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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
84b659 | modular_product_range_v1_601307018_8053 | Let $m = \min\{ |x - y| : x, y > 0,\, xy = 12324 \}$. Define $M = \prod_{i=m}^{141} i$. Let $R = M \bmod 10357$. Find the remainder when $80259 \cdot R$ is divided by $67582$. | 11,558 | graphs = [
Graph(
let={
"_n": Const(80259),
"prod": MathProduct(expr=Var("i"), var="i", start=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")), C... | NT | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"B3_DIFF"
] | b47ea7 | modular_product_range_v1 | null | 5 | 0 | [
"B3_DIFF",
"POLY_ORBIT_HENSEL"
] | 2 | 0.077 | 2026-03-10T08:34:22.079202Z | {
"verified": true,
"answer": 11558,
"timestamp": "2026-03-10T08:34:22.155800Z"
} | 9d59ea | 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": 11756
},
"timestamp": "2026-04-19T08:10:46.840Z",
"answer": 11558
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e72c9b | diophantine_fbi2_min_v1_655260480_4717 | Let $n = 75665$. For each integer $k_1$ from 1 to 9, define $c_{k_1} = \phi(k_1) \left\lfloor \frac{m}{k_1} \right\rfloor$, where $m$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 18$. Let $\text{upper} = \sum_{k_1=1}^{9} c_{k_1}$. Let $d$ be the smallest integer such that ... | 7,123 | graphs = [
Graph(
let={
"_n": Const(75665),
"k": Const(35),
"upper": Summation(var="k1", start=Const(1), end=Const(9), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1/K2"
] | 613e04 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"COMB1",
"K2"
] | 2 | 0.009 | 2026-02-08T18:04:32.979163Z | {
"verified": true,
"answer": 7123,
"timestamp": "2026-02-08T18:04:32.987847Z"
} | f2dcf7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1823
},
"timestamp": "2026-02-18T12:51:13.403Z",
"answer": 7123
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb432b | antilemma_k3_v1_1918700295_70 | Let $S$ be the set of all real numbers $x$ such that $x^2 - 5838x - 533520 = 0$. Let $n$ be the sum of all elements of $S$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. | 5,838 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Ref(name='_n')), Mul(Const(value=-5838), Var(name='x')), Const(value=-533520)), right=Const(value=0)))), var='d', expr=Euler... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K3",
"K3"
] | 78a626 | antilemma_k3_v1 | null | 6 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T02:58:18.491906Z | {
"verified": true,
"answer": 5838,
"timestamp": "2026-02-08T02:58:18.492637Z"
} | 7dd0f7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 597
},
"timestamp": "2026-02-10T12:04:21.701Z",
"answer": 5838
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
a735af | antilemma_cartesian_v1_1978505735_5803 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 19$ and $1 \leq b \leq 33$. Compute the value of $Q = 44100 - x$. | 43,473 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(19)), right=IntegerRange(start=Const(1), end=Const(33)))),
"_c": Const(44100),
"Q": Sub(Ref("_c"), Ref("x")),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T19:13:44.150941Z | {
"verified": true,
"answer": 43473,
"timestamp": "2026-02-08T19:13:44.153125Z"
} | d93707 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 312
},
"timestamp": "2026-02-25T01:00:58.088Z",
"answer": 43473
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||
4b65f5 | geo_count_lattice_triangle_v1_2051736721_1951 | Let $A$ be the absolute value of $111 \cdot 400 + 233 \cdot (-171)$. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates of the points $(0,0)$, $(111,171)$, and $(233,400)$, taken pairwise. Specifically, $$ B = \gcd(|111|, |171|) + \gcd(|233 - 111|, |400 - 171|) + \gcd(|0 -... | 2,277 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=400)), Mul(Const(value=233), Sub(left=Const(value=0), right=Const(value=171))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=171))), GCD(a=Abs(arg=Sub(left=Const(value=233), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.006 | 2026-02-08T16:22:50.262433Z | {
"verified": true,
"answer": 2277,
"timestamp": "2026-02-08T16:22:50.267967Z"
} | 9435ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 836
},
"timestamp": "2026-02-17T02:34:21.648Z",
"answer": 2277
},
{
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
082475 | nt_num_divisors_compute_v1_397696148_1007 | Compute the number of positive divisors of $27556$. | 9 | graphs = [
Graph(
let={
"n": Const(27556),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T12:15:44.532365Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T12:15:44.539188Z"
} | 1fc0f0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 58,
"completion_tokens": 797
},
"timestamp": "2026-02-14T23:47:22.952Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
67df4f | sequence_count_fib_divisible_v1_717093673_2824 | Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 940$. Let $d = 20$. Compute the number of positive integers $k$ with $1 \leq k \leq n$ such that $d$ divides the $k$-th Fibonacci number. | 15 | graphs = [
Graph(
let={
"_n": Const(940),
"upper": 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 | COUNT | sympy | MAX_DIVISOR | [
"COMB1"
] | 567f58 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"COMB1",
"MAX_DIVISOR"
] | 2 | 0.067 | 2026-02-08T17:13:09.887161Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T17:13:09.954446Z"
} | e5d066 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 2976
},
"timestamp": "2026-02-17T21:53:16.533Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21b591 | nt_min_coprime_above_v1_655260480_5634 | Let $ t $ be an integer satisfying $ 14 \leq t \leq 224 $. Determine the number of values of $ t $ for which there exist integers $ a $ and $ b $ such that $ 1 \leq a \leq 12 $, $ 1 \leq b \leq 26 $, and $ t = 10a + 4b $. Denote this number by $ m $.\\
Let $ n $ be the smallest integer greater than 17956 and at most 1... | 17,958 | graphs = [
Graph(
let={
"start": Const(17956),
"upper": Const(18068),
"modulus": 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(n... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.013 | 2026-02-08T18:35:22.872726Z | {
"verified": true,
"answer": 17958,
"timestamp": "2026-02-08T18:35:22.885289Z"
} | 13b74c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 5665
},
"timestamp": "2026-02-18T17:56:06.038Z",
"answer": 17958
},
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
37c49d | modular_count_residue_v1_1520064083_1762 | Let $p$ be the largest prime number less than or equal to $17$. Let $m$ be the smallest divisor of $35$ that is at least $2$. Define $S$ as the set of all integers $n$ such that $\sum_{d \mid \gcd(p, 19)} \mu(d) \leq n \leq 45796$ and $n \equiv 3 \pmod{m}$, where $\mu$ denotes the M\"obius function. Compute the number ... | 9,159 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(17)), IsPrime(Var("n"))))),
"upper": Const(45796),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divi... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MIN_PRIME_FACTOR/MOBIUS_COPRIME"
] | b32ba6 | modular_count_residue_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 3 | 1.741 | 2026-02-08T04:16:14.149883Z | {
"verified": true,
"answer": 9159,
"timestamp": "2026-02-08T04:16:15.890402Z"
} | e3b624 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 567
},
"timestamp": "2026-02-18T10:12:08.342Z",
"answer": 9159
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma":... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
