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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3c35f1 | nt_count_divisors_in_range_v1_1978505735_3416 | Let $m = 4368$. Define $\_n$ to be the number of positive integers $n_1$ with $1 \leq n_1 \leq m$ such that $13$ divides the $n_1$-th Fibonacci number. Let $n = 720$, $a = 1$, and define $b$ to be the number of positive integers $n_2$ with $1 \leq n_2 \leq \_n$ such that $6$ divides $n_2$ and $\gcd(n_2, 35) = 1$. Compu... | 22 | graphs = [
Graph(
let={
"_m": Const(4368),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_m")), Divides(divisor=Const(13), dividend=Fibonacci(arg=Var(name='n1')))))),
"n": Const(720),
"a": Const(... | NT | null | COUNT | sympy | LIN_FORM | [
"COUNT_FIB_DIVISIBLE/C5"
] | 33774d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"C5",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 0.101 | 2026-02-08T17:38:00.172120Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T17:38:00.273239Z"
} | 670a21 | 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": 3204
},
"timestamp": "2026-02-18T04:52:36.484Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
87aada | antilemma_k2_v1_1742523217_4777 | Compute $$
\sum_{k=1}^{118} \phi(k) \left\lfloor \frac{118}{k} \right\rfloor,
$$ where $\phi(k)$ denotes Euler's totient function. | 7,021 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(118), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(118), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T09:06:52.499442Z | {
"verified": true,
"answer": 7021,
"timestamp": "2026-02-08T09:06:52.499835Z"
} | 2bb6e4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 441
},
"timestamp": "2026-02-14T00:25:31.464Z",
"answer": 7021
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
58b920 | comb_sum_binomial_row_v1_1353956133_829 | Let $w = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $e = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$. Define $r = (2w)^{12}$. Let $c$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 49$ and $1 \leq j \leq 49$, plus $e$. Compute the remainder when $c - r$ is divided by $73919$. | 72,224 | graphs = [
Graph(
let={
"n2": Const(0),
"w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Const(2),
"b": Const(2),
"n1": Sum(Ref("a"), Ref("b")),
"e": Summat... | COMB | null | SUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING"
] | 59cbf7 | comb_sum_binomial_row_v1 | negation_mod | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T11:52:54.775366Z | {
"verified": true,
"answer": 72224,
"timestamp": "2026-02-08T11:52:54.777221Z"
} | 074047 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 563
},
"timestamp": "2026-02-24T14:52:57.237Z",
"answer": 72224
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma":... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
6f860c | geo_count_lattice_triangle_v1_48377204_2551 | Let $n = 121$. Define the quantity
$$
\text{area\_2x} = \left| 121n - 48 \cdot 19 \right|.
$$
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 22$. Define
$$
m = \max_{(x,y) \in S} (xy).
$$
Now define the boundary term
$$
\text{boundary} = \gcd(|m|, 19) + \gcd(|48 - 121|, |121 - ... | 14,422 | graphs = [
Graph(
let={
"_n": Const(121),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_n'), Const(value=121)), Mul(Const(value=48), Sub(left=Const(value=0), right=Const(value=19))))),
"boundary": Sum(GCD(a=Abs(arg=MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Va... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.006 | 2026-02-08T16:48:45.381941Z | {
"verified": true,
"answer": 14422,
"timestamp": "2026-02-08T16:48:45.387591Z"
} | 16f555 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 1353
},
"timestamp": "2026-02-17T12:11:54.803Z",
"answer": 14422
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f0b664 | alg_qf_psd_min_v1_601307018_279 | Find the minimum value of $$1648a d + 824c d + 11124 a^2 + 7416a c + 10300 c^2 + 5356 b^2 - 4120a b + 9064b c + 4120b d + \min\{ |x - y| : x > 0, y > 0, xy = 12228985 \} \cdot d^2$$ over all ordered quadruples $(a, b, c, d)$ of positive integers with $1 \le a, b, c, d \le 3$. | 48,204 | graphs = [
Graph(
let={
"_n": Const(11124),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(3)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(3)), Geq(Var("c"... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | alg_qf_psd_min_v1 | null | 4 | 0 | [
"B3_DIFF"
] | 1 | 0.025 | 2026-03-10T00:49:40.502812Z | {
"verified": true,
"answer": 48204,
"timestamp": "2026-03-10T00:49:40.528277Z"
} | 296d30 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T22:42:18.742Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.99,
"mid": 6.05,
"hi": 8.63
} | ||
093d0e | comb_count_surjections_v1_865884756_1074 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 7$. Let $k$ be the number of ordered pairs $(x_{11}, x_{21})$ of positive odd integers such that $x_{11} + x_{21} = 10$. Compute $k!$ multiplied by the Stirling number of the second kind $S(n, k)$. | 1,800 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(nam... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.008 | 2026-02-08T15:46:46.127212Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T15:46:46.135002Z"
} | be0eef | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 769
},
"timestamp": "2026-02-24T18:35:55.758Z",
"answer": 1800
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
df75b9 | antilemma_k2_v1_655260480_1973 | Let $n = 174$. Compute the sum
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $m$ be the absolute value of this sum plus 2. Find the smallest positive integer $Q$ such that the $Q$-th Fibonacci number is divisible by $m$. Compute $Q$. | 15,228 | graphs = [
Graph(
let={
"_n": Const(174),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(174), Var("k"))))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("... | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.004 | 2026-02-08T16:29:45.936181Z | {
"verified": true,
"answer": 15228,
"timestamp": "2026-02-08T16:29:45.940406Z"
} | a75bf9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 2118
},
"timestamp": "2026-02-17T04:30:36.941Z",
"answer": 15228
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
730911 | nt_sum_gcd_range_mod_v1_1520064083_5876 | Let $N$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 39$ and $1 \leq b \leq 52$. Compute the sum $\sum_{n=1}^{N} \gcd(n, 168)$, and let $r$ be the remainder when this sum is divided by $10753$. Find the value of $|r| \bmod 50414$. | 4,897 | graphs = [
Graph(
let={
"N": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(39)), right=IntegerRange(start=Const(1), end=Const(52)))),
"k": Const(168),
"M": Const(10753),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), ex... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.178 | 2026-02-08T07:42:00.765793Z | {
"verified": true,
"answer": 4897,
"timestamp": "2026-02-08T07:42:00.943338Z"
} | 448a42 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 2418
},
"timestamp": "2026-02-13T11:41:00.203Z",
"answer": 4897
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
1fb08f | comb_count_derangements_v1_1440796553_1284 | Let $ n $ be the largest prime number such that $ 2 \leq n \leq 7 $.
Define $ D_n $ to be the number of derangements of $ n $ elements. Let $ Q $ be the remainder when $ 44121 \cdot D_n $ is divided by $ 66502 $.
