7)), modulus=Const(37)),
"p4": ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.018 | 2026-02-25T08:19:55.768599Z | {
"verified": true,
"answer": 2184,
"timestamp": "2026-02-25T08:19:55.786253Z"
} | 75b554 | 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": 7447
},
"timestamp": "2026-03-30T02:58:48.809Z",
"answer": 6
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
2b3307 | antilemma_k3_v1_458359167_3180 | Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $28695$. | 28,695 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=28695), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T07:00:55.594881Z | {
"verified": true,
"answer": 28695,
"timestamp": "2026-02-08T07:00:55.595375Z"
} | 469e3d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 1504
},
"timestamp": "2026-02-15T18:49:24.334Z",
"answer": 30960
},
{
"id": 11,... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
9a5fc5 | comb_sum_binomial_row_v1_168721529_1781 | Let $n = 11$ and $r = 2^n$. Let $c$ be the largest prime number $p$ such that $2 \le p \le 6$. Compute the remainder when $c - r$ is divided by $54218$. | 52,175 | graphs = [
Graph(
let={
"n": Const(11),
"result": Pow(Const(2), Ref("n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6)), IsPrime(Var("n"))))),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modul... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | comb_sum_binomial_row_v1 | negation_mod | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:54:55.428696Z | {
"verified": true,
"answer": 52175,
"timestamp": "2026-02-08T13:54:55.430548Z"
} | ca6082 | 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": 452
},
"timestamp": "2026-02-09T21:33:24.368Z",
"answer": 52175
},
{
"i... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
e21537 | nt_count_coprime_v1_784195855_8800 | Let $n = 2$ and let $k$ be the smallest integer $d \geq n$ such that $d$ divides $640987$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq 89401$ such that $\gcd(n, k) = 1$. Compute the number of elements in $S$. Let $c = 24025$, and let $Q$ be the remainder when $c$ minus this count is divided by $66815$. F... | 5,326 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(89401),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(640987))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), co... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 13.007 | 2026-02-08T16:21:58.960405Z | {
"verified": true,
"answer": 5326,
"timestamp": "2026-02-08T16:22:11.967474Z"
} | c78f94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1193
},
"timestamp": "2026-02-17T01:11:13.355Z",
"answer": 5326
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
62e88e | nt_min_phi_inverse_v1_865884756_269 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 84$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 14$, and $t = 7a + 2b$. Let $n = |T|$. Now, let $U$ be the set of all positive integers $n$ such that $1 \leq n \leq 70$ and $n$ is divisible by $n$. Let $S$ be the su... | 60,261 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=V... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/SUM_DIVISIBLE",
"ONE_PHI_1"
] | 7415f6 | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"LIN_FORM",
"ONE_PHI_1",
"SUM_DIVISIBLE"
] | 3 | 0.015 | 2026-02-08T15:17:26.775579Z | {
"verified": true,
"answer": 60261,
"timestamp": "2026-02-08T15:17:26.790549Z"
} | 11eba4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 304,
"completion_tokens": 4067
},
"timestamp": "2026-02-10T06:20:57.152Z",
"answer": 60261
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status... | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
d66043 | geo_visible_lattice_v1_1520064083_1110 | Let $n = 90$. A visible lattice point $(x, y)$ from the origin is a point with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Let $R$ be the number of such visible lattice points. Given that $c = 11449$, compute $c - R$. | 6,490 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(11449),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.176 | 2026-02-08T03:47:51.841055Z | {
"verified": true,
"answer": 6490,
"timestamp": "2026-02-08T03:47:52.017522Z"
} | 45d3ba | 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": 6617
},
"timestamp": "2026-02-10T15:45:28.179Z",
"answer": 6490
},
{
"i... | 1 | [] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||||
f0a555 | nt_count_with_divisor_count_v1_458359167_1449 | Let $r$ be the number of positive integers $n$ such that $n \leq 32761$ and $n$ has exactly $9$ positive divisors. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x,y)$ such that $xy = 36$. Let $p$ be the largest prime number $n$ such that $2 \leq n \leq s$. Compute the remainder when the ... | 50,071 | graphs = [
Graph(
let={
"_m": Const(65904),
"_n": Const(2),
"upper": Const(32761),
"div_count": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var... | NT | COMB | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | 2f1f5e | nt_count_with_divisor_count_v1 | bell_mod | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 6.436 | 2026-02-08T04:37:03.216216Z | {
"verified": true,
"answer": 50071,
"timestamp": "2026-02-08T04:37:09.652592Z"
} | 7610ac | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 3631
},
"timestamp": "2026-02-10T17:21:08.177Z",
"answer": 50071
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
7308f6 | modular_mod_compute_v1_655260480_4915 | Let $a$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 128$. Let $m$ be the largest positive integer at most $8192$ that divides $67248128$. Compute the remainder when $a$ is divided by $m$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(8192),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(128)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"B1"
] | 059db4 | modular_mod_compute_v1 | null | 3 | 0 | [
"B1",
"MAX_DIVISOR"
] | 2 | 0.006 | 2026-02-08T18:12:51.330903Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T18:12:51.336776Z"
} | c97288 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 351
},
"timestamp": "2026-02-16T12:12:11.055Z",
"answer": 4096
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6e7c2d | antilemma_cartesian_v1_784195855_3557 | Let $x$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 19$ and $1 \le j \le 34$. Compute the value of $$ x + \phi(|x| + 1) + \tau(|x| + \binom{13}{0}), $$ where $\phi(n)$ is Euler's totient function and $\tau(n)$ is the number of positive divisors of $n$. | 1,294 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(19)), right=IntegerRange(start=Const(1), end=Const(34)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Binom(... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_BINOM_0"
] | 674433 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_0"
] | 2 | 0.002 | 2026-02-08T06:30:07.826832Z | {
"verified": true,
"answer": 1294,
"timestamp": "2026-02-08T06:30:07.828343Z"
} | 4d7b1c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 766
},
"timestamp": "2026-02-24T06:19:15.103Z",
"answer": 1294
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