26ef81 | nt_count_digit_sum_v1_798873815_460 | Let $T$ be the set of all integers $t$ such that $5 \le t \le 17$ and there exist positive integers $a \in [1,4]$, $b \in [1,3]$ satisfying $t = 2a + 3b$. Let $k$ be the number of elements in $T$. Let $N = 379749833583241 \cdot 14641$. Define $s$ as the largest integer such that $k^s$ divides $N$. Let $U$ be the set of... | 16,718 | graphs = [
Graph(
let={
"_n": Const(14641),
"upper": Const(305809),
"target_sum": MaxKDivides(target=Mul(Const(379749833583241), Ref("_n")), base=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/K13",
"ONE_PHI_1"
] | 6a539c | nt_count_digit_sum_v1 | null | 7 | 0 | [
"K13",
"LIN_FORM",
"ONE_PHI_1"
] | 3 | 10.165 | 2026-02-08T02:38:50.717182Z | {
"verified": true,
"answer": 16718,
"timestamp": "2026-02-08T02:39:00.882288Z"
} | 9f70fc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 6077
},
"timestamp": "2026-02-09T17:25:50.939Z",
"answer": 16718
},
{
... | 1 | [
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": 4.29,
"mid": 7.01,
"hi": 10
} | ||
4b9614 | nt_sum_gcd_range_mod_v1_655260480_5422 | Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 63916$ and $19$ divides $k$. Let $k = 288$ and $M = 11423$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Let $r$ be the remainder when $\text{sum}$ is divided by $M$. Compute the remainder when $r^2 + 3r + 30$ is divided by $85512$. | 64,696 | graphs = [
Graph(
let={
"_n": Const(2),
"N": CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k1"), Const(1)), Leq(Var("k1"), Const(63916)), Divides(divisor=Const(19), dividend=Var("k1"))), domain='positive_integers')),
"k": Const(288),
"M":... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"C2"
] | 7d2684 | nt_sum_gcd_range_mod_v1 | quadratic_mod | 5 | 0 | [
"C2",
"SUM_ARITHMETIC"
] | 2 | 0.162 | 2026-02-08T18:27:50.440440Z | {
"verified": true,
"answer": 64696,
"timestamp": "2026-02-08T18:27:50.602544Z"
} | d739d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 3000
},
"timestamp": "2026-02-18T17:10:13.704Z",
"answer": 64696
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
db5ec4 | modular_min_linear_v1_458359167_1543 | Let $a = 27982$ and $m = 29253$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2196324$. Define $b$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. | 26,811 | graphs = [
Graph(
let={
"a": Const(27982),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2196324)))), expr=Sum(Var("x"), Var("y"))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_linear_v1 | null | 6 | 0 | [
"B3"
] | 1 | 3.87 | 2026-02-08T04:44:11.174606Z | {
"verified": true,
"answer": 26811,
"timestamp": "2026-02-08T04:44:15.045069Z"
} | b93041 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2205
},
"timestamp": "2026-02-11T21:51:57.130Z",
"answer": 26811
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VA... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
648f57_l | lin_form_endings_v1_1248542787_17 | Let $a$ and $b$ be positive integers such that $1 \leq a \leq 31$ and $1 \leq b \leq 42$. Let $t$ be an integer satisfying $50 \leq t \leq 1880$ and $t = 20a + 30b$. Determine the number of possible values of $t$. Multiply this number by 6607, and compute the remainder when the result is divided by 96267. | 53,877 | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:53:49.728933Z | {
"verified": false,
"answer": 47270,
"timestamp": "2026-02-08T02:53:49.730287Z"
} | 83cb0c | 648f57 | 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": 217,
"completion_tokens": 5631
},
"timestamp": "2026-02-08T20:04:07.854Z",
"answer": 47270
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 2.44,
"mid": 3.95,
"hi": 5.27
} | |
da67d1 | nt_count_divisors_in_range_v1_971394319_1950 | Let $n = 45360$. Define
$$
A = \frac{6}{48} \sum_{k=1}^{4} \sum_{j=1}^{8} \varphi(k) \left\lfloor \frac{4}{k} \right\rfloor.
$$
Let $a$ be the value of $A$, and let $b = 22681$. Consider the set of all positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $r$ be the number of such divisors.
Compute the value o... | 24,874 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Const(45360),
"a": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=Integ... | NT | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.191 | 2026-02-08T14:01:33.311685Z | {
"verified": true,
"answer": 24874,
"timestamp": "2026-02-08T14:01:33.502860Z"
} | b16a74 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1939
},
"timestamp": "2026-02-15T23:35:45.920Z",
"answer": 24874
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
85cd9c | v7_endings_v1_124444284_1145 | Let $ k $ be an integer such that $ 0 \leq k \leq 2163 $. For each such $ k $, define $ v_2\left(\binom{2163}{k}\right) $ to be the largest integer $ m $ such that $ 2^m $ divides $ \binom{2163}{k} $. Let $ M $ be the maximum value of $ v_2\left(\binom{2163}{k}\right) $ over all such $ k $. Compute the remainder when $... | 17,025 | graphs = [
Graph(
let={
"_inner_result": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(2163)))), expr=MaxKDivides(target=Binom(n=Const(2163), k=Var("k")), base=Const(2)))),
"_scale_k": Const(9818),
"_sc... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.003 | 2026-02-08T03:42:25.404461Z | {
"verified": true,
"answer": 17025,
"timestamp": "2026-02-08T03:42:25.407089Z"
} | 2d572a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 7481
},
"timestamp": "2026-02-09T10:12:02.224Z",
"answer": 17025
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
e5955f | comb_count_permutations_fixed_v1_1125832087_1247 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = 16$. Compute $\binom{n}{1} \cdot !(n - 1)$, where $!k$ denotes the number of derangements of $k$ elements. | 14,832 | graphs = [
Graph(
let={
"_n": Const(16),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:37:51.124849Z | {
"verified": true,
"answer": 14832,
"timestamp": "2026-02-08T03:37:51.126405Z"
} | 0407c5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 768
},
"timestamp": "2026-02-10T15:11:00.723Z",
"answer": 14832
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status":... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
842823 | algebra_poly_eval_v1_48377204_2272 | Let $n$ be an integer. Consider the set of all prime numbers $n$ such that $2 \leq n \leq 10$. Let $t$ be the maximum value in this set. Compute $2t^2 - 7t - 10$. | 39 | graphs = [
Graph(
let={
"_n": Const(2),
"t": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(10)), IsPrime(Var("n"))))),
"result": Sum(Mul(Const(2), Pow(Ref("t"), Const(2))), Mul(Const(-7), Ref("t")), Const(-10)),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:42:06.809298Z | {
"verified": true,
"answer": 39,
"timestamp": "2026-02-08T16:42:06.811567Z"
} | 199ace | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 174
},
"timestamp": "2026-02-16T07:43:57.761Z",
"answer": 39
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
4109d5 | comb_bell_compute_v1_677425708_1823 | Let $n = 8$. Define $r$ to be the Bell number $B_n$, the number of partitions of an $n$-element set. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 28$. Let $p_{\text{max}}$ be the maximum value of $xy$ over all pairs $(x, y) \in S$. Find the value of $(p_{\text{max}} - r) \bmo... | 89,309 | graphs = [
Graph(
let={
"n": Const(8),
"result": Bell(Ref("n")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")),... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | comb_bell_compute_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T04:28:58.618606Z | {
"verified": true,
"answer": 89309,
"timestamp": "2026-02-08T04:28:58.620567Z"
} | f3a444 | 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": 1165
},
"timestamp": "2026-02-10T01:29:37.030Z",
"answer": 89309
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
d40ebe | sequence_fibonacci_compute_v1_798873815_271 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 10$.
Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. | 75,025 | graphs = [
Graph(
let={
"_n": Const(10),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T02:31:58.046921Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T02:31:58.047816Z"
} | 1615fa | 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": 629
},
"timestamp": "2026-02-08T19:17:46.283Z",
"answer": 75025
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -6.29,
"mid": -4.59,
"hi": -2.8
} | ||
ca3d87 | algebra_vieta_sum_v1_784195855_4563 | Let $m = 14$. Let $p$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 16$. Let $t$ be the number of integers between $7$ and $106$, inclusive, that can be expressed in the form $5a + 2b$ for positive integers $a \leq 18$ and $b \leq 8$. Find the absolute value of the product... | 96 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(16)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"B1/LIN_FORM"
] | 7f6ba8 | algebra_vieta_sum_v1 | null | 7 | 0 | [
"B1",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.103 | 2026-02-08T07:10:26.115540Z | {
"verified": true,
"answer": 96,
"timestamp": "2026-02-08T07:10:26.218533Z"
} | 50b66b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 3628
},
"timestamp": "2026-02-13T08:43:25.769Z",
"answer": 96
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8d38b4 | geo_count_lattice_rect_v1_1431428450_226 | Compute the number of lattice points in the rectangle $[0, 121] \times [0, 343]$, including the boundary. That is, find the number of points $(x, y)$ where $x$ and $y$ are integers such that $0 \leq x \leq 121$ and $0 \leq y \leq 343$. | 41,968 | graphs = [
Graph(
let={
"a": Const(121),
"b": Const(343),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T13:18:41.660528Z | {
"verified": true,
"answer": 41968,
"timestamp": "2026-02-08T13:18:41.662354Z"
} | f2c272 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 271
},
"timestamp": "2026-02-24T17:54:17.738Z",
"answer": 41968
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
845ed6 | lin_form_endings_v1_124444284_6795 | Let $a = 50$ and $b = 40$. Let $k = 2$, and let $\ell$ be the least common multiple of $a$ and $b$. Define $s = k \cdot \ell + a + b$. Compute the remainder when $5908 \cdot s$ is divided by $81889$. | 28,805 | graphs = [
Graph(
let={
"a_coeff": Const(50),
"b_coeff": Const(40),
"k_val": Const(2),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:38:39.989985Z | {
"verified": true,
"answer": 28805,
"timestamp": "2026-02-08T08:38:39.990485Z"
} | 38476a | 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": 750
},
"timestamp": "2026-02-13T20:12:14.933Z",
"answer": 28805
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6d7999 | modular_min_linear_v1_1125832087_1395 | Let $a = 14276$. Let $b$ be the number of integers $t$ such that $9 \leq t \leq 1390$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 88$, $1 \leq b' \leq 387$, and $t = 7a' + 2b'$. Let $m = 48160$, and let $x$ be the smallest positive integer such that $1 \leq x \leq m$ and
$$
14276x \equiv b \pm... | 55,480 | graphs = [
Graph(
let={
"a": Const(14276),
"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'), right=Const(value=88)), Geq(left=Va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 5.324 | 2026-02-08T03:42:42.226194Z | {
"verified": true,
"answer": 55480,
"timestamp": "2026-02-08T03:42:47.549904Z"
} | f482ec | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 7773
},
"timestamp": "2026-02-10T14:12:36.991Z",
"answer": 55480
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
ca2224 | comb_bell_compute_v1_601307018_8110 | Let $B_n$ denote the $n$-th Bell number, and let $R = B_9$. Let $M = 5$, $S = 3$, and $N = 0$. Define $s = \sum_{k=0}^{N} (-1)^k \binom{N}{k}$, $t = \sum_{k=0}^{M} (-1)^k \binom{M}{k}$, and $w = \sum_{k=0}^{S} (-1)^k \binom{S}{k}$. Let $T = (20164 + t + w) \cdot s$. Find the remainder when $T - R$ is divided by $80902$... | 79,919 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(4),
"n3": Sum(Ref("a"), Ref("b")),
"t": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"u": Const(2),
"n2": Sum(Re... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 4 | 3 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-03-10T08:36:04.655592Z | {
"verified": true,
"answer": 79919,
"timestamp": "2026-03-10T08:36:04.658233Z"
} | 6a2038 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 653
},
"timestamp": "2026-04-19T08:19:30.534Z",
"answer": 79919
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
103593 | lin_form_endings_v1_1520064083_3003 | Let $A$ be the set of all integers $t$ such that $45 \leq t \leq 1242$ and there exist integers $a$ and $b$ with $1 \leq a \leq 12$, $1 \leq b \leq 51$, and $t = 27a + 18b$. Let $k = 12209$ and let $N$ be the number of elements in $A$. Compute the remainder when $k \cdot N$ is divided by $93315$. | 25,233 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=12)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:24:21.836638Z | {
"verified": true,
"answer": 25233,
"timestamp": "2026-02-08T05:24:21.837706Z"
} | 76e387 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2738
},
"timestamp": "2026-02-24T03:35:23.630Z",
"answer": 37442
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
6f83f4 | nt_count_gcd_equals_v1_865884756_2360 | Let $k$ be the number of integers $t$ such that $5 \leq t \leq 45$ and there exist integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 6$, and $t = 3a + 2b$. Let $d = 1$. Let $n$ range from $1$ to $17161$, inclusive. Define $\text{result}$ to be the number of such $n$ for which $\gcd(n, k) = d$. Compute the re... | 26,269 | graphs = [
Graph(
let={
"upper": Const(17161),
"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_gcd_equals_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 4.336 | 2026-02-08T16:43:07.050794Z | {
"verified": true,
"answer": 26269,
"timestamp": "2026-02-08T16:43:11.386477Z"
} | 30988a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 3560
},
"timestamp": "2026-02-17T11:00:18.708Z",
"answer": 26269
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2acb65 | comb_count_partitions_v1_458359167_2352 | Let $n = \sum_{k=1}^{9} \phi(k) \left\lfloor \frac{9}{k} \right\rfloor$, where $\phi(k)$ is Euler's totient function. Let $p(n)$ denote the number of integer partitions of $n$. Let $c = 35535$. Find the remainder when $c \cdot p(n)$ is divided by 68216. | 39,594 | graphs = [
Graph(
let={
"_n": Const(35535),
"n": Summation(var="k", start=Const(1), end=Const(9), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(9), Var("k"))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=Con... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_partitions_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T05:20:01.594396Z | {
"verified": true,
"answer": 39594,
"timestamp": "2026-02-08T05:20:01.595281Z"
} | daed04 | 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": 1477
},
"timestamp": "2026-02-12T07:57:16.021Z",
"answer": 39594
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6989da | comb_count_derangements_v1_1915831931_2208 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 4410$, $\gcd(p, q) = 1$, and $p < q$. Let $Q$ be the remainder when $71461 \cdot !n$ is divided by $97339$, where $!n$ denotes the number of derangements of $n$ elements. Compute $Q$. | 56,642 | graphs = [
Graph(
let={
"_n": Const(97339),
"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=4410)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:40:29.814936Z | {
"verified": true,
"answer": 56642,
"timestamp": "2026-02-08T16:40:29.817194Z"
} | 9ea205 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2220
},
"timestamp": "2026-02-17T09:03:32.353Z",
"answer": 56642
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9c71e1 | nt_sum_gcd_range_mod_v1_677425708_1674 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 198$. For each pair $(x, y)$ in $S$, compute $xy$, and let $T$ be the set of all such products. Let $N$ be the maximum value in $T$. Compute $$\sum_{n=1}^{N} \gcd(n, 84).$$ Find the remainder when this sum is divided by $10399$. | 8,642 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(198)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(84),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.54 | 2026-02-08T04:22:23.533876Z | {
"verified": true,
"answer": 8642,
"timestamp": "2026-02-08T04:22:24.073494Z"
} | 003f85 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 3450
},
"timestamp": "2026-02-09T23:14:54.015Z",
"answer": 8642
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