Compute $ Q $. | 2,874 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("resul... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:38:16.541509Z | {
"verified": true,
"answer": 2874,
"timestamp": "2026-02-08T13:38:16.543242Z"
} | 102887 | 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": 1638
},
"timestamp": "2026-02-15T19:24:24.983Z",
"answer": 2874
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
219180 | diophantine_fbi2_count_v1_1520064083_2580 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 44100$. Let $S$ be the set of all integers $d$ satisfying the following conditions:
- $d \geq 3$,
- $d \leq t$, where $t$ is the number of positive integers $n \leq 260$ such that the sum of the decimal digits ... | 18 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(44100),
"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")), Ref("_n")))), expr... | NT | null | COUNT | sympy | K2 | [
"L3B",
"B3"
] | e8deef | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"K2",
"L3B"
] | 3 | 0.11 | 2026-02-08T04:52:09.076268Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T04:52:09.186535Z"
} | f1e3bc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 4089
},
"timestamp": "2026-02-11T22:23:57.256Z",
"answer": 18
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ac9f9e | comb_binomial_compute_v1_458359167_3815 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 282$ such that $\binom{282}{j}$ is odd. Compute $\binom{n}{9}$. | 11,440 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(282)), Eq(Mod(value=Binom(n=Const(282), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k": Const(9),
"result"... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_binomial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T11:22:44.556567Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T11:22:44.558286Z"
} | 56fb79 | 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": 918
},
"timestamp": "2026-02-24T13:34:41.415Z",
"answer": 11440
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
0f119c | nt_lcm_compute_v1_124444284_2287 | Let $a$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 5720$. Let $b = 1064$, and let $L$ be the least common multiple of $a$ and $b$. Find the remainder when $86253 \cdot L$ is divided by $72511$. | 17,984 | graphs = [
Graph(
let={
"_n": Const(5720),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_lcm_compute_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T04:35:09.489878Z | {
"verified": true,
"answer": 17984,
"timestamp": "2026-02-08T04:35:09.491378Z"
} | e6576f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2680
},
"timestamp": "2026-02-10T17:14:45.793Z",
"answer": 17984
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
890141 | comb_bell_compute_v1_717093673_3796 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 18$. Define $\text{result} = B_n$, where $B_n$ denotes the $n$-th Bell number, the number of partitions of a set of $n$ elements. Let $Q$ be the remainder when $44121 \cdot \text{result}$ is divided by $57280$. Compute $... | 50,147 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_bell_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T17:52:16.928899Z | {
"verified": true,
"answer": 50147,
"timestamp": "2026-02-08T17:52:16.930677Z"
} | c9a40e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2248
},
"timestamp": "2026-02-18T09:02:08.676Z",
"answer": 50147
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b05688 | comb_catalan_compute_v1_1742523217_1105 | Let $ S $ be the set of all ordered pairs $ (x_1, x_2) $ of positive odd integers such that $ x_1 + x_2 = t $, where $ t $ is an integer for which there exist integers $ a $ and $ b $ with $ 1 \leq a \leq 5 $, $ 1 \leq b \leq 4 $, $ 21 \leq t \leq 96 $, and $ t = 12a + 9b $. Let $ n $ be the number of elements in $ S $... | 6,005 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T03:25:28.374648Z | {
"verified": true,
"answer": 6005,
"timestamp": "2026-02-08T03:25:28.376981Z"
} | d1ad0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:21:02.188Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
c2617b | nt_sum_divisors_mod_v1_2051736721_3792 | Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq 360$ and $j^5 \leq 6046617600000$. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $10243$. | 1,170 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(360)), Leq(Pow(Var("j"), Const(5)), Const(6046617600000))), domain='positive_integers')),
"M": Const(10243),
"sigma": SumDivisors(n=Ref("n")... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.006 | 2026-02-08T17:33:18.716683Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T17:33:18.722625Z"
} | 80ce92 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1271
},
"timestamp": "2026-02-18T04:21:55.060Z",
"answer": 1170
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
950b15 | antilemma_k2_v1_1918700295_4178 | Let $n = 252$. Compute
$$
\sum_{k=1}^{n} \varphi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 252} \varphi(d) \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. | 31,878 | graphs = [
Graph(
let={
"_n": Const(252),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=252), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T09:12:22.943188Z | {
"verified": true,
"answer": 31878,
"timestamp": "2026-02-08T09:12:22.943948Z"
} | 2b3b70 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 1128
},
"timestamp": "2026-02-14T01:46:18.868Z",
"answer": 31878
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemm... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
997111_n | alg_poly4_min_v1_1419126231_858 | Two engineers adjust settings $a$ and $b$, each between 1 and 190, to minimize the power consumption of a machine. The power used is given by $12806 b^{4} + 65664 a^{2} b^{2} - 12768 a^{3} b + 12806 a^{4} + 12768 a b^{3}$ watts. What is the lowest possible power consumption in whole watts? | 91,276 | ALG | null | COMPUTE | sympy | C3 | [
"C3/STARS_BARS",
"B3"
] | 12a7e8 | alg_poly4_min_v1 | null | 3 | null | [
"B3",
"C3",
"STARS_BARS"
] | 3 | 0.17 | 2026-02-25T10:20:06.869327Z | null | 5bfded | 997111 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 29335
},
"timestamp": "2026-03-31T04:04:46.561Z",
"answer": 91276
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "STARS_BARS",
"status": "ok_later"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
afc4a4 | comb_sum_binomial_row_v1_1419126231_343 | Find the number of non-negative integers $j$ with $0 \leq j \leq 33304$ such that $\binom{33304}{j}$ is odd, and compute $2$ raised to this number. | 65,536 | graphs = [
Graph(
let={
"_n": Const(33304),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(33304), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | SUM | sympy | V8 | [
"V8"
] | 86348e | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-25T09:51:13.005314Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-25T09:51:13.007068Z"
} | 5f0454 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2243
},
"timestamp": "2026-03-30T08:07:51.453Z",
"answer": 65536
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma":... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
8d7163 | algebra_poly_eval_v1_48377204_805 | Let $x = 22$ and $n = 3$. Compute the value of
$$
x^3 + \left( \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor \right) x^2 - 10x - 3.
$$ | 13,329 | graphs = [
Graph(
let={
"_n": Const(3),
"x": Const(22),
"result": Sum(Pow(Ref("x"), Const(3)), Mul(Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))), Pow(Ref("x"), Const(2))), Mul(Const(-10), Ref("x")), Const... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T15:42:43.669679Z | {
"verified": true,
"answer": 13329,
"timestamp": "2026-02-08T15:42:43.672271Z"
} | f4173c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 691
},
"timestamp": "2026-02-16T06:14:57.779Z",
"answer": 13339
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
85c97d | alg_poly4_count_v1_601307018_2678 | Let $A = \sum_{\substack{a_1,b_1,c \geq 1 \\ a_1^2 + b_1^2 + c^2 = a_1b_1 + b_1c + ca_1 \\ 4a_1 + \left|\left\{ (a_2,b_2) \in [1,30]^2 : 64a_2^3 + 27b_2^3 + 144a_2^2b_2 + 108a_2b_2^2 = 493039 \right\}\right| \cdot b_1 + 2c = 65}} (a_1^3 + b_1^3 + c^3)$ and $B = \sum_{\substack{a_3,b_3,c_1 \geq 1 \\ a_3^2 + b_3^2 + c_1^... | 375 | graphs = [
Graph(
let={
"_c": Const(30),
"_m": Const(4),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple... | ALG | null | COUNT | sympy | POLY3_COUNT | [
"POLY3_COUNT/SUM_SQUARES_IDENTITY"
] | c95cc6 | alg_poly4_count_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"SUM_SQUARES_IDENTITY"
] | 2 | 1.869 | 2026-03-10T03:21:26.100562Z | {
"verified": true,
"answer": 375,
"timestamp": "2026-03-10T03:21:27.969861Z"
} | 455e8c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 427,
"completion_tokens": 4977
},
"timestamp": "2026-03-29T06:08:23.808Z",
"answer": 375
},
{
"id... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok_later"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
de35f0 | alg_poly_orbit_hensel_v1_601307018_2854 | Let $N = (a^2 + a + 1750) \bmod 6859$, $M = (N^2 + N + 1750) \bmod 6859$, $R = (M^2 + M + 1750) \bmod 6859$, $S = (R^2 + R + 1750) \bmod 6859$, $T = (S^2 + S + 1750) \bmod 6859$, and $K = (T^2 + T + 1750) \bmod 6859$. Let $Q$ be the number of non-negative integers $a$ with $0 \leq a \leq 5665533$ such that $K = a$, but... | 14,868 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(1750)), modulus=Const(6859)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(1750)), modulus=Const(6859)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(1... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.086 | 2026-03-10T03:28:56.867008Z | {
"verified": true,
"answer": 14868,
"timestamp": "2026-03-10T03:28:56.953077Z"
} | 16dc49 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 20839
},
"timestamp": "2026-03-29T06:42:48.145Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
edc9e7 | comb_bell_compute_v1_898971024_568 | Let $n = 8$. The Bell number $B_n$ is the number of partitions of a set of $n$ elements. Let $R = B_8$. Compute the remainder when $44121 \cdot R$ is divided by 55141. | 33,948 | graphs = [
Graph(
let={
"n": Const(8),
"result": Bell(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(55141)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/B1"
] | 844731 | comb_bell_compute_v1 | null | 3 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.008 | 2026-02-08T15:32:30.951737Z | {
"verified": true,
"answer": 33948,
"timestamp": "2026-02-08T15:32:30.959693Z"
} | 3a83f6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1088
},
"timestamp": "2026-02-24T17:57:16.773Z",
"answer": 33948
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"stat... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