76ad20 | sequence_lucas_compute_v1_865884756_5649 | Let $n = \sum_{k=1}^{6} k$. Define $r = L_n$, where $L_n$ denotes the $n$th Lucas number. Compute the remainder when $21367 \cdot r$ is divided by $58208$. | 38,020 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"_c": Const(21367),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(58208)),
},
... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T18:44:52.290437Z | {
"verified": true,
"answer": 38020,
"timestamp": "2026-02-08T18:44:52.291454Z"
} | b9a8a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 1727
},
"timestamp": "2026-02-18T18:59:14.039Z",
"answer": 38020
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bc15da | comb_count_permutations_fixed_v1_1470522791_431 | Let $m = 525$ and $n$ be the number of integers $t$ such that $5 \leq t \leq 14$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $k$ be the smallest divisor of $m$ that is at least $2$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!x$ denotes the nu... | 43,944 | graphs = [
Graph(
let={
"_m": Const(525),
"_n": Const(52120),
"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'), righ... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T13:01:13.456455Z | {
"verified": true,
"answer": 43944,
"timestamp": "2026-02-08T13:01:13.459971Z"
} | a01b84 | 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": 1506
},
"timestamp": "2026-02-15T08:25:56.001Z",
"answer": 43944
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
097a6a | comb_catalan_compute_v1_898971024_1944 | Let $T$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 5$, $1 \le b \le 6$, $5 \le t \le 28$, and $t = 2a + 3b$. Let $N = |T|$. Define $S$ as the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = N$. Let $n = |S|$. Compute the $n$... | 20,178 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=V... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T16:26:11.518224Z | {
"verified": true,
"answer": 20178,
"timestamp": "2026-02-08T16:26:11.520851Z"
} | 3b0dfc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 3403
},
"timestamp": "2026-02-24T21:10:02.696Z",
"answer": 20178
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
e12349 | lte_diff_endings_v1_168721529_1240 | Let $ a = 21 $, $ b = 6 $, $ p = 5 $, $ K = 4 $, and $ N = 9003210 $. Let $ d = a - b $, and let $ v_p(d) $ be the largest integer $ k $ such that $ p^k $ divides $ d $. Define $ m = K - v_p(d) $ and let $ p^m $ be the $ m $-th power of $ p $. Finally, let $ x $ be the greatest integer less than or equal to $ \frac{N}{... | 72,025 | graphs = [
Graph(
let={
"a_val": Const(21),
"b_val": Const(6),
"p_val": Const(5),
"K_val": Const(4),
"N_val": Const(9003210),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_va... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T13:32:49.674606Z | {
"verified": true,
"answer": 72025,
"timestamp": "2026-02-08T13:32:49.675193Z"
} | fbcedb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 531
},
"timestamp": "2026-02-09T14:57:14.028Z",
"answer": 72025
},
{
"i... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.5,
"hi": -3.01
} | ||
94fb6f_n | alg_qf_psd_min_v1_1218484723_5190 | An engineer is designing a triangular support frame with side parameters represented by positive integers $(a,b,c)$, each constrained by $1 \le a \le 59$, $1 \le b \le 59$, and $1 \le c \le 59$. The total cost of the frame is modeled by
$$\sum_{k=1}^{\min\{ x + y : (x, y),\ x > 0, y > 0, x y = 2601 \}} \varphi(k) \cdot... | 19,982 | ALG | null | COMPUTE | sympy | B3 | [
"B3/K2"
] | 9f3175 | alg_qf_psd_min_v1 | null | 7 | null | [
"B3",
"K2"
] | 2 | 2.305 | 2026-02-25T06:49:12.678961Z | null | 2d3434 | 94fb6f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 349,
"completion_tokens": 13820
},
"timestamp": "2026-03-30T22:58:20.098Z",
"answer": 19982
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
caf6dd | geo_count_lattice_rect_v1_458359167_3744 | Let $a = 81$ and $b = 146$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Let $Q$ be the remainder when $38106 \cdot \text{result}$ is divided by $98407$. Compute $Q$. | 64,255 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(146),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(38106), Ref("result")), modulus=Const(98407)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T11:18:48.287109Z | {
"verified": true,
"answer": 64255,
"timestamp": "2026-02-08T11:18:48.287688Z"
} | a416a4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1831
},
"timestamp": "2026-02-24T13:34:35.308Z",
"answer": 64255
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
ce6b01 | antilemma_cartesian_v1_1116507919_77 | Let $x$ be the number of ordered pairs $(a, b)$ where $a$ is an integer from 1 to 20 and $b$ is an integer from 1 to 27. Let $Q$ be the remainder when $11537 \cdot x$ is divided by 75297. Find the value of $Q$. | 55,626 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(27)))),
"_c": Const(11537),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(75297)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T02:25:18.320886Z | {
"verified": true,
"answer": 55626,
"timestamp": "2026-02-08T02:25:18.321422Z"
} | 45d4dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 2,
"correct": {
"strict": false,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2906
},
"timestamp": "2026-02-08T19:00:44.900Z",
"answer": 36095
},
{
... | 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": 0.5,
"mid": 1.97,
"hi": 3.3
} | ||
cd80c1 | diophantine_sum_product_min_v1_1248542787_482 | Let $S = 16$ and $P = 64$. Find the smallest positive integer $x$ such that $1 \leq x \leq 15$ and $x(S - x) = P$. | 8 | graphs = [
Graph(
let={
"S": Const(16),
"P": Const(64),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(15)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 0.017 | 2026-02-08T03:10:10.948848Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T03:10:10.965662Z"
} | 4aad39 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 269
},
"timestamp": "2026-02-09T04:37:12.918Z",
"answer": 8
},
{
"id": ... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -10,
"mid": -7.3,
"hi": -4.6
} | ||
11bc44 | comb_count_partitions_v1_1820931509_623 | Let $n$ be the number of integers $t$ such that $21 \leq t \leq 150$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 10$, $1 \leq b \leq 5$, and $t = 9a + 12b$. Let $p(n)$ denote the number of integer partitions of $n$. Compute $p(n)$. | 26,015 | 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=10)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T11:48:22.510875Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T11:48:22.513722Z"
} | c59bc3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5866
},
"timestamp": "2026-02-24T14:44:07.148Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
5857f3 | comb_count_surjections_v1_1218484723_4596 | Let $k = 5$ and let $M = k! \cdot S(7, k)$, where $S(7, k)$ denotes the Stirling number of the second kind. Find the remainder when $2584 - M$ is divided by $98467$. | 84,251 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": Const(2584),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(98467)),