7d764a | diophantine_fbi2_count_v1_1440796553_1186 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 8100$. For each pair, compute $x + y$, and let $k$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive integers $d$ such that $6 \leq d \leq 71$, $d$ divides $k$, and $\frac{k}{d}$ is an integer betwe... | 9 | graphs = [
Graph(
let={
"_n": Const(5),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(8100)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T12:13:41.646729Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T12:13:41.654536Z"
} | e1fcd1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1331
},
"timestamp": "2026-02-15T18:23:43.993Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
82e523 | antilemma_cartesian_v1_717093673_283 | Compute the number of ordered pairs $(a, b)$ of positive integers such that $1 \leq a \leq 36$ and $1 \leq b \leq 40$. | 1,440 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(36)), right=IntegerRange(start=Const(1), end=Const(40)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T15:17:33.425266Z | {
"verified": true,
"answer": 1440,
"timestamp": "2026-02-08T15:17:33.426000Z"
} | 9abfbf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 161
},
"timestamp": "2026-02-24T20:28:12.173Z",
"answer": 1440
},
{
"id... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
65ba24 | geo_count_lattice_rect_v1_1978505735_3593 | Let $R$ be the number of lattice points $(x,y)$ such that $0 \leq x \leq 200$ and $0 \leq y \leq 200$.
Compute the remainder when $529 - R$ is divided by $87066$. | 47,194 | graphs = [
Graph(
let={
"a": Const(200),
"b": Const(200),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Sub(Const(529), Ref("result")), modulus=Const(87066)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T17:43:35.615221Z | {
"verified": true,
"answer": 47194,
"timestamp": "2026-02-08T17:43:35.617496Z"
} | 97d660 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 410
},
"timestamp": "2026-02-18T07:26:09.416Z",
"answer": 47194
},
{... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
b903e5 | nt_sum_over_divisible_v1_458359167_215 | Let $A$ be the sum of all positive integers $n \leq 48841$ that are divisible by 178. Let $B$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 202500$. Compute the value of $$(A^2 + 3A + B) \mod 81051.$$ | 27,907 | graphs = [
Graph(
let={
"upper": Const(48841),
"divisor": Const(178),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"Q": Mod... | NT | null | SUM | sympy | B3 | [
"B3"
] | d720b5 | nt_sum_over_divisible_v1 | quadratic_mod | 4 | 0 | [
"B3"
] | 1 | 1.659 | 2026-02-08T03:04:31.660777Z | {
"verified": true,
"answer": 27907,
"timestamp": "2026-02-08T03:04:33.320122Z"
} | 63a3a1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1967
},
"timestamp": "2026-02-10T13:17:33.900Z",
"answer": 27907
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3ecc5c | antilemma_k3_v1_1470522791_102 | Let $x = \sum_{d \mid 75253} \phi(d)$, where $\phi$ is Euler's totient function.
Let $s = \sum_{i=0}^{\mathrm{num\_digits}(|x|)-1} \left( \mathrm{digit}_i(|x|) \cdot (i+1)^2 \right)$, where $\mathrm{digit}_i(|x|)$ is the $i$-th decimal digit of $|x|$ (starting from the units place at $i=0$).
Let $Q = s + 120$.
Compu... | 416 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=75253), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='x')), k=Var(name='i'), base=N... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:49:41.965230Z | {
"verified": true,
"answer": 416,
"timestamp": "2026-02-08T12:49:41.966331Z"
} | 052414 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 527
},
"timestamp": "2026-02-15T05:21:02.666Z",
"answer": 416
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9ab2bc | comb_binomial_compute_v1_798873815_397 | Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 48$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 10a + 4b$. Let $n$ be the number of elements in $T$. Compute the binomial coefficient $\binom{n}{7}$. Report the result. | 3,432 | 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=2)), Geq(left=Var(name='b'), right=Const(value=1... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:37:44.433269Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T02:37:44.434212Z"
} | 20a9e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 927
},
"timestamp": "2026-02-08T19:28:00.710Z",
"answer": 3432
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.89,
"hi": 0.06
} | ||
febd30 | antilemma_cartesian_v1_1742523217_522 | Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 29$ and $1 \leq j \leq 49$. | 1,421 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=Const(49)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:06:41.246771Z | {
"verified": true,
"answer": 1421,
"timestamp": "2026-02-08T03:06:41.247409Z"
} | df9106 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 111
},
"timestamp": "2026-02-09T19:01:30.034Z",
"answer": 1421
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
b2fc38 | comb_sum_binomial_row_v1_124444284_264 | Let $n$ be the largest integer such that $37^n$ divides $1874161^4$. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(37),
"n": MaxKDivides(target=Pow(Const(1874161), Const(4)), base=Ref("_n")),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | K14 | [
"K14"
] | a49bcb | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"K14"
] | 1 | 0.001 | 2026-02-08T03:07:10.137440Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T03:07:10.137998Z"
} | 96841c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1172
},
"timestamp": "2026-02-09T15:25:59.564Z",
"answer": 65536
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
5ab463 | nt_min_crt_v1_458359167_259 | Let $n = 7$. Compute
$$
\sum_{k=1}^{7} \varphi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
and denote the result by $\text{upper}$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq \text{upper}$, $n \equiv 3 \pmod{4}$, and $n \equiv 0 \pmod{7}$. Let $\text{result}$ be the smallest element of $... | 7,457 | graphs = [
Graph(
let={
"_n": Const(7),
"m": Const(4),
"k": Const(7),
"a": Const(3),
"b": Const(0),
"upper": Summation(var="k", start=Const(1), end=Const(7), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 6897ab | nt_min_crt_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.005 | 2026-02-08T03:06:16.608943Z | {
"verified": true,
"answer": 7457,
"timestamp": "2026-02-08T03:06:16.614086Z"
} | 3dcb4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 736
},
"timestamp": "2026-02-10T13:19:45.706Z",
"answer": 7457
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
cc2986 | nt_sum_totient_over_divisors_v1_153355830_2266 | Let $n = 69466$. Define $r = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 197136$. Compute $r^2 + 19r + s$, and find the remainder when this value is divided by $94263$. Determine the valu... | 14,720 | graphs = [
Graph(
let={
"_n": Const(19),
"n": Const(69466),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Ref("_n"), Ref("result")), MinOverSet(set=MapOverSet(set=Solut... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | d720b5 | nt_sum_totient_over_divisors_v1 | quadratic_mod | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T07:01:29.228148Z | {
"verified": true,
"answer": 14720,
"timestamp": "2026-02-08T07:01:29.230641Z"
} | ffeb8e | 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": 1280
},
"timestamp": "2026-02-13T07:21:27.580Z",
"answer": 14720
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1fa70b | nt_sum_totient_over_divisors_v1_48377204_1270 | Let $n = 69535$. Define $\text{result} = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Let $p$ be the largest prime number less than or equal to 11. Compute the Bell number $B_k$, where $k$ is the remainder when $|\text{result}|$ is divided by $p$. Find the value of this Bell number. | 15 | graphs = [
Graph(
let={
"_n": Const(11),
"n": Const(69535),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(G... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_totient_over_divisors_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:00:18.720265Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T16:00:18.722638Z"
} | 4c1da2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 429
},
"timestamp": "2026-02-16T18:27:47.872Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8d7b99 | nt_count_coprime_and_v1_2051736721_1830 | Let $U = 23681$. Compute the number of positive integers $n$ such that $1 \le n \le U$, $\gcd(n, 5) = 1$, and $\gcd(n, 11) = 1$.
Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6002500$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all such pairs.
Find the remainder ... | 78,056 | graphs = [
Graph(
let={
"upper": Const(23681),
"k1": Const(5),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_coprime_and_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 15.48 | 2026-02-08T16:15:09.423388Z | {
"verified": true,
"answer": 78056,
"timestamp": "2026-02-08T16:15:24.903383Z"
} | 6c2e49 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1491
},
"timestamp": "2026-02-17T00:13:47.946Z",
"answer": 78056
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b6b676 | antilemma_k2_v1_458359167_571 | Let $m = 370$ and define $n = \sum_{d \mid m} \phi(d)$, where the sum is taken over all positive divisors $d$ of $m$ and $\phi$ denotes Euler's totient function. Compute the value of
$$
\sum_{k=1}^{370} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$ | 68,635 | graphs = [
Graph(
let={
"_m": Const(370),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Const(370), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Re... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.002 | 2026-02-08T03:25:39.260449Z | {
"verified": true,
"answer": 68635,
"timestamp": "2026-02-08T03:25:39.262389Z"
} | 51d081 | 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": 5520
},
"timestamp": "2026-02-10T14:20:56.313Z",
"answer": 68635
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
25f80b | nt_euler_phi_compute_v1_1116507919_331 | Let $\mu(n)$ denote the M\"obius function and $\omega(n)$ denote the number of distinct prime factors of $n$. Define $a$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 25000000$. Let $b = 20 \cdot \omega(29)$. Let $d_0 = \gcd(a, b)$, and define $v = \sum_{d \mid d_0} \mu... | 26,880 | graphs = [
Graph(
let={
"_n": Const(78400),
"n1": Const(29),
"w": SmallOmega(n=Ref(name='n1')),
"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'))... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3/MOBIUS_COPRIME",
"OMEGA_ONE"
] | c619e0 | nt_euler_phi_compute_v1 | null | 6 | 2 | [
"B3",
"MOBIUS_COPRIME",
"OMEGA_ONE"
] | 3 | 0.004 | 2026-02-08T02:31:38.168263Z | {
"verified": true,
"answer": 26880,
"timestamp": "2026-02-08T02:31:38.172051Z"
} | 724090 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 2230
},
"timestamp": "2026-02-08T19:23:11.074Z",
"answer": 26880
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.44,
"mid": -4.14,
"hi": -0.84
} | ||
35ee42 | comb_binomial_compute_v1_677425708_2933 | Let $n$ be the number of integers $t$ such that $26 \leq t \leq 89$ and there exist positive integers $a \in \{1,2,3,4\}$ and $b \in \{1,2,3,4\}$ satisfying
$$
t = 9a + 12b + 5.
$$
Let $k$ be the number of integers $t$ such that $5 \leq t \leq 15$ and there exist positive integers $a \in \{1,2,3\}$ and $b \in \{1,2,3\}... | 27,240 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(90940),
"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'), ri... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T05:22:51.987261Z | {
"verified": true,
"answer": 27240,
"timestamp": "2026-02-08T05:22:51.991464Z"
} | 1f97c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 2236
},
"timestamp": "2026-02-24T03:20:31.817Z",
"answer": 27240
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
cfe15b | comb_count_surjections_v1_1520064083_9405 | Compute $7! \cdot S(7,7)$, where $S(n,k)$ denotes the Stirling number of the second kind. Let $c$ be the number of integers $t$ with $10 \leq t \leq 61$ that can be expressed as $t = 7a + 3b$ for positive integers $a \leq 4$ and $b \leq 11$. Compute the remainder when $c$ minus the previous value is divided by $74111$. | 69,111 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(7),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), con... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | comb_count_surjections_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T10:43:20.092498Z | {
"verified": true,
"answer": 69111,
"timestamp": "2026-02-08T10:43:20.094080Z"
} | 6be89e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2230
},
"timestamp": "2026-02-24T12:13:19.235Z",
"answer": 69111
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
518743 | comb_count_surjections_v1_458359167_730 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers between 1 and 9 inclusive such that $i + j = 9$. Let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 5$. Compute the remainder when $64729 \cdot k! \cdot S(n, k)$ is divided by $84837$, wher... | 20,070 | graphs = [
Graph(
let={
"_n": Const(9),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T03:31:29.205698Z | {
"verified": true,
"answer": 20070,
"timestamp": "2026-02-08T03:31:29.218147Z"
} | 27d1d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1720
},
"timestamp": "2026-02-10T14:42:25.855Z",
"answer": 20070
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
454ab6 | sequence_fibonacci_compute_v1_865884756_5304 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 120$ and $8$ divides the $n_1$-th Fibonacci number. Compute the $n$-th Fibonacci number. | 6,765 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(120)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n1')))))),
"result": Fibonacci(arg=Ref(name='n')),
... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T18:30:27.723857Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T18:30:27.724844Z"
} | d19e94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 2148
},
"timestamp": "2026-02-18T17:47:53.589Z",
"answer": 6765
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0a87fb | antilemma_sum_equals_v1_1978505735_2387 | Let $n = 2 \cdot 41$. Define $x$ to be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 81$, $1 \leq j \leq 82$, and $i + j = n$. Compute the value of $$ x + \phi(|x| + 1) + \tau(|x| + \binom{9}{0}), $$ where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes the number of p... | 125 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(41)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | fedc97 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 3 | 0.007 | 2026-02-08T16:52:38.717976Z | {
"verified": true,
"answer": 125,
"timestamp": "2026-02-08T16:52:38.725447Z"
} | 9d8b3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 771
},
"timestamp": "2026-02-24T22:00:10.076Z",
"answer": 125
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -5.09,
"mid": -2.96,
"hi": -0.71
} | ||
36c006 | lin_form_endings_v1_1742523217_147 | Let $a = 42$ and $b = 70$. Let $k = 47$, and let $s = \gcd(a, b)$. Define $r = \left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$. Let $x$ be the remainder when $9496 \cdot r$ is divided by $77221$. Find the value of $x$. | 60,207 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(70),
"k_val": Const(47),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(94... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:53:41.767264Z | {
"verified": true,
"answer": 60207,
"timestamp": "2026-02-08T02:53:41.768296Z"
} | 8aa77b | 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": 721
},
"timestamp": "2026-02-09T14:06:26.761Z",
"answer": 60207
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.88,
"mid": -1.29,
"hi": 0.91
} | ||
57bb75 | diophantine_sum_product_min_v1_2051736721_3177 | Let $n = 12$ and $S = 73$. Let $P$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 439569$. Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 864$ such that $n$ divides the $n$th Fibonacci number. Determine the value of $\sum_{n=1}^{|r|} \phi(n)$, wh... | 360 | graphs = [
Graph(
let={
"_n": Const(12),
"S": Const(73),
"P": 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(439569)))), exp... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"B3"
] | a63611 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.014 | 2026-02-08T17:09:15.969749Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T17:09:15.983653Z"
} | 70514f | 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": 3179
},
"timestamp": "2026-02-17T20:46:00.697Z",
"answer": 360