5f1032 | nt_count_digit_sum_v1_1520064083_9056 | Let $S$ be the set of all positive integers $n \leq 19998$ such that the sum of the digits of $n$ is even. Let $T$ be the set of all positive integers $n \leq |S|$ such that the sum of the digits of $n$ is 16. Compute the remainder when $64 - |T|$ is divided by 56050. | 55,481 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19998)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"target_sum": Const(16),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | nt_count_digit_sum_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.712 | 2026-02-08T10:31:56.613202Z | {
"verified": true,
"answer": 55481,
"timestamp": "2026-02-08T10:31:57.325508Z"
} | 85f317 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 2946
},
"timestamp": "2026-02-14T07:39:14.710Z",
"answer": 55481
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8c02a5 | antilemma_cartesian_v1_1918700295_424 | Compute the value of $Q = (21 \times 37) - (15 \times 21)$. Find the value of $Q$. | 462 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Const(21)))),
"_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_CARTESIAN"
] | f9c395 | antilemma_cartesian_v1 | negation_mod | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T03:13:08.790526Z | {
"verified": true,
"answer": 462,
"timestamp": "2026-02-08T03:13:08.792140Z"
} | d6f7db | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 143
},
"timestamp": "2026-02-10T13:25:50.681Z",
"answer": 462
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
4c9b00 | geo_count_lattice_rect_v1_1874849503_354 | Let $a = 64$ and $b = 206$. Define the rectangle $R$ as the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points in $R$. | 13,455 | graphs = [
Graph(
let={
"a": Const(64),
"b": Const(206),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.003 | 2026-02-08T12:57:47.437914Z | {
"verified": true,
"answer": 13455,
"timestamp": "2026-02-08T12:57:47.441223Z"
} | 88354b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 237
},
"timestamp": "2026-02-09T16:08:03.443Z",
"answer": 13455
},
{
"i... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
b14dac | modular_count_residue_v1_1353956133_259 | Let $m$ be the largest prime number less than or equal to $11$. Let $p$ be a positive integer and $q$ an integer such that $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Let $n$ be the number of such integers $p$. Let $S$ be the set of all prime numbers between $n$ and $m$, inclusive, and let $m'$ be the largest element of... | 7,384 | graphs = [
Graph(
let={
"_m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), cond... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 4eefd3 | modular_count_residue_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 4.737 | 2026-02-08T11:21:41.124439Z | {
"verified": true,
"answer": 7384,
"timestamp": "2026-02-08T11:21:45.861125Z"
} | 1330ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1332
},
"timestamp": "2026-02-14T13:17:08.542Z",
"answer": 7384
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6c401a | modular_mod_compute_v1_971394319_1659 | Let $m$ be the number of integers $j$ with $0 \leq j \leq 8191$ such that $\binom{8191}{j}$ is odd. Compute the remainder when $18496$ is divided by $m$. | 2,112 | graphs = [
Graph(
let={
"_n": Const(8191),
"a": Const(18496),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8191)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegativ... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.011 | 2026-02-08T13:49:49.546646Z | {
"verified": true,
"answer": 2112,
"timestamp": "2026-02-08T13:49:49.557738Z"
} | daaa0d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 566
},
"timestamp": "2026-02-24T19:10:15.644Z",
"answer": 2112
},
{
"id... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.9,
"mid": -1.69,
"hi": 1.31
} | ||
0865f0 | comb_factorial_compute_v1_124444284_5066 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 77$ and $n$ is divisible by $77$. Let $n_0$ be the smallest integer at least $2$ that divides the sum of the elements of $S$. Compute $n_0!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(77),
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n")... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MIN_PRIME_FACTOR"
] | 57d6d0 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 2 | 0.001 | 2026-02-08T06:22:48.744868Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T06:22:48.746355Z"
} | 225e40 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 343
},
"timestamp": "2026-02-12T23:16:03.775Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"sta... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
892181 | diophantine_fbi2_min_v1_1742523217_4798 | Let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 33$, and $\gcd(i, j) = 1$. Let $d$ be a positive integer such that $4 \leq d \leq 82$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. Define $\text{result}$ to be the smallest such $d$. Let $Q$ be the remainder ... | 47,636 | graphs = [
Graph(
let={
"_n": Const(7),
"k": 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(3)), right=IntegerRange(start=Const(1), end=Co... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"SUM_ARITHMETIC"
] | 5912d6 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"SUM_ARITHMETIC"
] | 2 | 0.006 | 2026-02-08T09:08:16.917008Z | {
"verified": true,
"answer": 47636,
"timestamp": "2026-02-08T09:08:16.923368Z"
} | 2e7775 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1086
},
"timestamp": "2026-02-14T02:35:51.117Z",
"answer": 47636
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8a25be | antilemma_sum_primes_v1_458359167_1497 | Let $a = 7$. Let $b$ be the number of nonnegative integers $j \leq 2144$ such that $\binom{2144}{j}$ is odd. Let $s = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ is the M\"obius function. Let $n = s$, and let $e = \sum_{d \mid n} \mu(d)$. Let $x$ be the sum of all prime numbers $n$ such that $2 \leq n \leq 3$. Compute... | 22,217 | graphs = [
Graph(
let={
"a": Const(7),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2144)), Eq(Mod(value=Binom(n=Const(2144), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"s": S... | NT | null | COMPUTE | sympy | V8 | [
"V8/MOBIUS_COPRIME",
"MOBIUS_SUM",
"SUM_PRIMES"
] | 2ea00a | antilemma_sum_primes_v1 | null | 7 | 2 | [
"MOBIUS_COPRIME",
"MOBIUS_SUM",
"SUM_PRIMES",
"V8"
] | 4 | 0.002 | 2026-02-08T04:39:09.404059Z | {
"verified": true,
"answer": 22217,
"timestamp": "2026-02-08T04:39:09.406225Z"
} | f56b8b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 827
},
"timestamp": "2026-02-18T13:04:42.821Z",
"answer": 22217
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "SUM_PRIMES",
"stat... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
e7c24d | sequence_fibonacci_compute_v1_971394319_473 | Let $m = 15$. Let $A$ be the set of all positive integers $n$ with $1 \leq n \leq 480$ such that $m$ divides the $n$-th Fibonacci number. Let $N$ be the number of elements in $A$. Let $B$ be the set of all prime numbers $n$ such that $2 \leq n \leq N$. Let $p$ be the largest element of $B$. Compute the $p$-th Fibonacci... | 28,657 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(480)), Divides(divisor=Ref("_m"), dividend=Fibonacci(arg=Var(name='n')))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n")... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW"
] | c3fe6d | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T13:06:46.717021Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T13:06:46.720171Z"
} | 0fcc83 | 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": 1050
},
"timestamp": "2026-02-15T09:44:52.422Z",
"answer": 28657
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cb23c5 | modular_count_residue_v1_677425708_1055 | Let $N = 36$ and $U = 60516$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = N$. Define $r$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $T$ be the set of all positive integers $n$ such that $1 \le n \le U$ and $n \equiv r \pmod{17}$. Compute $55440 - |T|$. | 51,880 | graphs = [
Graph(
let={
"_n": Const(36),
"upper": Const(60516),
"m": Const(17),
"r": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 4 | 0 | [
"B3"
] | 1 | 2.268 | 2026-02-08T03:59:01.516753Z | {
"verified": true,
"answer": 51880,
"timestamp": "2026-02-08T03:59:03.785051Z"
} | 1471c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 963
},
"timestamp": "2026-02-09T15:15:16.256Z",
"answer": 51880
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
93a3be | alg_poly3_min_v1_601307018_8359 | Let $V = \left|\left\{ j : 0 \leq j \leq 15223,\ \binom{15223}{j} \bmod 2 = 1 \right\}\right|$, and let $W = \left|\left\{ v : 32 \leq v \leq V,\ \text{there exist integers } a, b \text{ with } 1 \leq a, b \leq 8 \text{ such that } 18b^2 + 12ab + 2a^2 = v \right\}\right|$. Find the remainder when
$$
\min\left\{ -242a^3... | 10,472 | graphs = [
Graph(
let={
"_m": Const(29),
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), con... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8/QF_PSD_DISTINCT"
] | df60d6 | alg_poly3_min_v1 | null | 7 | 0 | [
"QF_PSD_DISTINCT",
"V8"
] | 2 | 0.089 | 2026-03-10T08:51:13.862456Z | {
"verified": true,
"answer": 10472,
"timestamp": "2026-03-10T08:51:13.951931Z"
} | c0e8b7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 368,
"completion_tokens": 13052
},
"timestamp": "2026-04-19T08:53:32.065Z",
"answer": 10472
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"statu... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
113d7c | diophantine_fbi2_count_v1_1520064083_6316 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 44100$. Let $T$ be the set of integers $t$ such that $22 \le t \le 186$ and $t = 14a + 8b$ for some integers $a, b$ with $1 \le a \le 7$ and $1 \le b \le 11$. Let $s$ be the number of divisors $d$ of $k$ such that $2 \l... | 24 | graphs = [
Graph(
let={
"_n": Const(65),
"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(44100)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.015 | 2026-02-08T08:01:16.810873Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T08:01:16.825709Z"
} | 652641 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 4135
},
"timestamp": "2026-02-13T14:02:15.900Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f2f583 | nt_lcm_compute_v1_1439011603_803 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 1064$. Let $b = 607$. Let $r = \mathrm{lcm}(a, b)$. Find the remainder when $15269 \cdot r$ is divided by $87718$. | 49,941 | graphs = [
Graph(
let={
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1064)), IsPrime(Var("n"))))),
"b": Const(607),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(Const(15269), Ref("result... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_lcm_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:44:27.072604Z | {