},
goal=R... | COMB | null | COUNT | sympy | K3 | [
"COUNT_CARTESIAN/STARS_BARS"
] | c8e63c | comb_count_surjections_v1 | negation_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"K3",
"STARS_BARS"
] | 3 | 0.047 | 2026-02-25T06:16:13.584819Z | {
"verified": true,
"answer": 84251,
"timestamp": "2026-02-25T06:16:13.632183Z"
} | f3bf50 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 880
},
"timestamp": "2026-03-29T16:27:44.734Z",
"answer": 84251
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "STARS_BARS",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
523df1 | nt_count_with_divisor_count_v1_2080023795_152 | Let $n = 10$. Define $S$ as the set of all positive integers $m$ such that $1 \leq m \leq 399$ and $\gcd(m, n) = 1$. Let $t = |S|$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = t$. Define $u$ as the maximum value of $xy$ over all such pairs. Let $r$ be the number of positive in... | 159 | graphs = [
Graph(
let={
"_n": Const(10),
"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")), CountOverSet(set=SolutionsSet(var=Var("n"), c... | NT | null | COUNT | sympy | L3B | [
"C4/B1"
] | b8fbda | nt_count_with_divisor_count_v1 | null | 7 | 0 | [
"B1",
"C4",
"L3B"
] | 3 | 3.868 | 2026-02-08T11:35:01.217774Z | {
"verified": true,
"answer": 159,
"timestamp": "2026-02-08T11:35:05.085846Z"
} | e3ddfd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 5657
},
"timestamp": "2026-02-08T20:47:14.967Z",
"answer": 159
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",... | {
"lo": -0.14,
"mid": 2.22,
"hi": 4.26
} | ||
3f7f92 | comb_count_surjections_v1_717093673_870 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k = 3$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 1,806 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(7)))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1"
] | 1007b3 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T15:44:08.367240Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T15:44:08.369292Z"
} | 35f3ad | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1325
},
"timestamp": "2026-02-24T18:26:26.662Z",
"answer": 1806
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
03e85c | nt_num_divisors_compute_v1_971394319_691 | Let $n = 85849$. Compute the number of positive divisors of $n$. | 3 | graphs = [
Graph(
let={
"n": Const(85849),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B1 | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B1",
"COPRIME_PAIRS"
] | 2 | 0.014 | 2026-02-08T13:15:31.879719Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T13:15:31.893652Z"
} | bdc69e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 1209
},
"timestamp": "2026-02-15T11:44:45.293Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5057ae | comb_bell_compute_v1_865884756_7247 | Let $n = 6$. Consider all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the maximum value of $xy$ over all such pairs. Compute the Bell number $B_P$, which counts the number of partitions of a set of $P$ elements. Find the remainder when $44121$ multiplied by this Bell number is divided ... | 52,272 | graphs = [
Graph(
let={
"_n": Const(6),
"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")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T19:41:38.577029Z | {
"verified": true,
"answer": 52272,
"timestamp": "2026-02-08T19:41:38.578301Z"
} | 91e96b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1521
},
"timestamp": "2026-02-18T23:14:28.289Z",
"answer": 52272
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
7c3bf0 | comb_count_derangements_v1_124444284_9343 | Let $m = 2$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $n$ be the maximum value of $xy$ over all such pairs. Define $n'$ to be the largest prime number $n$ such that $m \leq n \leq n$. Let $\text{result}$ be the number of derangements of $n'$ elements. Compute $\text... | 1,854 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | B1 | [
"B1/MAX_PRIME_BELOW"
] | 2fc9f0 | comb_count_derangements_v1 | null | 5 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T12:25:04.492408Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T12:25:04.495287Z"
} | 587ef7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 789
},
"timestamp": "2026-02-15T00:48:14.171Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
973267 | modular_modexp_compute_v1_168721529_1021 | Let $e$ be the sum of $\phi(d)$ over all positive divisors $d$ of $6724$, where $\phi$ denotes Euler's totient function. Compute the remainder when $37^e$ is divided by $55225$. Find the value of this remainder. | 19,861 | graphs = [
Graph(
let={
"a": Const(37),
"e": SumOverDivisors(n=Const(value=6724), var='d', expr=EulerPhi(n=Var(name='d'))),
"m": Const(55225),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | modular_modexp_compute_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:24:35.180474Z | {
"verified": true,
"answer": 19861,
"timestamp": "2026-02-08T13:24:35.181741Z"
} | 49927b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 4365
},
"timestamp": "2026-02-09T12:31:35.595Z",
"answer": 12186
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": 1.84,
"mid": 5.05,
"hi": 8.38
} | ||
de1810 | alg_poly_orbit_count_v1_1419126231_162 | Let $N = (2a^3 + 3a) \bmod 41$ and $M = (2N^3 + 3N) \bmod 41$. Find the number of non-negative integers $a$ with $0 \le a \le 75152$ such that $M = a$ and $N \ne a$. | 10,998 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(3), Var("a"))), modulus=Const(41)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(3), Ref("p1"))), modulus=Const(41)),
"result": CountOverSet(set=Solutio... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.011 | 2026-02-25T09:44:24.725621Z | {
"verified": true,
"answer": 10998,
"timestamp": "2026-02-25T09:44:24.736335Z"
} | 004745 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 19630
},
"timestamp": "2026-03-30T07:23:03.707Z",
"answer": 6
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
cf392a | nt_sum_gcd_range_mod_v1_1915831931_675 | Let $N = 1000$. Define $k$ to be the number of positive integers less than or equal to $194400$ that are divisible by $324$. Let $s = \sum_{n=1}^{N} \gcd(n, k)$. Define $r$ to be the remainder when $s$ is divided by $10687$. Let $c = 38019$. Compute the remainder when $c \cdot r$ is divided by $77788$. Find the value o... | 40,310 | graphs = [
Graph(
let={
"N": Const(1000),
"k": CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k1"), Const(1)), Leq(Var("k1"), Const(194400)), Divides(divisor=Const(324), dividend=Var("k1"))), domain='positive_integers')),
"M": Const(10687),
... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | nt_sum_gcd_range_mod_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.315 | 2026-02-08T15:36:39.190312Z | {
"verified": true,
"answer": 40310,
"timestamp": "2026-02-08T15:36:39.504894Z"
} | f98bcb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 3803
},
"timestamp": "2026-02-16T10:17:54.512Z",