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
89efa6_n | alg_qf_psd_orbit_v1_1218484723_7374 | A survey team is selecting locations for signal towers on a grid. They choose integer coordinates $(a, b)$ with $1 \le a \le b$. However, due to terrain constraints, the vertical coordinate $b$ cannot exceed the total number of grid points $(a_1, b_1)$ with $1 \le a_1 \le 20$, $1 \le b_1 \le 20$ that satisfy the inequa... | 5 | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3"
] | 3a349f | alg_qf_psd_orbit_v1 | null | 7 | null | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.111 | 2026-02-25T08:46:37.616243Z | null | 7edf19 | 89efa6 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T02:17:49.823Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
f4682a | modular_inverse_v1_865884756_2463 | Let $a = 469$ and let $m$ be the number of positive integers $n$ such that $n \leq 9297$, $9$ divides $n$, and $\gcd(n, 35) = 1$. Compute the smallest positive integer $x$ such that $x \leq 708$ and $469x \equiv 1 \pmod{m}$. | 322 | graphs = [
Graph(
let={
"a": Const(469),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(9297)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"upper": Const(708),
... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | modular_inverse_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.032 | 2026-02-08T16:47:09.487294Z | {
"verified": true,
"answer": 322,
"timestamp": "2026-02-08T16:47:09.519198Z"
} | 1a8ce1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1395
},
"timestamp": "2026-02-17T11:49:26.483Z",
"answer": 322
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b44d95 | alg_qf_psd_min_v1_1218484723_2746 | Let $S$ be the set of ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 30$. Define $E(a, b, c) = 6540ab + 15805c^2 + m \cdot ac + 20710b^2 + 14170a^k + 35970bc$, where $m = \min\{x + y : x, y > 0,\, xy = 7425625\}$ and $k = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 15,\, 91a_1^3 + 48a_1b_1^2 - 96... | 98,645 | graphs = [
Graph(
let={
"_m": Const(35970),
"_n": Const(20710),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"),... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT",
"B3"
] | 7e1382 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"B3",
"POLY3_COUNT"
] | 2 | 0.078 | 2026-02-25T04:27:32.930394Z | {
"verified": true,
"answer": 98645,
"timestamp": "2026-02-25T04:27:33.008863Z"
} | 81ce2a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 318,
"completion_tokens": 29226
},
"timestamp": "2026-03-29T06:22:14.563Z",
"answer": 98645
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
f72993 | antilemma_k2_v1_1978505735_6860 | Let $x = \sum_{k=1}^{378} \phi(k) \left\lfloor \frac{378}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $a = |x| + 1$. Define $Q$ to be the remainder when $x + \phi(a) + \tau(a)$ is divided by $70228$, where $\tau(a)$ denotes the number of positive divisors of $a$. Compute $Q$. | 33,113 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(378), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(378), Var("k"))))),
"Q": Mod(value=Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))), mo... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T19:50:32.882583Z | {
"verified": true,
"answer": 33113,
"timestamp": "2026-02-08T19:50:32.884333Z"
} | 41f881 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1701
},
"timestamp": "2026-02-18T23:36:25.581Z",
"answer": 33113
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fa1674 | nt_count_squarefree_v1_1116507919_143 | Let $n = 97570$ and let $u = 40000$. Define $r$ to be the number of integers $k$ such that $1 \leq k \leq u$ and $\mu(k)^2 = 1$, where $\mu$ denotes the M\"obius function. Let $c$ be the smallest divisor of $16387202345537$ that is greater than or equal to 2. Compute the remainder when $r \bmod 251 + c \cdot (r \bmod 3... | 88,923 | graphs = [
Graph(
let={
"_n": Const(97570),
"upper": Const(40000),
"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'))), Const(1))))),
... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | nt_count_squarefree_v1 | two_moduli | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 4.822 | 2026-02-08T02:26:34.772395Z | {
"verified": true,
"answer": 88923,
"timestamp": "2026-02-08T02:26:39.594793Z"
} | bd795b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 7988
},
"timestamp": "2026-02-09T16:18:41.210Z",
"answer": 65701
},... | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status"... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
e7a28b | comb_sum_binomial_row_v1_124444284_6242 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of positive integers $t$ such that $9 \leq t \leq 28$ and $t = 2a + 7b$ for some integers $a$ and $b$ with $1 \leq a \leq 7$ and $1 \leq b \leq 2$. Let $... | 8,192 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM/MAX_PRIME_BELOW"
] | 56a8ee | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.005 | 2026-02-08T08:14:14.046278Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T08:14:14.051714Z"
} | c022d7 | 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": 1984
},
"timestamp": "2026-02-13T16:29:24.640Z",
"answer": 8192
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6ec0d0 | sequence_fibonacci_compute_v1_1874849503_667 | Let $m_1$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 6718464$. Let $m_2$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m_1$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy... | 46,368 | graphs = [
Graph(
let={
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6718464)))), expr=Sum(Var("x"), Var("y")))),
"_n": MinOverS... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:15:01.968048Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T13:15:01.971497Z"
} | 1cd7d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 983
},
"timestamp": "2026-02-09T19:37:36.809Z",
"answer": 46368
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
b5a7dc | diophantine_fbi2_min_v1_1439011603_1540 | Let $n = 3364$ and $k = 48$. Define $\text{upper}$ to be the number of positive integers $j$ such that $1 \leq j \leq 58$ and $j^2 \leq n$. Let $S$ be the set of all integers $d$ satisfying $7 \leq d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Determine the value of $44121$ times the smallest element... | 59,823 | graphs = [
Graph(
let={
"_n": Const(3364),
"k": Const(48),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(58)), Leq(Pow(Var("j"), Const(2)), Ref("_n"))), domain='positive_integers')),
"result": M... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"C3"
] | 146f10 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C3",
"SUM_ARITHMETIC"
] | 2 | 0.006 | 2026-02-08T16:09:56.236758Z | {
"verified": true,
"answer": 59823,
"timestamp": "2026-02-08T16:09:56.242549Z"
} | c5bd11 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 744
},
"timestamp": "2026-02-16T22:04:19.634Z",
"answer": 59823
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6080d | modular_modexp_compute_v1_601307018_3107 | Let $a$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = \min\{x_1 + y_1 : x_1, y_1 > 0,\ x_1 y_1 = 568516\}$. Let $e$ be the minimum value of $x_2 + y_2$ over all ordered pairs $(x_2, y_2)$ of positive integers with $1 \le x_2 \le y_2$ and $x_2 y_2 = 6350400$. Comp... | 31,827 | graphs = [
Graph(
let={
"_n": Const(2),
"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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tup... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3_DIFF"
] | 181426 | modular_modexp_compute_v1 | null | 7 | 0 | [
"B3",
"B3_DIFF"
] | 2 | 0.008 | 2026-03-10T03:42:13.456962Z | {
"verified": true,
"answer": 31827,
"timestamp": "2026-03-10T03:42:13.465433Z"
} | 577a87 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 18347
},
"timestamp": "2026-03-29T07:31:39.885Z",
"answer": 20369
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
1c9e47 | modular_inverse_v1_717093673_2893 | Let $a = 268$. Let $m$ be the smallest divisor of $212768993$ that is at least $2$. Let $S$ be the set of all integers $x$ such that $1 \le x \le 592$ and
$$
268x \equiv 1 \pmod{m}.