"verified": true,
"answer": 49941,
"timestamp": "2026-02-08T15:44:27.074614Z"
} | bac472 | 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": 1639
},
"timestamp": "2026-02-16T12:43:17.261Z",
"answer": 49941
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
509857 | modular_inverse_v1_1470522791_1594 | Let $a$ be the sum of all positive integers $n \leq 125$ such that $n$ is divisible by $125$. Let $m = 419$. Find the smallest positive integer $x \leq 418$ such that $a \cdot x \equiv 1 \pmod{m}$. Compute the remainder when $44121$ times this value of $x$ is divided by $62501$. | 630 | graphs = [
Graph(
let={
"_n": Const(125),
"a": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(125)), Const(0))))),
"m": Const(419),
"upper": Const(418),
... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | modular_inverse_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.021 | 2026-02-08T13:46:15.927373Z | {
"verified": true,
"answer": 630,
"timestamp": "2026-02-08T13:46:15.948533Z"
} | 91f52d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1833
},
"timestamp": "2026-02-15T20:17:17.712Z",
"answer": 630
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
92a6c4 | antilemma_sum_primes_v1_1125832087_622 | Let $n$ be the largest integer such that $31^n$ divides $31^{21}$. Compute the sum of all prime numbers $p$ such that $2 \leq p \leq n$. | 77 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxKDivides(target=Pow(Const(31), Const(21)), base=Const(31))), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"K14/SUM_PRIMES",
"SUM_PRIMES"
] | 4b6635 | antilemma_sum_primes_v1 | null | 3 | 0 | [
"K14",
"MAX_PRIME_BELOW",
"SUM_PRIMES"
] | 3 | 0.012 | 2026-02-08T03:10:14.026969Z | {
"verified": true,
"answer": 77,
"timestamp": "2026-02-08T03:10:14.039066Z"
} | f99f81 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 302
},
"timestamp": "2026-02-17T20:11:07.559Z",
"answer": 77
}
] | 2 | [
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
}... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
22e5d4 | comb_catalan_compute_v1_1116507919_428 | Let $n$ be the number of integers $t$ such that $15 \leq t \leq 51$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 6a + 9b$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when $74486 \cdot C_n$ is divided by 52241. | 50,099 | graphs = [
Graph(
let={
"_n": Const(52241),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T02:34:11.413825Z | {
"verified": true,
"answer": 50099,
"timestamp": "2026-02-08T02:34:11.415575Z"
} | efd581 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 3438
},
"timestamp": "2026-02-08T19:32:39.041Z",
"answer": 50099
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"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"
}
] | {
"lo": 2.05,
"mid": 3.37,
"hi": 4.63
} | ||
6ee945 | diophantine_product_count_v1_1470522791_1284 | Let $m = 976$ and $n = 86944$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Let $u$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of positive integers $x$ such that $1 \leq x \le... | 82,980 | graphs = [
Graph(
let={
"_m": Const(976),
"_n": Const(86944),
"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(129600))))... | NT | null | COUNT | sympy | COMB1 | [
"COMB1",
"B3"
] | 44bb30 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.018 | 2026-02-08T13:33:06.380071Z | {
"verified": true,
"answer": 82980,
"timestamp": "2026-02-08T13:33:06.398434Z"
} | 0f1b65 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 2750
},
"timestamp": "2026-02-15T18:10:45.140Z",
"answer": 82980
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
460925 | nt_count_divisible_and_v1_865884756_181 | Let $d_1$ be the largest integer $k$ such that $3^k \le 55296$, and let $d_2 = 12$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \le n \le 164376$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute $\text{result}$. | 4,566 | graphs = [
Graph(
let={
"_n": Const(55296),
"upper": Const(164376),
"d1": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(3), Var("k")), Ref("_n")))),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"MAX_VAL"
] | 1 | 7.303 | 2026-02-08T15:15:00.686415Z | {
"verified": true,
"answer": 4566,
"timestamp": "2026-02-08T15:15:07.989260Z"
} | af3551 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 830
},
"timestamp": "2026-02-10T05:11:13.601Z",
"answer": 4566
},
{
"id... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"s... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
28b36e | comb_count_partitions_v1_971394319_422 | Let $c = 6$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = c$. Define $m$ to be the maximum value of $xy$ as $(x,y)$ ranges over $S$. Let $a$ and $b$ be positive integers with $1 \le a \le 3$ and $1 \le b \le 3$. Let $T$ be the set of all integers $t$ such that $15 \le t \le 45... | 48,749 | graphs = [
Graph(
let={
"_c": Const(6),
"_m": 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("_c")))), expr=Mul(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | B1 | [
"B1/LIN_FORM/K2"
] | 4c01d9 | comb_count_partitions_v1 | null | 6 | 0 | [
"B1",
"K2",
"LIN_FORM"
] | 3 | 0.003 | 2026-02-08T13:04:47.717351Z | {
"verified": true,
"answer": 48749,
"timestamp": "2026-02-08T13:04:47.720423Z"
} | 1c9e36 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 2198
},
"timestamp": "2026-02-15T08:57:11.050Z",
"answer": 48749
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok_lat... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0bc997 | alg_poly3_count_v1_1218484723_4794 | Let $S = \{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 152, 1 \leq b \leq 59 \text{ such that } t = 2a + 3b + 13,\, 18 \leq t \leq 494 \}$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 475$ and $1 \leq b \leq |S|$ such that $-8a^3 - 24a^2b - 24ab^2 - 8b^3 = -... | 344 | graphs = [
Graph(
let={
"_n": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(475)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exi... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"LIN_FORM"
] | 7b2633 | alg_poly3_count_v1 | null | 6 | 0 | [
"LIN_FORM",
"QF_PSD_DISTINCT"
] | 2 | 1.874 | 2026-02-25T06:27:16.358969Z | {
"verified": true,
"answer": 344,
"timestamp": "2026-02-25T06:27:18.232510Z"
} | 32ed27 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 7867
},
"timestamp": "2026-03-29T17:42:06.593Z",
"answer": 344
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
5163d9 | antilemma_k2_v1_397696148_1831 | Let $n = 165$. Compute the value of
$$
\sum_{k=1}^{\sum_{d \mid 165} \phi(d)} \phi(k) \left\lfloor \frac{165}{k} \right\rfloor.
$$ | 13,695 | graphs = [
Graph(
let={
"_n": Const(165),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=165), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.001 | 2026-02-08T12:47:51.810774Z | {
"verified": true,
"answer": 13695,
"timestamp": "2026-02-08T12:47:51.812264Z"
} | 752d65 | 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": 937
},
"timestamp": "2026-02-15T05:44:02.526Z",
"answer": 13695
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
207674 | nt_sum_totient_over_divisors_v1_48377204_1119 | Let $n = 81665$. Define $\phi(d)$ to be the number of positive integers less than or equal to $d$ that are relatively prime to $d$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Let $Q$ be the remainder when $74955$ times this sum is divided by $56713$. Find the value of $Q$. | 52,559 | graphs = [
Graph(
let={
"n": Const(81665),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(74955),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(56713)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V5"
] | e79893 | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"LIN_FORM",
"V5"
] | 2 | 0.033 | 2026-02-08T15:54:27.894063Z | {
"verified": true,
"answer": 52559,
"timestamp": "2026-02-08T15:54:27.927525Z"
} | a6d84a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1799
},
"timestamp": "2026-02-16T16:16:37.968Z",
"answer": 52559
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
763528 | modular_sum_quadratic_residues_v1_865884756_2231 | Let $p$ be the largest prime number less than or equal to 618. Compute $\frac{p(p-1)}{4}$. | 95,018 | graphs = [
Graph(
let={
"_n": Const(618),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:38:55.301121Z | {
"verified": true,
"answer": 95018,
"timestamp": "2026-02-08T16:38:55.303310Z"
} | a64ead | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 606
},
"timestamp": "2026-02-17T08:03:23.058Z",
"answer": 95018
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
363160 | diophantine_product_count_v1_397696148_2284 | Let $k = 60$. Define $S$ as the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 400$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Let $\text{upper}$ be the minimum element of $T$. Now consider the set of all positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divide... | 10 | graphs = [
Graph(
let={
"k": Const(60),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(400)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.107 | 2026-02-08T13:05:24.496008Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T13:05:24.602971Z"
} | 03b757 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1121
},
"timestamp": "2026-02-16T04:24:48.768Z",
"answer": 11
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
1fc69d | nt_max_prime_below_v1_898971024_1531 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $S$. Determine the largest prime number $n$ such that $c \leq n \leq 51529$. | 51,521 | graphs = [
Graph(
let={
"upper": Const(51529),
"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 | 2.875 | 2026-02-08T16:11:16.411373Z | {
"verified": true,
"answer": 51521,
"timestamp": "2026-02-08T16:11:19.286385Z"
} | 725588 | 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": 3687
},
"timestamp": "2026-02-16T22:29:53.592Z",
"answer": 51521
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc6547_l | antilemma_sum_equals_v1_458359167_5191 | Let $n = 88$. Define $x$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 88$, $1 \leq i \leq 87$, and $1 \leq j \leq 88$. Let $c = 45360$. Compute the value of
$$
\sum_{i=0}^{\lfloor \log_{10} |x| \rfloor} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^2 + c.
$$ | 45,396 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T12:20:28.806755Z | {
"verified": false,
"answer": 45399,
"timestamp": "2026-02-08T12:20:28.810285Z"
} | 231d0a | dc6547 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 7740
},
"timestamp": "2026-02-24T15:35:00.926Z",
"answer": 45396
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | |
5db9b7 | modular_mod_compute_v1_971394319_1748 | Let $S$ be the set of all positive integers $t$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 955$, $1 \leq b \leq 25$, $7 \leq t \leq 2035$, and $t = 2a + 5b$.