"answer": 40310
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
df63ff | comb_count_permutations_fixed_v1_1080341949_216 | Let $n = 11$ and let $k$ be the smallest divisor of $847$ that is at least $2$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the subfactorial of $m$. | 2,970 | graphs = [
Graph(
let={
"_n": Const(847),
"n": Const(11),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T13:18:11.710842Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T13:18:11.713777Z"
} | fc7f84 | 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": 632
},
"timestamp": "2026-02-15T12:15:26.004Z",
"answer": 2970
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
d08ca6 | sequence_count_fib_divisible_v1_458359167_3103 | Let $N$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 37$ and $1 \leq j \leq 39$ such that $\gcd(i, j) = 1$. Determine the number of positive integers $n$ with $1 \leq n \leq N$ for which the $n$th Fibonacci number is divisible by 7. | 113 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(37)), right=IntegerRange(start=Const(1), end=Const(39))))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"COUNT_COPRIME_GRID"
] | 20ec03 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 0.088 | 2026-02-08T06:56:53.802007Z | {
"verified": true,
"answer": 113,
"timestamp": "2026-02-08T06:56:53.890356Z"
} | 8640a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 3429
},
"timestamp": "2026-02-13T06:59:49.531Z",
"answer": 113
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
0b90c5 | nt_count_phi_equals_v1_677425708_1801 | Let $n$ be a positive integer. Define $k = 571$ and $U = 2916$. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq U$ and $\phi(n) = k$. Let $c$ be the largest prime number less than or equal to $5004$. Compute the value of $(r \bmod 307) + c \cdot (r \bmod 317)$. | 0 | graphs = [
Graph(
let={
"_n": Const(307),
"upper": Const(2916),
"k": Const(571),
"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"))))),
"_c": ... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_phi_equals_v1 | two_moduli | 7 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.366 | 2026-02-08T04:28:38.207534Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T04:28:38.574008Z"
} | 7ba4a4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3046
},
"timestamp": "2026-02-10T01:07:24.239Z",
"answer": 0
},
{
"id":... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
4ce750 | comb_count_surjections_v1_48377204_2000 | Let $n = |\{1, 2\} \times \{1, 2, 3, 4\}|$ and let $k$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 4$, $1 \leq j \leq 4$, and $i + j = 6$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the smallest positive integer such th... | 672 | graphs = [
Graph(
let={
"_n": Const(6),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Su... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | e4fc6a | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.021 | 2026-02-08T16:32:54.741522Z | {
"verified": true,
"answer": 672,
"timestamp": "2026-02-08T16:32:54.762963Z"
} | c05747 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1893
},
"timestamp": "2026-02-17T06:24:26.088Z",
"answer": 672
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
410121 | nt_max_prime_below_v1_717093673_1941 | Let $m$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 72$. Determine the largest prime number $n$ such that $m \leq n \leq 50000$. | 49,999 | graphs = [
Graph(
let={
"upper": Const(50000),
"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 | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.281 | 2026-02-08T16:24:49.894582Z | {
"verified": true,
"answer": 49999,
"timestamp": "2026-02-08T16:24:51.176067Z"
} | 6fbc7e | 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": 4946
},
"timestamp": "2026-02-17T03:06:27.006Z",
"answer": 49999
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f078be | nt_sum_divisors_mod_v1_1520064083_8487 | Let $S$ be the set of ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 21$, $1 \le j \le 64$, and $\gcd(i, j) = 1$. Let $n = |S|$, and let $\sigma(n)$ denote the sum of all positive divisors of $n$. Let $M = 11621$. Compute the remainder when $41019 \cdot (\sigma(n) \bmod M)$ is divided by 75335. | 9,440 | graphs = [
Graph(
let={
"_n": Const(75335),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), e... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.005 | 2026-02-08T10:13:09.799125Z | {
"verified": true,
"answer": 9440,
"timestamp": "2026-02-08T10:13:09.804391Z"
} | 82708e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 2674
},
"timestamp": "2026-02-14T06:49:07.975Z",
"answer": 9440
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d75f79 | antilemma_sum_equals_v1_124444284_3827 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $i + j = 13$, $1 \leq i \leq 11$, and $1 \leq j \leq 11$. Compute the value of
$$
353702 \cdot (|x| \bmod 97) + 329703 \cdot ((|x|^2 + 1) \bmod 101) + 215534 \cdot ((|x| + 6) \bmod 103),
$$
then find the remainder when this sum is divided by $1009091... | 40,003 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(13)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(11))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T05:37:50.659286Z | {
"verified": true,
"answer": 40003,
"timestamp": "2026-02-08T05:37:50.668975Z"
} | 9090e9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 965
},
"timestamp": "2026-02-24T04:05:16.565Z",
"answer": 40003
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
afc885 | diophantine_fbi2_count_v1_655260480_4598 | Let $d$ be an integer such that $3 \leq d \leq 171$, $d$ divides $480$, and $5 \leq \frac{480}{d} \leq m$, where $m$ is the smallest integer greater than or equal to 2 that divides $5543093$. Compute the number of such integers $d$, and let this count be $c$. Find the remainder when $44121 \cdot c$ is divided by $80897... | 66,105 | graphs = [
Graph(
let={
"_n": Const(171),
"k": Const(480),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(5)), Leq(Div(... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.011 | 2026-02-08T18:00:30.106164Z | {
"verified": true,
"answer": 66105,
"timestamp": "2026-02-08T18:00:30.117171Z"
} | 9be0e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2691
},
"timestamp": "2026-02-18T11:47:12.620Z",
"answer": 66105
},
... | 1 | [
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9566b5 | comb_catalan_compute_v1_655260480_4725 | Let $n$ be the number of integers $t$ such that $21 \leq t \leq 60$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 6a + 15b$. 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 | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:04:55.772942Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T18:04:55.775425Z"
} | 7215c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 897
},
"timestamp": "2026-02-18T13:57:11.216Z",
"answer": 16796
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
9b51dc | comb_count_permutations_fixed_v1_655260480_5883 | Let $k$ be the smallest integer $d \geq 2$ that divides $2695$.