$$
Let $r$ be the smallest element of $S$. Compute $r$. | 104 | graphs = [
Graph(
let={
"a": Const(268),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(212768993))))),
"upper": Const(592),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), con... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_inverse_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.057 | 2026-02-08T17:15:33.925760Z | {
"verified": true,
"answer": 104,
"timestamp": "2026-02-08T17:15:33.983179Z"
} | bc0395 | 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": 2786
},
"timestamp": "2026-02-17T23:08:10.726Z",
"answer": 104
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2b0467 | comb_count_derangements_v1_784195855_5261 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 36928$ and $\binom{36928}{j}$ is odd. Let $d_n$ denote the number of derangements of $n$ elements. Compute the remainder when $13483 \cdot d_n$ is divided by $91611$. | 6,526 | graphs = [
Graph(
let={
"_n": Const(13483),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(36928)), Eq(Mod(value=Binom(n=Const(36928), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T07:48:37.608994Z | {
"verified": true,
"answer": 6526,
"timestamp": "2026-02-08T07:48:37.609955Z"
} | 4b58c1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1963
},
"timestamp": "2026-02-24T08:28:40.906Z",
"answer": 6526
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
eae287 | comb_count_permutations_fixed_v1_655260480_2154 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 185220$, $\gcd(p, q) = 1$, and $p < q$. Let $k = 6$. Compute $\binom{n}{k} \cdot ! (n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 28 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=185220)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:35:33.296728Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T16:35:33.299003Z"
} | f874ac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2462
},
"timestamp": "2026-02-17T07:05:06.622Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
64caf5 | modular_mod_compute_v1_1526740231_204 | Let $m$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 166$. Let $a = -14535$ and $n = 88917$. Compute the remainder when $n \cdot (a \bmod m)$ is divided by 56750. | 41,794 | graphs = [
Graph(
let={
"_n": Const(88917),
"a": Const(-14535),
"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")), Const(166)))),... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T11:23:39.646652Z | {
"verified": true,
"answer": 41794,
"timestamp": "2026-02-08T11:23:39.649078Z"
} | 3a3685 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 976
},
"timestamp": "2026-02-14T13:04:13.130Z",
"answer": 41794
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f74703 | comb_count_permutations_fixed_v1_784195855_2455 | Let $n$ be the smallest integer greater than or equal to 2 that divides 11011. Compute $\binom{n}{4} \cdot !(n - 4)$, where $!m$ denotes the number of derangements of $m$ elements. | 70 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(11011))))),
"k": Const(4),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.012 | 2026-02-08T05:45:12.207055Z | {
"verified": true,
"answer": 70,
"timestamp": "2026-02-08T05:45:12.218965Z"
} | bd8d25 | 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": 862
},
"timestamp": "2026-02-12T14:42:21.112Z",
"answer": 70
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
d74698 | nt_max_prime_below_v1_1520064083_1524 | Let $ S $ be the set of all positive integers $ p $ for which there exists a positive integer $ q $ such that $ pq = 36 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ T $ be the set of all prime numbers $ n $ such that $ n \geq |S| $ and $ n \leq 68644 $. Determine the value of the largest element in $ T $. | 68,639 | graphs = [
Graph(
let={
"upper": Const(68644),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.938 | 2026-02-08T04:04:30.879533Z | {
"verified": true,
"answer": 68639,
"timestamp": "2026-02-08T04:04:32.817967Z"
} | b75466 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 3917
},
"timestamp": "2026-02-10T15:24:35.738Z",
"answer": 68639
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
689321 | sequence_count_fib_divisible_v1_1978505735_3368 | Let $d$ be the number of positive integers $n$ such that $1 \le n \le 43$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Determine the value of the number of positive integers $n_1$ such that $1 \le n_1 \le 778$ and $d$ divides the $n_1$-th Fibonacci number. | 194 | graphs = [
Graph(
let={
"_n": Const(43),
"upper": Const(778),
"d": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=C... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"L3C"
] | 73f8b0 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"L3C",
"MOBIUS_COPRIME"
] | 2 | 0.055 | 2026-02-08T17:35:35.993381Z | {
"verified": true,
"answer": 194,
"timestamp": "2026-02-08T17:35:36.048172Z"
} | 448204 | 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": 2070
},
"timestamp": "2026-02-18T04:55:28.784Z",
"answer": 194
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
53f9f2 | modular_min_modexp_v1_124444284_10057 | Let $ a = 3 $, $ b = 504 $, and $ m = 751 $. Find the smallest positive integer $ x $ such that $ 1 \leq x \leq 750 $ and $ a^x \equiv b \pmod{m} $. | 401 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(504),
"m": Const(751),
"upper": Const(750),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(ModExp(base=Ref("a"), exp=Var("... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | modular_min_modexp_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.051 | 2026-02-08T12:47:43.583519Z | {
"verified": true,
"answer": 401,
"timestamp": "2026-02-08T12:47:43.634265Z"
} | 7bd677 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 5144
},
"timestamp": "2026-02-15T05:32:38.175Z",
"answer": 401
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
0e1a61 | modular_mod_compute_v1_898971024_2855 | Let $a = 70000$ and $m = 81225$. Define $r = a \bmod m$. Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $s = |T|$. Let $S = \sum_{k=1}^{5} k = 15$, and define $e = r \bmod S$. Compute $r + s^e \bmod 92223$. | 71,024 | graphs = [
Graph(
let={
"_n": Const(92223),
"a": Const(70000),
"m": Const(81225),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Sum(Ref("result"), Mod(value=Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(na... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | 1ddb0e | modular_mod_compute_v1 | mod_exp | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.005 | 2026-02-08T17:01:35.299185Z | {
"verified": true,
"answer": 71024,
"timestamp": "2026-02-08T17:01:35.303796Z"
} | 74fc06 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1346
},
"timestamp": "2026-02-17T17:36:49.054Z",
"answer": 71024
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