Let $n$ be the number of elements in $S$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $a... | 20,424 | graphs = [
Graph(
let={
"_n": Const(11779),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"), co... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | modular_mod_compute_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T13:53:18.101155Z | {
"verified": true,
"answer": 20424,
"timestamp": "2026-02-08T13:53:18.104596Z"
} | 9764b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 3772
},
"timestamp": "2026-02-15T21:40:24.685Z",
"answer": 20424
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
72a9f2_l | algebra_quadratic_discriminant_v1_677425708_3896 | Let $a = 2$, $b = -12$, and $c = 18$. Let $D = b^2 - 4ac \cdot N$, where $N$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 600$, $\gcd(p, q) = 1$, and $p < q$. Compute $$ 2 \cdot [D > 0] + [D = 0], $$ where $[P]$ denotes the Iverson bracket, which is $1$ if ... | 0 | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"COPRIME_PAIRS"
] | 2 | 0.009 | 2026-02-08T06:01:18.356865Z | {
"verified": false,
"answer": 1,
"timestamp": "2026-02-08T06:01:18.365892Z"
} | 1ea0cd | 72a9f2 | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1446
},
"timestamp": "2026-02-12T18:29:04.623Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | |
1dff09 | nt_count_coprime_and_v1_1978505735_795 | Let $k_1$ be the smallest integer $d \geq 2$ that divides $35$, and let $k_2 = 11$. Compute the number of positive integers $n$ such that $1 \leq n \leq 25320$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 18,415 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(25320),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(35))))),
"k2": Const(11),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.84 | 2026-02-08T15:36:25.663934Z | {
"verified": true,
"answer": 18415,
"timestamp": "2026-02-08T15:36:28.503866Z"
} | 9be846 | 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": 786
},
"timestamp": "2026-02-16T09:47:10.274Z",
"answer": 18415
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5e0034 | lte_diff_endings_v1_151522320_351 | Let $a = 7$, $b = 1$, $p = 2$, and $K = 9$. Let $v_p(n)$ denote the largest integer $k$ such that $p^k$ divides $n$. Compute the largest integer $t$ such that $p^t$ divides $(a - b)$ but $p^{t+1}$ does not divide $(a + b)$, adjusted by $t = (K + 1) - v_p(a - b) - v_p(a + b)$. Let $p^t$ and $p^{t+1}$ divide $N = 7916939... | 61,851 | graphs = [
Graph(
let={
"a_val": Const(7),
"b_val": Const(1),
"p_val": Const(2),
"K_val": Const(9),
"N_val": Const(7916939),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("ab_diff"), base=Ref(... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 5 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:09:56.182927Z | {
"verified": true,
"answer": 61851,
"timestamp": "2026-02-08T03:09:56.183832Z"
} | b3e24f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 345,
"completion_tokens": 1216
},
"timestamp": "2026-02-09T01:44:50.080Z",
"answer": 61851
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
bbb405 | nt_count_intersection_v1_784195855_5757 | Let $a$ be the smallest divisor of $5929$ that is at least $2$. Let $N = 50000$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, 15) = 1$. | 3,810 | graphs = [
Graph(
let={
"_n": Const(5929),
"N": Const(50000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"b": Const(15),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.064 | 2026-02-08T08:06:40.251266Z | {
"verified": true,
"answer": 3810,
"timestamp": "2026-02-08T08:06:42.314841Z"
} | ceecad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1105
},
"timestamp": "2026-02-13T14:29:55.607Z",
"answer": 3810
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
909de0_n | modular_sum_quadratic_residues_v1_601307018_739 | A rectangular garden has area $107646$ square meters, with side lengths that are positive integers. The gardener wants to minimize the absolute difference between the length and width. Let $p$ be this minimal difference. Define $M = \frac{p(p - 1)}{4}$. Compute the remainder when $44121M$ is divided by $69127$. | 14,376 | NT | null | SUM | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | modular_sum_quadratic_residues_v1 | null | 4 | null | [
"B3_DIFF"
] | 1 | 0.002 | 2026-03-10T01:23:00.234279Z | null | 29bf2a | 909de0 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 9019
},
"timestamp": "2026-03-29T14:25:58.261Z",
"answer": 14376
},
{
"... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
5ef91a | nt_sum_totient_over_divisors_v1_397696148_2313 | Let $n = 29160$. Define $\text{result}$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Let $\_n = 10090$, and let $\_c$ be the number of positive integers $n$ with $1 \leq n \leq 10090$ such that $5$ divides the $n$th Fibonacci number. Compute the value of
$$
Q = \sum_{i=0}^{... | 2,245 | graphs = [
Graph(
let={
"_n": Const(10090),
"n": Const(29160),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 926637 | nt_sum_totient_over_divisors_v1 | digits_weighted_mod | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.004 | 2026-02-08T13:06:09.189075Z | {
"verified": true,
"answer": 2245,
"timestamp": "2026-02-08T13:06:09.193308Z"
} | b84d87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1344
},
"timestamp": "2026-02-15T09:17:01.087Z",
"answer": 2245
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
27e3d1 | alg_poly_preperiod_count_v1_601307018_1008 | Let $N = (a^2 - 7) \bmod 83$, $M = (N^2 - 7) \bmod 83$, $R = (M^2 - 7) \bmod 83$, and $S = (R^2 - 7) \bmod 83$. Find the number of non-negative integers $a$ with $0 \leq a \leq 131056$ such that $S = N$, $M \neq N$, and $R \neq N$. | 9,474 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-7)), modulus=Const(83)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-7)), modulus=Const(83)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-7)), modulus=Const(83)),
"p4... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.019 | 2026-03-10T01:34:43.932735Z | {
"verified": true,
"answer": 9474,
"timestamp": "2026-03-10T01:34:43.951427Z"
} | d146e9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T00:59:28.081Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.84,
"mid": 4.95,
"hi": 7.12
} | ||
ccb1af | comb_count_surjections_v1_677425708_2880 | Let $n = 4$ and $k = 4$. Define $s$ to be the number of ways to partition a set of $n$ elements into $k$ nonempty subsets, multiplied by $k!$. Compute the remainder when $53420 \cdot s$ is divided by $96229$. | 31,103 | graphs = [
Graph(
let={
"n": Const(4),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Mul(Const(53420), Ref("result")), modulus=Const(96229)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_count_surjections_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.038 | 2026-02-08T05:21:46.712605Z | {
"verified": true,
"answer": 31103,
"timestamp": "2026-02-08T05:21:46.750120Z"
} | ac7863 | 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": 898
},
"timestamp": "2026-02-24T03:18:12.045Z",
"answer": 31103
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
b350dd | geo_count_lattice_rect_v1_655260480_3382 | Let $a = 144$ and $b = 440$. Define $\mathrm{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Compute the remainder when $2026 - \mathrm{result}$ is divided by $69684$. | 7,765 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(440),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(2026),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(69684)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.005 | 2026-02-08T17:21:30.140709Z | {
"verified": true,
"answer": 7765,
"timestamp": "2026-02-08T17:21:30.145285Z"
} | 32252d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 614
},
"timestamp": "2026-02-18T00:48:08.269Z",
"answer": 7765
},
{
... | 1 | [] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||||
efd0f7 | geo_count_lattice_rect_v1_1431428450_37 | Compute the remainder when $44121$ multiplied by the number of lattice points in the rectangle $[0, 128] \times [0, 157]$ is divided by $77038$. (A lattice point is a point with integer coordinates.) | 9,648 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(157),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(77038)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T13:09:23.999907Z | {
"verified": true,
"answer": 9648,
"timestamp": "2026-02-08T13:09:24.000976Z"
} | 189e6e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1388
},
"timestamp": "2026-02-24T17:29:41.782Z",
"answer": 8648
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
d0d1eb | modular_mod_compute_v1_865884756_6479 | Let $a$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 10070$ and $\binom{10070}{j} \equiv 1 \pmod{2}$. Compute the remainder when $a$ is divided by $12769$. | 256 | graphs = [
Graph(
let={
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(10070)), Eq(Mod(value=Binom(n=Const(10070), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"m... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T19:13:39.042367Z | {
"verified": true,
"answer": 256,
"timestamp": "2026-02-08T19:13:39.043861Z"
} | 2bd628 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 2521
},
"timestamp": "2026-02-18T21:38:31.520Z",
"answer": 256
},
{
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
cd1aa3 | nt_min_coprime_above_v1_1439011603_2691 | Let $ m = 54574 $ and $ n = 15 $. Define $ S $ to be the set of all positive integers $ t $ such that $ 33 \leq t \leq 23064 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 179 $, $ 1 \leq b \leq 996 $, and $ t = 12a + 21b $. Let $ k $ be the number of positive integers $ \nu $ such that $ 1 \l... | 49,319 | graphs = [
Graph(
let={
"_m": Const(54574),
"_n": Const(15),
"start": Const(50000),
"upper": Const(50393),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE"
] | 95eec8 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.078 | 2026-02-08T16:54:47.891947Z | {
"verified": true,
"answer": 49319,
"timestamp": "2026-02-08T16:54:47.969692Z"
} | ff0b1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 3786
},
"timestamp": "2026-02-17T16:20:15.362Z",
"answer": 49319
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
65ee1b | comb_bell_compute_v1_1742523217_4531 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 33800$ and $\binom{33800}{j}$ is odd. Compute the Bell number $B_n$, which counts the number of partitions of a set of size $n$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(33800),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(33800), 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 | 2026-02-08T08:53:36.701767Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T08:53:36.703091Z"