Compute $\binom{8}{k} \cdot !(8 - k)$, where $!n$ denotes the number of derangements of $n$ elements. | 112 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(8),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(2695))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(... | NT | COMB | COUNT | sympy | COUNT_SUM_EQUALS | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR"
] | 2 | 0.016 | 2026-02-08T18:41:55.610930Z | {
"verified": true,
"answer": 112,
"timestamp": "2026-02-08T18:41:55.626723Z"
} | f29746 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 1017
},
"timestamp": "2026-02-18T19:00:25.135Z",
"answer": 112
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
649937 | comb_factorial_compute_v1_2051736721_4477 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 16464$ and
$$
\binom{16464}{j} \equiv 1 \pmod{d}
$$
for all positive divisors $d$ of $10$ that are at most $2$. Compute the value of $n!$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(16464),
"_n": Const(16464),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=MaxOverSet(set=SolutionsSet(var=Var("d"),... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/V8"
] | 3e2ce1 | comb_factorial_compute_v1 | null | 5 | 0 | [
"MAX_DIVISOR",
"V8"
] | 2 | 0.002 | 2026-02-08T18:00:32.328497Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T18:00:32.330764Z"
} | 0922fc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1313
},
"timestamp": "2026-02-18T11:32:40.034Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e7c0f2 | diophantine_fbi2_min_v1_865884756_1905 | Let $n = 15625$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $s$ be the sum $x + y$ for such a pair. Define $\text{upper}$ to be the minimum possible value of $s$ over all such pairs. Let $k = 240$. Determine the value of
$$
\sum_{i=1}^{49} i - \min\left\{ d \in \mathbb{Z... | 1,217 | graphs = [
Graph(
let={
"_n": Const(15625),
"k": Const(240),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))),... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | c64b17 | diophantine_fbi2_min_v1 | negation_mod | 5 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.012 | 2026-02-08T16:23:19.707621Z | {
"verified": true,
"answer": 1217,
"timestamp": "2026-02-08T16:23:19.719630Z"
} | 0cb57d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 789
},
"timestamp": "2026-02-16T07:20:37.385Z",
"answer": 1217
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
e8e7b2 | modular_inverse_v1_2051736721_2139 | Let $m = 1319$ and $u = 1318$. Let $a$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 114244$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3686400$. Let $r$ be the smallest positive intege... | 1,996 | 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(3686400)))), expr=Sum(Var("x"), Var("y")))),
"a": MinOverSe... | NT | null | EXTREMUM | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 84eb3e | modular_inverse_v1 | affine_mod | 7 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.065 | 2026-02-08T16:30:03.720420Z | {
"verified": true,
"answer": 1996,
"timestamp": "2026-02-08T16:30:03.785062Z"
} | 13459d | 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": 2948
},
"timestamp": "2026-02-17T05:21:52.005Z",
"answer": 1996
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
227b55 | sequence_fibonacci_compute_v1_655260480_2705 | Let $n = 20$. Define $F_n$ to be the $n$th Fibonacci number, where $F_0 = 0$, $F_1 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 2$. Let $r$ be the remainder when $|F_n|$ is divided by the largest prime number $p$ such that $2 \leq p \leq 11$. Compute the Bell number $B_r$, which counts the number of partitions of a ... | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(20),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(11... | NT | COMB | COMPUTE | sympy | V5 | [
"MAX_PRIME_BELOW"
] | 88ea9c | sequence_fibonacci_compute_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW",
"V5"
] | 2 | 0.036 | 2026-02-08T16:55:06.945269Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:55:06.981484Z"
} | f70db2 | 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": 872
},
"timestamp": "2026-02-17T15:13:56.111Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
022810 | modular_inverse_v1_1915831931_1763 | Let $a = 203$ and $m = 1373$. Let $u$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 28$ and $1 \leq j \leq 49$. Compute the smallest positive integer $x$ such that $1 \leq x \leq u$ and $203x \equiv 1 \pmod{1373}$. | 372 | graphs = [
Graph(
let={
"a": Const(203),
"m": Const(1373),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), end=Const(49)))),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), con... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_inverse_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.059 | 2026-02-08T16:25:11.236971Z | {
"verified": true,
"answer": 372,
"timestamp": "2026-02-08T16:25:11.295659Z"
} | 7c617a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 663
},
"timestamp": "2026-02-16T07:24:26.188Z",
"answer": 433
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"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
} | ||