} | 4d0900 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1046
},
"timestamp": "2026-02-24T10:10:15.756Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6c3582 | nt_count_squarefree_v1_124444284_80 | Let $N = 38416$. Compute the number of positive integers $n$ such that $1 \le n \le N$ and $\mu(n)^2 = \phi(1)$, where $\mu$ denotes the Möbius function and $\phi$ denotes Euler's totient function. | 23,353 | graphs = [
Graph(
let={
"upper": Const(38416),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mul(MoebiusMu(n=Var(name='n')), MoebiusMu(n=Var(name='n'))), EulerPhi(n=Const(1)))))),
},
goal=R... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_squarefree_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 5.116 | 2026-02-08T02:57:01.334137Z | {
"verified": true,
"answer": 23353,
"timestamp": "2026-02-08T02:57:06.449963Z"
} | 17e652 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 602
},
"timestamp": "2026-02-17T16:34:26.171Z",
"answer": 8
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
}
] | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
ccc9e0 | comb_count_partitions_v1_124444284_3051 | Let $m = 15$ and let $s = 1 + 2 + \cdots + m$. Determine the number of positive integers $n$ such that $1 \leq n \leq s$ and $$n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}.$$ Let $p$ be the number of integer partitions of this number. Compute $p$. | 37,338 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(le... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/L3C"
] | 480637 | comb_count_partitions_v1 | null | 6 | 0 | [
"L3C",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T05:10:00.366798Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T05:10:00.368815Z"
} | b87b96 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1459
},
"timestamp": "2026-02-11T23:06:56.447Z",
"answer": 37338
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"l... | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
c2ac9d | nt_lcm_compute_v1_124444284_3189 | Let $a = 2952$ and let $b$ be the number of integers $t$ in the range $5 \leq t \leq 1173$ for which there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 31$, $1 \leq b' \leq 540$, and $t = 3a' + 2b'$. Let $\text{result} = \text{lcm}(a, b)$. Compute the remainder when $27523 \cdot \text{result}$ is divided ... | 34,414 | graphs = [
Graph(
let={
"_n": Const(74674),
"a": Const(2952),
"b": 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 | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_lcm_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:17:12.678643Z | {
"verified": true,
"answer": 34414,
"timestamp": "2026-02-08T05:17:12.680188Z"
} | a31167 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 5131
},
"timestamp": "2026-02-12T05:49:44.757Z",
"answer": 34414
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ae9b31 | sequence_lucas_compute_v1_168721529_1940 | Let $ m = 18 $. Let $ n $ be the maximum value of $ x \cdot y $ over all ordered pairs $ (x, y) $ of positive integers such that $ x + y = m $. Let $ s $ be the minimum value of $ x + y $ over all ordered pairs $ (x, y) $ of positive integers such that $ x \cdot y = n $. Define $ L $ to be the $ s $-th Lucas number. Co... | 11,558 | graphs = [
Graph(
let={
"_m": Const(18),
"_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("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T14:01:35.123132Z | {
"verified": true,
"answer": 11558,
"timestamp": "2026-02-08T14:01:35.125539Z"
} | 63a6e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 7795
},
"timestamp": "2026-02-09T23:55:17.040Z",
"answer": 11558
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
a67ca5 | comb_count_permutations_fixed_v1_458359167_61 | Let $k$ be the smallest integer $d \geq 2$ that divides $6125$. Compute the value of $\binom{10}{k} \cdot !(10 - k)$, where $!m$ denotes the subfactorial of $m$. Find the value of this expression. | 11,088 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(10),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(6125))))),
"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 | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T02:59:12.307566Z | {
"verified": true,
"answer": 11088,
"timestamp": "2026-02-08T02:59:12.310294Z"
} | 3d7074 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 907
},
"timestamp": "2026-02-10T12:01:10.776Z",
"answer": 11088
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
ae1736 | antilemma_k2_v1_865884756_2213 | Compute the value of
$$
\sum_{k=1}^{250} \varphi(k) \left\lfloor \frac{250}{k} \right\rfloor,
$$
where $\varphi(k)$ denotes the number of positive integers at most $k$ that are relatively prime to $k$. | 31,375 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(250), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(250), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T16:38:29.204407Z | {
"verified": true,
"answer": 31375,
"timestamp": "2026-02-08T16:38:29.205165Z"
} | 455f7d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 495
},
"timestamp": "2026-02-17T08:01:37.847Z",
"answer": 31375
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e937a8 | diophantine_fbi2_min_v1_971394319_904 | Let $k = 120$ and let $u = 130$. Consider the set of all integers $d$ such that $4 \le d \le u$, $d$ divides $k$, and $\frac{k}{d} \ge 7$. Determine the minimum value of such $d$. | 4 | graphs = [
Graph(
let={
"k": Const(120),
"a": Const(3),
"b": Const(6),
"upper": Const(130),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | null | EXTREMUM | sympy | V5 | [
"LIN_FORM",
"K2"
] | b46b5e | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"K2",
"LIN_FORM",
"V5"
] | 3 | 0.231 | 2026-02-08T13:22:41.784387Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T13:22:42.015060Z"
} | adcffe | 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": 893
},
"timestamp": "2026-02-15T14:14:01.152Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"le... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
53a70c | antilemma_k3_v1_784195855_8453 | Let $n = 22691$. Define
$$
x = \sum_{d \mid n} \phi(d),
$$
where the sum is over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function. Compute the remainder when $2500 - x$ is divided by $59762$. | 39,571 | graphs = [
Graph(
let={
"_n": Const(22691),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(2500), Ref("x")), modulus=Const(59762)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:05:07.524840Z | {
"verified": true,
"answer": 39571,
"timestamp": "2026-02-08T16:05:07.525368Z"
} | 57cf82 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1039
},
"timestamp": "2026-02-16T06:55:52.648Z",
"answer": 48458
},
{
"id": 1... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
83e942_n | geo_visible_lattice_v1_1218484723_2885 | A grid of size $128 \times 128$ has points labeled from $(1,1)$ to $(128,128)$. A point $(x,y)$ is visible from the origin if no other grid point lies on the line segment between $(0,0)$ and $(x,y)$, which occurs exactly when $\gcd(x,y) = 1$. Let $N$ be the number of such visible points in the grid. Compute the remaind... | 59,688 | GEOM | GEOM | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 2 | null | null | null | 0.453 | 2026-02-25T04:38:20.871284Z | null | e308f1 | 83e942 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 4306
},
"timestamp": "2026-03-30T19:12:32.635Z",
"answer": 59673
},
{
... | 1 | [] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |||
806518 | comb_bell_compute_v1_1978505735_1338 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 10290$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $37498 \cdot B_n$ is divided by $93475$. | 73,220 | graphs = [
Graph(
let={
"_n": Const(93475),
"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=10290)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:05:38.592381Z | {
"verified": true,
"answer": 73220,
"timestamp": "2026-02-08T16:05:38.595271Z"
} | d0ab67 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 2472
},
"timestamp": "2026-02-16T20:55:12.430Z",
"answer": 73220
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"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
} | ||
f340da | geo_visible_lattice_v1_1520064083_2824 | Let $n = 100$. Define $L$ as the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $71878 \cdot L$ is divided by $91509$. | 16,857 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(71878),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(91509)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.223 | 2026-02-08T05:14:22.357658Z | {
"verified": true,
"answer": 16857,
"timestamp": "2026-02-08T05:14:22.581133Z"
} | 044666 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 12813
},
"timestamp": "2026-02-24T02:59:11.043Z",
"answer": 16857
},
{
... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
3595a4 | comb_count_surjections_v1_601307018_10034 | Let $n = \sum_{k_1 = \binom{15}{0} - 1}^{2} 2^{k_1}$ and let $M = 2! \cdot S(n, 2)$, where $S(n, 2)$ denotes the Stirling number of the second kind. Compute $55696 - M$. | 55,570 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Sub(Binom(n=Const(15), k=Const(0)), Const(1)), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": Const(5569... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 71c45c | comb_count_surjections_v1 | null | 3 | 0 | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 2 | 0.002 | 2026-03-10T10:31:14.771257Z | {
"verified": true,
"answer": 55570,
"timestamp": "2026-03-10T10:31:14.773747Z"
} | fd2add | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 546
},
"timestamp": "2026-04-19T12:48:21.053Z",
"answer": 55570
},
{
"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
f77461 | alg_telescope_v1_601307018_9063 | Let $M = \sum_{k=0}^{586} \left(3k^2 + \min\{d : d \geq 2,\, d \mid 75\} \cdot k + 1\right) \bmod 4489$. Find the remainder when $28537M$ is divided by $82679$. | 2,000 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(586), expr=Sum(Mul(Const(3), Pow(Var("k"), Ref("_n"))), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Con... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_telescope_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.043 | 2026-03-10T09:28:40.765413Z | {
"verified": true,
"answer": 2000,
"timestamp": "2026-03-10T09:28:40.808810Z"
} | ff4083 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1349
},
"timestamp": "2026-04-19T10:32:46.917Z",
"answer": 2000
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f7879d | diophantine_fbi2_count_v1_1456120455_69 | Let $a_1 = 6$ and $b_1 = 13$. Define $n_1 = a_1 b_1 + 1$. Let $m = \tau(n_1) \bmod 2$, where $\tau(n)$ is the number of positive divisors of $n$. Let $p$ be the smallest prime divisor of $18588623$. Define $n = p^3$ and $t = \lambda(n) + 1$, where $\lambda(n)$ is the Liouville function. Let $k = 60 + t$. Determine the ... | 3,593 | graphs = [
Graph(
let={
"_m": Const(86865),
"_n": Const(2),
"a1": Const(6),
"b1": Const(13),
"n1": Sum(Mul(Ref("a1"), Ref("b1")), Const(1)),
"m": Mod(value=NumDivisors(n=Ref("n1")), modulus=Ref("_n")),
"p": MinOverSet(set=So... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/LIOUVILLE_MINUS_ONE",
"DIVISOR_PARITY",
"MAX_PRIME_BELOW"
] | 10a4c9 | diophantine_fbi2_count_v1 | null | 6 | 2 | [
"DIVISOR_PARITY",
"LIOUVILLE_MINUS_ONE",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 4 | 0.015 | 2026-02-08T02:52:53.028266Z | {
"verified": true,
"answer": 3593,
"timestamp": "2026-02-08T02:52:53.043098Z"
} | 6cc538 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1301
},
"timestamp": "2026-02-10T01:33:40.106Z",
"answer": 3593
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok_later"
},
{
"lemm... | {
"lo": -6.5,
"mid": 0,
"hi": 6.5
} | ||
a5d26c | modular_min_linear_v1_1820931509_153 | Let $x_0$ be the smallest positive integer $x$ such that $1 \leq x \leq 59028$ and $55883x \equiv 48065 \pmod{59028}$. Let $c$ be the number of positive integers $j$ such that $1 \leq j \leq 1369$ and $j^4 \leq 3512479453921$. Compute the remainder when $c - x_0$ is divided by $56440$. | 4,990 | graphs = [
Graph(
let={
"a": Const(55883),
"b": Const(48065),
"m": Const(59028),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Ref("b... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | a45c54 | modular_min_linear_v1 | negation_mod | 5 | 0 | [
"C3"
] | 1 | 2.789 | 2026-02-08T11:23:33.807557Z | {
"verified": true,
"answer": 4990,
"timestamp": "2026-02-08T11:23:36.596394Z"
} | 842f48 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 3002
},
"timestamp": "2026-02-14T13:09:51.571Z",
"answer": 4990
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8b326b | nt_lcm_compute_v1_655260480_941 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 2129$, and let $b = 1002$. Let $l = \mathrm{lcm}(a, b)$. Compute the Bell number $B_{l \bmod 11}$. | 203 | graphs = [
Graph(
let={
"_n": Const(2129),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"b": Const(1002),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Bell(Mod(... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_lcm_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:46:47.575762Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T15:46:47.578109Z"
} | ea824d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 1389
},
"timestamp": "2026-02-16T12:57:17.447Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0bb3e0 | sequence_fibonacci_compute_v1_168721529_1820 | 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$, $27 \le t \le 150$, and $t = 12a + 15b$. Let $m$ be the number of elements in $T$.\\
Let $S$ be the set of all positive integers $n \le 539$ such that $7$ divides $n$ and $\gcd(n, m) = 1$. L... | 4,244 | graphs = [
Graph(
let={
"_m": Const(94359),
"_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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C5"
] | 683493 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T13:56:45.770961Z | {
"verified": true,
"answer": 4244,
"timestamp": "2026-02-08T13:56:45.773891Z"
} | afc336 | 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": 3472
},
"timestamp": "2026-02-09T22:02:18.750Z",
"answer": 4244
},
{
"i... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
6b63dc | modular_inverse_v1_1918700295_1367 | Let $a = 708$. Let $m$ be the largest prime number less than or equal to $1301$. Let $S$ be the set of all positive integers $x$ such that $x \leq 1300$ and $708x \equiv 1 \pmod{m}$. Find the minimum value of $S$. | 939 | graphs = [
Graph(
let={
"a": Const(708),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1301)), IsPrime(Var("n"))))),
"upper": Const(1300),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.053 | 2026-02-08T05:48:30.607725Z | {
"verified": true,
"answer": 939,
"timestamp": "2026-02-08T05:48:30.661191Z"
} | 2c4914 | 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": 1268
},
"timestamp": "2026-02-12T14:13:44.318Z",
"answer": 939
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
de5f89 | nt_count_coprime_v1_168721529_771 | Let $k$ be the number of integers $t$ such that $22 \leq t \leq 144$ and $t = 8a + 14b$ for some positive integers $a \leq 11$ and $b \leq 4$. Let $r$ be the number of positive integers $n \leq 11491$ such that $\gcd(n, k) = 1$. Compute the smallest positive integer $m$ such that the $m$-th Fibonacci number is divisibl... | 1,428 | graphs = [
Graph(
let={
"upper": Const(11491),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 5.785 | 2026-02-08T13:17:14.760871Z | {
"verified": true,
"answer": 1428,
"timestamp": "2026-02-08T13:17:20.546033Z"
} | 5c4efd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 6659
},
"timestamp": "2026-02-11T07:40:58.010Z",
"answer": 2136
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
707feb | comb_catalan_compute_v1_124444284_8057 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Define $C_n$ to be the $n$-th Catalan number. Compute the remainder when $88501 \cdot C_n$ is divided by $90046$. | 32,044 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(22))))),
"res... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T09:31:45.454637Z | {
"verified": true,
"answer": 32044,
"timestamp": "2026-02-08T09:31:45.457422Z"
} | d48703 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T11:30:05.696Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"statu... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
b873ac | nt_max_prime_below_v1_1978505735_4520 | Let $m = 2$ and $n = 8$. Define $S$ as the set of all positive integers $j$ such that $1 \le j \le 2$ and $$ j^{\max\{ p \mid p \text{ is prime and } m \le p \le 3 \}} \le n. $$ Let $L$ be the number of elements in $S$. Define $T$ as the set of all prime numbers $p$ such that $L \le p \le 18225$. Compute the maximum el... | 18,223 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(8),
"upper": Const(18225),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Cons... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C3"
] | c6ca6f | nt_max_prime_below_v1 | null | 5 | 0 | [
"C3",
"MAX_PRIME_BELOW"
] | 2 | 0.415 | 2026-02-08T18:17:40.550329Z | {
"verified": true,
"answer": 18223,
"timestamp": "2026-02-08T18:17:40.965403Z"
} | 7f32f7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 471
},
"timestamp": "2026-02-16T12:16:46.208Z",
"answer": 18223
},
{
"id": 11,
... | 2 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
1357b9 | algebra_poly_eval_v1_1978505735_5631 | Let $z = 7$ and $n = 9$. Define $r = z^3 + 7z^2 - z + n$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $347633$. Let $Q = B_{|r| \bmod d_{\text{min}}}$, where $B_m$ denotes the $m$th Bell number. Find the value of $Q$. | 203 | graphs = [
Graph(
let={
"_n": Const(9),
"z": Const(7),
"result": Sum(Pow(Ref("z"), Const(3)), Mul(Const(7), Pow(Ref("z"), Const(2))), Mul(Const(-1), Ref("z")), Ref("_n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | algebra_poly_eval_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T19:07:20.081838Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T19:07:20.085919Z"
} | 61d777 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
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},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1124
},
"timestamp": "2026-02-18T21:21:21.374Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
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},
{
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"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b671c1 | sequence_fibonacci_compute_v1_124444284_1999 | Let $ m = 96 $. Let $ S $ be the set of positive integers $ n \leq m $ such that $ n $ is divisible by 48. Let $ \_n $ be the sum of all elements in $ S $. Consider all ordered pairs $ (x, y) $ of positive integers such that $ xy = \_n $. Let $ n $ be the minimum value of $ x + y $ over all such pairs. Compute the $ n ... | 46,368 | graphs = [
Graph(
let={
"_m": Const(96),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(Mod(value=Var("n"), modulus=Const(48)), Const(0))))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(ele... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_DIVISIBLE/B3"
] | 07ffbd | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC",
"SUM_DIVISIBLE"
] | 3 | 0.018 | 2026-02-08T04:14:40.261161Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T04:14:40.278793Z"
} | 700356 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 995
},
"timestamp": "2026-02-10T15:58:36.824Z",
"answer": 46368
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
f27443 | nt_count_coprime_and_v1_2051736721_1411 | Let $k_1$ be the smallest divisor of $1001$ that is at least $2$. Let $k_2$ be the number of integers $t$ with $23 \leq t \leq 33$ such that $t = 2a + 3b + 18$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 3$ and $1 \leq b \leq 3$. Determine the number of positive integers $n$ such that $1 \leq n \leq 15471$,... | 8,840 | graphs = [
Graph(
let={
"upper": Const(15471),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1001))))),
"k2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), ... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | nt_count_coprime_and_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 1.961 | 2026-02-08T16:02:13.154774Z | {
"verified": true,
"answer": 8840,
"timestamp": "2026-02-08T16:02:15.115954Z"
} | 930869 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1851
},
"timestamp": "2026-02-16T19:43:47.479Z",
"answer": 8840
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69dc68_l | sequence_count_fib_divisible_v1_1116507919_51 | Let $a$, $b$, and $t$ be positive integers such that $t = 5a + 4b$, $1 \leq a \leq 148$, $1 \leq b \leq 29$, and $9 \leq t \leq 856$. Define $\alpha$ to be the number of possible values of $t$ for which there exist such $a$ and $b$. Compute the number of positive integers $n$ at most $\alpha$ such that the $n$-th Fibon... | 56 | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.035 | 2026-02-08T02:24:06.379067Z | {
"verified": false,
"answer": 55,
"timestamp": "2026-02-08T02:24:06.413878Z"
} | fa311d | 69dc68 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 6827
},
"timestamp": "2026-02-23T13:19:42.891Z",
"answer": 55
},
{