fdf4f4 | comb_catalan_compute_v1_1419126231_178 | Let $n = \sum_{k=1}^{4} \varphi(k) \cdot \left\lfloor \frac{4}{k} \right\rfloor$, and let $C_n$ denote the $n$-th Catalan number. Compute $C_n$. | 16,796 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": Catalan(Ref("n")),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | COMB | NT | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_catalan_compute_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.014 | 2026-02-25T09:45:02.336447Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-25T09:45:02.350839Z"
} | 473f41 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 516
},
"timestamp": "2026-03-30T07:27:14.924Z",
"answer": 16796
},
{
"i... | 2 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
154c48 | nt_count_coprime_and_v1_809748730_343 | Let $k_1 = 9$. Let $k_2$ be the number of integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 2$, $1 \le b \le 8$, $9 \le t \le 30$, and $t = 7a + 2b$. Compute the number of positive integers $n \le 74574$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 24,858 | graphs = [
Graph(
let={
"upper": Const(74574),
"k1": Const(9),
"k2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ri... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 8.317 | 2026-02-08T11:28:44.962140Z | {
"verified": true,
"answer": 24858,
"timestamp": "2026-02-08T11:28:53.278730Z"
} | 250ba9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 911
},
"timestamp": "2026-02-15T22:06:49.199Z",
"answer": 62347
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
63815a | geo_count_lattice_rect_v1_677425708_1106 | Let $a = 333$ and $b = 139$. Consider the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of points with integer coordinates that lie inside or on the boundary of this rectangle. | 46,760 | graphs = [
Graph(
let={
"a": Const(333),
"b": Const(139),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0 | 2026-02-08T04:00:12.451392Z | {
"verified": true,
"answer": 46760,
"timestamp": "2026-02-08T04:00:12.451862Z"
} | 7e8af6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 311
},
"timestamp": "2026-02-09T15:42:35.461Z",
"answer": 46760
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||||
a3e73e | comb_bell_compute_v1_1520064083_9862 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 16648$ such that $\binom{16648}{j}$ is odd. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. | 4,140 | graphs = [
Graph(
let={
"_n": Const(16648),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16648)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T11:01:30.258051Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T11:01:30.259532Z"
} | 508ffb | 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": 1469
},
"timestamp": "2026-02-24T12:42:44.425Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"s... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
fb1f6a | antilemma_sum_equals_v1_717093673_1144 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 24$, $1 \leq i \leq 22$, and $1 \leq j \leq 23$. Compute the value of
$$
x + 2^{x \bmod 16} \bmod 56228.
$$ | 86 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(24)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(22)), right=IntegerRange(start=Const(1), end=Const(23))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.031 | 2026-02-08T15:53:26.296914Z | {
"verified": true,
"answer": 86,
"timestamp": "2026-02-08T15:53:26.327739Z"
} | 0e6fb5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 583
},
"timestamp": "2026-02-24T18:53:27.831Z",
"answer": 86
},
{
"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
} | ||
bea22b | alg_sum_powers_v1_1218484723_494 | Let $T = \left|\left\{ (a, b) \in \mathbb{Z}^+ \times \mathbb{Z}^+ \mid 1 \le a, b \le 40,\ 32a^4 - 128ab^3 + 192a^2b^2 - 128a^3b + 32b^4 = 8192 \right\}\right|$. Find the remainder when $\sum_{k=1}^T k^3$ is divided by $5413$. | 4,809 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=Summation(var="k", start=Const(1), end=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"), Const(40)... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_sum_powers_v1 | null | 4 | 0 | [
"POLY4_COUNT"
] | 1 | 0.003 | 2026-02-25T02:10:42.286976Z | {
"verified": true,
"answer": 4809,
"timestamp": "2026-02-25T02:10:42.289749Z"
} | b040cd | 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": 1577
},
"timestamp": "2026-03-28T22:47:56.787Z",
"answer": 4809
},
{
"i... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
19dfec | comb_sum_binomial_row_v1_1874849503_1642 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Define $n$ to be the minimum element of $T$. Compute the remainder when $44121 \cdot 2^n$ is divided by $93004$. | 12,844 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(36)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T14:00:40.726253Z | {
"verified": true,
"answer": 12844,
"timestamp": "2026-02-08T14:00:40.727763Z"
} | d1dda9 | 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": 4515
},
"timestamp": "2026-02-10T06:07:56.831Z",
"answer": 12844
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
ad8d70 | comb_count_surjections_v1_1520064083_8305 | Let $n$ be the number of integers $t$ such that $21 \leq t \leq 35$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 2$, and
$$
t = 4a + 6b + 11.