"id"... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
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"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 3.02,
"mid": 4.36,
"hi": 5.69
} | |
a80bca | antilemma_sum_equals_v1_1874849503_582 | Let $n$ be the number of integers $t$ with $9 \leq t \leq 121$ such that there exist positive integers $a \leq 9$ and $b \leq 19$ satisfying $t = 5a + 4b$. Compute the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 101$, $1 \leq j \leq 101$, and $i + j = n$. | 100 | 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=9)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.135 | 2026-02-08T13:11:49.611326Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T13:11:49.746032Z"
} | ef63de | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 15967
},
"timestamp": "2026-02-24T17:30:52.136Z",
"answer": 100
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
3797b0 | alg_sum_powers_v1_1218484723_4899 | Let $R$ be the number of integers $t$ with $21 \leq t \leq 11286$ such that $t = 6a + 15b$ for some integers $a,b$ satisfying $1 \leq a \leq 821$ and $1 \leq b \leq 424$. Let $T = \left|\left\{ n : 1 \leq n \leq R,\ S(n) \text{ is even} \right\}\right|$, where $S(n)$ is the sum of the digits of $n$. Let $S = \left( \su... | 53,567 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=821)), Geq(left=Var... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/L3B"
] | db250f | alg_sum_powers_v1 | null | 5 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.078 | 2026-02-25T06:31:48.815230Z | {
"verified": true,
"answer": 53567,
"timestamp": "2026-02-25T06:31:48.893509Z"
} | c9bafe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 6168
},
"timestamp": "2026-03-29T18:22:24.596Z",
"answer": 53567
},
{
"... | 1 | [
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
1548a9 | comb_count_surjections_v1_1978505735_8246 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 12$ and
$$
t = 2a + 3b
$$
for some integers $a, b$ satisfying $1 \leq a \leq 3$ and $1 \leq b \leq 2$. Likewise, let $k$ be the number of integers $t_1$ in the same range $[5, 12]$ that can be expressed in the same form $t_1 = 2a + 3b$ under the same constr... | 720 | 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 | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T20:44:35.893485Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-08T20:44:35.896208Z"
} | ea38d8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2992
},
"timestamp": "2026-02-19T01:02:03.979Z",
"answer": 62
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
11ec49 | comb_count_partitions_v1_1978505735_3999 | Let $n = 143$. Define $m$ to be the number of positive integers less than or equal to $n$ that are relatively prime to 30. Let $p$ be the number of integer partitions of $m$. Compute the Bell number $B_k$, where $k$ is the remainder when $|p|$ is divided by 11. | 1 | graphs = [
Graph(
let={
"_n": Const(143),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Eq(GCD(a=Var("n1"), b=Const(30)), Const(1))))),
"result": Partition(arg=Ref(name='n')),
"Q": Bell(Mod... | NT | COMB | COUNT | sympy | C4 | [
"C4"
] | 08d162 | comb_count_partitions_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-08T17:58:44.809589Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:58:44.811072Z"
} | e74824 | 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": 1417
},
"timestamp": "2026-02-18T10:42:16.123Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69238d | antilemma_sum_primes_v1_677425708_2118 | Let $ x $ be the sum of all prime numbers $ n $ such that $ 2 \leq n \leq 3 $. Compute $ x + \left( 2^{x \bmod 16} \bmod 51280 \right) $. | 37 | graphs = [
Graph(
let={
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3)), IsPrime(Var("n"))))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(16))), modulus=Const(51280))),
},
... | NT | null | COMPUTE | sympy | B3 | [
"SUM_PRIMES"
] | 83231d | antilemma_sum_primes_v1 | null | 2 | 0 | [
"B3",
"SUM_PRIMES"
] | 2 | 0.013 | 2026-02-08T04:47:59.054132Z | {
"verified": true,
"answer": 37,
"timestamp": "2026-02-08T04:47:59.067313Z"
} | d07e17 | 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": 239
},
"timestamp": "2026-02-10T06:05:05.776Z",
"answer": 37
},
{
"id":... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
8307db | alg_telescope_v1_1218484723_5516 | Find the remainder when $\sum_{k=0}^{94} (4k^3 + 6k^2 + 4k + 1)$ is divided by the largest prime number less than or equal to $8509$. | 2,544 | graphs = [
Graph(
let={
"_n": Const(8509),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(94), expr=Sum(Mul(Const(4), Pow(Var("k"), Const(3))), Mul(Const(6), Pow(Var("k"), Const(2))), Mul(Const(4), Var("k")), Const(1))), modulus=MaxOverSet(set=SolutionsSet(var=Var("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_telescope_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.009 | 2026-02-25T07:02:08.602731Z | {
"verified": true,
"answer": 2544,
"timestamp": "2026-02-25T07:02:08.611885Z"
} | 92acdf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2071
},
"timestamp": "2026-03-29T21:31:05.056Z",
"answer": 2544
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
50ac00 | sequence_fibonacci_compute_v1_717093673_2434 | Let $n$ be the number of positive integers $n_1$ with $1 \leq n_1 \leq 242$ such that $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{11}$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $30130 \cdot F_n$ is divided ... | 34,505 | graphs = [
Graph(
let={
"_n": Const(242),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T16:50:24.220947Z | {
"verified": true,
"answer": 34505,
"timestamp": "2026-02-08T16:50:24.222224Z"
} | 9fed6c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1701
},
"timestamp": "2026-02-17T12:34:07.330Z",
"answer": 34505
},
... | 1 | [
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c1ec9a | diophantine_product_count_v1_1742523217_4919 | Let $p_{\text{max}}$ be the largest prime number less than or equal to $269$. Determine the number of positive integers $x$ such that $1 \leq x \leq p_{\text{max}}$, $x$ divides $420$, and $\frac{420}{x} \leq p_{\text{max}}$. Let $r$ be this number. Compute the remainder when $44121 \times r$ is divided by $87020$. | 13,442 | graphs = [
Graph(
let={
"_n": Const(269),
"k": Const(420),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_product_count_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.011 | 2026-02-08T09:20:49.605584Z | {
"verified": true,
"answer": 13442,
"timestamp": "2026-02-08T09:20:49.616655Z"
} | 55c1fc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1338
},
"timestamp": "2026-02-14T08:16:46.448Z",
"answer": 13442
},
... | 1 | [
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
398d91 | comb_sum_binomial_row_v1_1440796553_714 | Let $n$ be the smallest divisor of $71383$ that is at least $2$. Define $\text{result} = 2^n$. Compute the remainder when $13567 \cdot \text{result}$ is divided by $61414$. Find the value of $Q$. | 42,938 | graphs = [
Graph(
let={
"_n": Const(71383),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Pow(Const(2), Ref("n")),
"_c": Const(13567),
"Q": Mod(valu... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:56:11.975484Z | {
"verified": true,
"answer": 42938,
"timestamp": "2026-02-08T11:56:11.976728Z"
} | 65cc3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1167
},
"timestamp": "2026-02-14T20:45:25.749Z",
"answer": 42938
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ec3d25 | sequence_count_fib_divisible_v1_865884756_530 | Let $d = 7$ and let $Q$ be the number of positive integers $n$ with $1 \leq n \leq 855$ such that the $n$th Fibonacci number is divisible by 7. Find the value of $Q$. | 106 | graphs = [
Graph(
let={
"upper": Const(855),
"d": Const(7),
"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')))))),
"Q": Ref(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.448 | 2026-02-08T15:29:18.183169Z | {
"verified": true,
"answer": 106,
"timestamp": "2026-02-08T15:29:18.631327Z"
} | 350a28 | 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": 1334
},
"timestamp": "2026-02-16T06:25:46.610Z",
"answer": 106
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4232b0 | modular_mod_compute_v1_50713871_47 | Let $ p $ be a positive integer. Determine the number of positive integers $ p $ for which there exists a positive integer $ q $ such that $ p < q $, $ \gcd(p, q) = 1 $, and $ p \cdot q = 35134094128743710100 $. Let $ a $ be this number. Compute the remainder when $ 44121 \cdot (a \bmod 52441) $ is divided by $ 83401 $... | 35,841 | graphs = [
Graph(
let={
"a": 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=35134094128743710100)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_mod_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T02:43:54.567784Z | {
"verified": true,
"answer": 35841,
"timestamp": "2026-02-08T02:43:54.570293Z"
} | 607820 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 23878
},
"timestamp": "2026-02-23T15:48:17.918Z",
"answer": 33841
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 3.94,
"mid": 5.6,
"hi": 7.62
} | ||
0e859c | nt_count_divisible_v1_1526740231_522 | Let $\mathcal{B}$ be the set of all integers $t$ such that $7 \leq t \leq 34$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 6$, and $t = 4a + 3b$. Let $d$ be the number of elements in $\mathcal{B}$.
Let $U$ be the set of all positive integers $n$ such that $1 \leq n \leq 65025$ a... | 2,955 | graphs = [
Graph(
let={
"upper": Const(65025),
"divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 2.14 | 2026-02-08T11:35:02.892737Z | {
"verified": true,
"answer": 2955,
"timestamp": "2026-02-08T11:35:05.032655Z"
} | 7f09dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1391
},
"timestamp": "2026-02-14T16:20:38.200Z",
"answer": 2955
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0a4594 | modular_count_residue_v1_1918700295_1694 | Let $m$ be the smallest divisor of $2695$ that is at least $2$. Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 83160$ such that $n \equiv 4 \pmod{m}$. Compute the remainder when $38645 \cdot N$ is divided by $64107$. | 6,858 | graphs = [
Graph(
let={
"upper": Const(83160),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2695))))),
"r": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 5.393 | 2026-02-08T05:58:02.877492Z | {
"verified": true,
"answer": 6858,
"timestamp": "2026-02-08T05:58:08.270724Z"
} | eda599 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 3793
},
"timestamp": "2026-02-12T17:23:52.550Z",
"answer": 6858
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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