$$
Let $k = 5$. Compute $k! \cdot S(n,k)$, where $S(n,k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty ... | 1,800 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T10:07:53.996289Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T10:07:53.998499Z"
} | 3a3dbc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 1058
},
"timestamp": "2026-02-24T11:49:14.734Z",
"answer": 1800
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
54bc46 | modular_min_linear_v1_1874849503_475 | Let $a = 644$ and $b = 541$. Let $m$ be the number of integers $t$ with $12 \leq t \leq 2392$ for which there exist positive integers $a'$ and $b'$ such that $a' \leq 260$, $b' \leq 156$, and $t = 5a' + 7b'$. Let $\text{result}$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and
$$
644x \equiv 541 \pm... | 8,554 | graphs = [
Graph(
let={
"a": Const(644),
"b": Const(541),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Co... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.126 | 2026-02-08T13:04:52.587070Z | {
"verified": true,
"answer": 8554,
"timestamp": "2026-02-08T13:04:52.712729Z"
} | 1812fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 8153
},
"timestamp": "2026-02-15T09:44:24.002Z",
"answer": 8554
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8db88c | nt_count_with_divisor_count_v1_1125832087_994 | Let $d$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 15$, $1 \leq j \leq 15$, and $i + j = 17$. Determine the number of positive integers $n$ with $1 \leq n \leq 85264$ such that $n$ has exactly $d$ positive divisors. Compute the remainder when $35930$ times this count is divided by $87737$. | 49,203 | graphs = [
Graph(
let={
"upper": Const(85264),
"div_count": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(17)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Con... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 3.866 | 2026-02-08T03:24:44.339067Z | {
"verified": true,
"answer": 49203,
"timestamp": "2026-02-08T03:24:48.205547Z"
} | c44763 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 10358
},
"timestamp": "2026-02-23T19:36:25.432Z",
"answer": 49203
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
9c5788 | comb_count_partitions_v1_397696148_2474 | Let $a = 1$ and $b = 3$, and define $n_2 = a + b$. Let $e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Define $n_1 = 7 + e$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$, and let $m = |S|$. Define $s = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$, where the summation ... | 37,338 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(3),
"n2": Sum(Ref("a"), Ref("b")),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(Const(7), Ref("e")),
... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING",
"COMB1/BINOMIAL_ALTERNATING"
] | 1b81bd | comb_count_partitions_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"LIN_FORM"
] | 3 | 0.005 | 2026-02-08T13:20:29.113469Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T13:20:29.118240Z"
} | ad47d4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 363,
"completion_tokens": 14434
},
"timestamp": "2026-02-24T18:03:43.748Z",
"answer": 37338
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"l... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
e60f53 | modular_inverse_v1_677425708_1375 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 148996$. Let $s$ be the minimum value of $x + y$ over all pairs in $P$. Let $u$ be the number of positive integers $j \le s$ such that $j^2 \le 595984$. Find the smallest positive integer $x \le u$ such that $612x \equiv 1 \pmod{773}$... | 24 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(612),
"m": Const(773),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y"... | NT | null | EXTREMUM | sympy | B3 | [
"B3/C3"
] | 3e4f89 | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"C3"
] | 2 | 0.05 | 2026-02-08T04:07:45.130747Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T04:07:45.180548Z"
} | 559588 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1034
},
"timestamp": "2026-02-09T19:09:55.405Z",
"answer": 24
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
3ebe00 | sequence_count_fib_divisible_v1_1978505735_8208 | Let $d = 3$ and let $n$ be a positive integer. Determine the number of positive integers $n \le 467$ such that $d$ divides the $n$-th Fibonacci number. | 116 | graphs = [
Graph(
let={
"upper": Const(467),
"d": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | C4 | [
"ONE_PHI_1",
"B3"
] | d3bb9b | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"B3",
"C4",
"ONE_PHI_1"
] | 3 | 0.058 | 2026-02-08T20:43:54.855636Z | {
"verified": true,
"answer": 116,
"timestamp": "2026-02-08T20:43:54.913713Z"
} | de11d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 1744
},
"timestamp": "2026-02-19T01:01:32.131Z",
"answer": 116
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"l... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b56ca4 | comb_count_partitions_v1_2051736721_588 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest integer $k$ such that $m^k \leq 2004955520766$. Define $n'$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1... | 31,185 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_VAL/COUNT_SUM_EQUALS"
] | 57c7ee | comb_count_partitions_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"COUNT_SUM_EQUALS",
"MAX_VAL"
] | 3 | 0.011 | 2026-02-08T15:33:00.996022Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T15:33:01.006951Z"
} | 417af7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1393
},
"timestamp": "2026-02-16T09:06:06.201Z",
"answer": 31185
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad01f5 | nt_sum_divisors_compute_v1_1520064083_4450 | Let $n = 21025$ and define $\text{result}$ to be the sum of all positive divisors of $n$. Let $c$ be the sum of $\phi(d)$ over all positive divisors $d$ of $99$, where $\phi$ denotes Euler's totient function. Let
$$
S = \sum_{i=a}^{b} \left( \text{digit}_i(\text{result}) \cdot (i + 1)^2 \right),
$$
where $\text{digit}_... | 262 | graphs = [
Graph(
let={
"_n": Const(99),
"n": Const(21025),
"result": SumDivisors(n=Ref("n")),
"_c": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), en... | COMB | NT | COMPUTE | sympy | K3 | [
"K3",
"BINOMIAL_ALTERNATING"
] | 4de11f | nt_sum_divisors_compute_v1 | digits_weighted_mod | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"K3"
] | 2 | 0.005 | 2026-02-08T06:17:15.682954Z | {
"verified": true,
"answer": 262,
"timestamp": "2026-02-08T06:17:15.687528Z"
} | f58d8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1428
},
"timestamp": "2026-02-12T22:09:48.631Z",
"answer": 262
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V7",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f98f2a | comb_count_derangements_v1_1742523217_532 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 14$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $r = !n$ denote the subfactorial of $n$. Compute the remainder when $49864 \cdot r$ is divided by $55261$.\n\nFind the value of this remainder. | 19,488 | graphs = [
Graph(
let={
"_n": Const(55261),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:06:47.572478Z | {
"verified": true,
"answer": 19488,
"timestamp": "2026-02-08T03:06:47.574713Z"
} | c6f4f7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 7240
},
"timestamp": "2026-02-09T19:11:04.576Z",
"answer": 19488
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
cc2713 | comb_catalan_compute_v1_124444284_1747 | Let $n$ be the number of integers $t$ such that $12 \leq t \leq 24$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 3a + 2b + 7$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by $78289$. | 60,825 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:07:52.764681Z | {
"verified": true,
"answer": 60825,
"timestamp": "2026-02-08T04:07:52.766547Z"
} | 0b3476 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2713
},
"timestamp": "2026-02-23T23:30:14.150Z",
"answer": 60825
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
32864e | geo_count_lattice_triangle_v1_1125832087_1286 | Let $A$ be twice the area of the triangle with vertices at $(100, 169)$, $(256, 377)$, and $(0, 0)$, given by
$$
|100 \cdot 377 - 256 \cdot 169|.
$$
Let $B$ be the sum of the greatest common divisors of the absolute differences in coordinates along each side of the triangle:
$$
\gcd(100, 169) + \gcd(156, 208) + \gcd(25... | 2,756 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=377)), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=169))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=169))), GCD(a=Abs(arg=Sub(left=Const(value=256), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T03:40:29.298437Z | {
"verified": true,
"answer": 2756,
"timestamp": "2026-02-08T03:40:29.300316Z"
} | cd0e24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 590
},
"timestamp": "2026-02-10T15:22:39.789Z",
"answer": 2756
},
{
"id... | 1 | [] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||||
f1e6d4 | geo_count_lattice_rect_v1_784195855_2544 | Let $a = 81$ and $b = 57$. Define the rectangle with corners at $(0,0)$ and $(a,b)$. Let $R$ be the number of lattice points contained in this rectangle, including the boundary. Compute the remainder when $88811 \cdot R$ is divided by $87376$. | 9,532 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(57),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(88811), Ref("result")), modulus=Const(87376)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T05:50:50.540833Z | {
"verified": true,
"answer": 9532,
"timestamp": "2026-02-08T05:50:50.541309Z"
} | f32b50 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1152
},
"timestamp": "2026-02-24T04:35:49.459Z",
"answer": 9532
},
{
"i... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
3bac61 | nt_sum_divisors_mod_v1_458359167_882 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 705600$. Let $\sigma$ be the sum of the positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10771$. | 5,952 | 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(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10771... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:08:54.045581Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T04:08:54.047919Z"
} | f45a2b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1407
},
"timestamp": "2026-02-10T15:34:52.111Z",
"answer": 5952
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f6108e | comb_count_partitions_v1_1874849503_1217 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 40$. Let $P$ be the maximum value of $xy$ over all pairs in $S$. Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = P$. Let $n$ be the minimum value of $x + y$ over all pairs in $T$. Let $p(n)$ de... | 28,810 | graphs = [
Graph(
let={
"_n": Const(78309),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var... | COMB | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_count_partitions_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T13:42:07.081074Z | {
"verified": true,
"answer": 28810,
"timestamp": "2026-02-08T13:42:07.083864Z"
} | a24556 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 8097
},
"timestamp": "2026-02-24T18:58:03.651Z",
"answer": 28810
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
00c28e | modular_mod_compute_v1_1520064083_6403 | Let $a = -29584$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 3694084$. Let $m$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when $a$ is divided by $m$. | 1,168 | graphs = [
Graph(
let={
"a": Const(-29584),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3694084)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:03:38.561479Z | {
"verified": true,
"answer": 1168,
"timestamp": "2026-02-08T08:03:38.562645Z"
} | e5f5c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1088
},
"timestamp": "2026-02-13T14:22:45.659Z",
"answer": 1168
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a3da34 | nt_count_coprime_and_v1_898971024_751 | Let $n = 57373$ and $u = 33606$. Compute the number of positive integers $m$ such that $1 \leq m \leq u$, $\gcd(m, 4) = 1$, and $\gcd(m, 9) = 1$. Let $r$ denote this count. Now consider the set of all pairs of positive integers $(x, y)$ such that $xy = 100$. Let $s$ be the minimum value of $x + y$ over all such pairs. ... | 4,648 | graphs = [
Graph(
let={
"_n": Const(57373),
"upper": Const(33606),
"k1": Const(4),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k... | NT | null | COUNT | sympy | B3 | [
"B3"
] | d720b5 | nt_count_coprime_and_v1 | quadratic_mod | 5 | 0 | [
"B3"
] | 1 | 4.416 | 2026-02-08T15:37:42.830899Z | {
"verified": true,
"answer": 4648,
"timestamp": "2026-02-08T15:37:47.246897Z"
} | 25bff1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1829
},
"timestamp": "2026-02-16T11:49:48.591Z",
"answer": 4648
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b94232_n | comb_count_partitions_v1_1419126231_1729 | A game show awards points in increments of 6 or 8, with a contestant selecting between 1 and 11 actions worth 6 points each, and between 1 and 5 actions worth 8 points each. The total score $t$ must be at least 14 and at most 106. Let $n$ be the number of distinct possible scores. The prize level $Q$ is equal to the nu... | 44,583 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-25T11:14:49.383749Z | null | 4bf939 | b94232 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 7248
},
"timestamp": "2026-03-31T05:04:34.282Z",
"answer": 44583
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
e0d127 | sequence_fibonacci_compute_v1_1915831931_3870 | Let $n$ be the number of integers $t$ such that $18 \leq t \leq 48$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 4$, and $t = 3a + 4b + 11$.
Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 75,025 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T17:58:14.027314Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T17:58:14.029896Z"
} | 39ea35 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1701
},
"timestamp": "2026-02-18T11:37:32.697Z",
"answer": 75025
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
696b76 | comb_binomial_compute_v1_784195855_1536 | Let $n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$. Compute $\binom{n}{6}$. | 5,005 | 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"))))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T05:07:48.624171Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T05:07:48.625257Z"
} | 23f582 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 713
},
"timestamp": "2026-02-11T22:16:37.689Z",
"answer": 5005
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
84c70e_n | comb_sum_binomial_mod_v1_1218484723_5613 | A coding competition has a scoring system where each participant earns points of the form $3a + 2b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$. Let $T$ be the set of all distinct scores between $5$ and $17$ inclusive that can be achieved. Separately, a data pipeline computes $\sum_{k=23}^{193} \binom{204}{k}$ and takes ... | 4,140 | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | comb_sum_binomial_mod_v1 | bell_mod | 5 | null | [
"LIN_FORM"
] | 1 | 0.023 | 2026-02-25T07:08:06.857409Z | null | fe6f3a | 84c70e | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T23:50:45.780Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} |
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