190b0a | antilemma_sum_equals_v1_1439011603_3139 | Let $n = 72$. Define $x$ to be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = n$, $1 \le i \le 71$, and $1 \le j \le 72$. Compute $x^2 + 13x + 1600$. | 7,564 | graphs = [
Graph(
let={
"_n": Const(72),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(71)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.008 | 2026-02-08T17:16:56.526536Z | {
"verified": true,
"answer": 7564,
"timestamp": "2026-02-08T17:16:56.534338Z"
} | b5dbf3 | 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": 542
},
"timestamp": "2026-02-17T23:22:11.750Z",
"answer": 7564
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
8a1334 | modular_mod_compute_v1_865884756_4105 | Let $a$ be the sum of all positive integers $n$ such that $1 \le n \le 88$ and $n$ is divisible by $8$. Find the remainder when $a$ is divided by $33333$. | 528 | graphs = [
Graph(
let={
"_n": Const(88),
"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(8)), Const(0))))),
"m": Const(33333),
"result": Mod(value=Ref("a"), mo... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | modular_mod_compute_v1 | null | 2 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T17:44:30.541043Z | {
"verified": true,
"answer": 528,
"timestamp": "2026-02-08T17:44:30.542468Z"
} | d577ec | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 404
},
"timestamp": "2026-02-16T11:32:20.736Z",
"answer": 528
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6757c2 | sequence_count_fib_divisible_v1_2080023795_165 | Let $N = 32896$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 233289$. Let $d$ be the number of nonnegative integers $j$ with $0 \leq j \leq 32896$ such that $\binom{32896}{j}$ is odd. Determine the number of positive integers $n$ with $1 \leq n \leq s$ such that ... | 161 | graphs = [
Graph(
let={
"_n": Const(32896),
"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(233289)))), expr=Sum(Var("x"), Var("... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"B3",
"V8"
] | a60b01 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"ONE_PHI_1",
"V8"
] | 3 | 0.045 | 2026-02-08T11:35:14.413682Z | {
"verified": true,
"answer": 161,
"timestamp": "2026-02-08T11:35:14.458858Z"
} | dbc96c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1371
},
"timestamp": "2026-02-08T20:48:03.219Z",
"answer": 161
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.76
} | ||
bcf631 | alg_poly3_min_v1_1218484723_3573 | Consider all integer pairs $(a,b)$ with $1 \le a \le \left|S\right|$ and $1 \le b \le 51$, where $S$ is the set of integers $v$ such that
\begin{itemize}
\item $\min\{ 41a_1^{\left|T\right|} + 82a_1b_1 + 41b_1^{2} : (a_1,b_1),\ 1 \le a_1 \le 8,\ 1 \le b_1 \le 8 \} \le v \le 110864$, and
\item there exist integers $... | 3,360 | graphs = [
Graph(
let={
"_c": Const(41),
"_m": Const(51),
"_n": Const(69252),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=Solutio... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/QF_PSD_MIN/QF_PSD_DISTINCT"
] | 17bfd1 | alg_poly3_min_v1 | null | 8 | 0 | [
"POLY3_COUNT",
"QF_PSD_DISTINCT",
"QF_PSD_MIN"
] | 3 | 0.038 | 2026-02-25T05:12:10.571819Z | {
"verified": true,
"answer": 3360,
"timestamp": "2026-02-25T05:12:10.609936Z"
} | 51346e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 476,
"completion_tokens": 7369
},
"timestamp": "2026-03-29T11:01:40.793Z",
"answer": 2760
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
8dbb82 | diophantine_product_count_v1_1520064083_2786 | Let $k$ be the number of integers $n$ with $1 \leq n \leq 1080$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq 143$, $x$ divides $k$, and $\frac{k}{x} \leq 143$. Find the value of $r$. | 20 | graphs = [
Graph(
let={
"_n": Const(1080),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | diophantine_product_count_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.008 | 2026-02-08T05:00:23.575216Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T05:00:23.582807Z"
} | baa9a6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 2538
},
"timestamp": "2026-02-11T23:07:43.264Z",
"answer": 20
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7eb88f | modular_modexp_compute_v1_865884756_5236 | Let $n = 44121$. Let $a = 2$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 64$. Let $e$ be the maximum value of $xy$ over all such pairs. Let $m = 33856$, and define $r = a^e \mod m$. Compute the remainder when $n \cdot r$ is divided by $74801$. | 400 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(2),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(64)))), expr=... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T18:28:03.181089Z | {
"verified": true,
"answer": 400,
"timestamp": "2026-02-08T18:28:03.184033Z"
} | 0a0635 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 3015
},
"timestamp": "2026-02-18T17:16:14.167Z",
"answer": 400
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ae3193 | comb_sum_binomial_row_v1_1742523217_5713 | Let $d$ be the smallest integer greater than or equal to 2 that divides 634933. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $S$. Compute $80089 - N^d$. | 71,897 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(80089),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(634933))))),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), c... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | a3b634 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T11:11:56.602235Z | {
"verified": true,
"answer": 71897,
"timestamp": "2026-02-08T11:11:56.603825Z"
} | 8e7022 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 883
},
"timestamp": "2026-02-14T10:42:01.905Z",
"answer": 71897
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0d5030 | alg_qf_psd_sum_v1_1218484723_218 | Find the remainder when $\sum_{\substack{a=1}}^{424} \sum_{b=1}^{B} \left(20b^2 + 10a^k - 4ab\right)$ is divided by $59730$, where $B = \left|\left\{(a_1, b_1) : 1 \le a_1, b_1 \le 40,\ -12a_1b_1 + 41a_1^2 + C \cdot b_1^2 \le 14096\right\}\right|$, $C = \left|\left\{(a_2, b_2) : 1 \le a_2, b_2 \le 20,\ -189a_2^3 = -120... | 51,290 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(40),
"_n": Const(10),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(424)), Geq(Var("b"), C... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/QF_PSD_COUNT_LEQ",
"QF_PSD_MIN"
] | 7f56c5 | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ",
"QF_PSD_MIN"
] | 3 | 0.677 | 2026-02-25T01:54:10.841942Z | {
"verified": true,
"answer": 51290,
"timestamp": "2026-02-25T01:54:11.519254Z"
} | e6cdc0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 344,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T08:58:05.153Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": 2.74,
"mid": 4.78,
"hi": 6.68
} | ||
471d98 | algebra_poly_eval_v1_151522320_558 | Let $x$ and $y$ be positive integers such that $xy = 49$. Define $s$ to be the minimum value of $x + y$ over all such pairs. Let $b = 13$. Compute the value of
$$
\frac{s \cdot b^5 + 111b^3 + 130b^2 + 115b + 77 - 57 \cdot b^4}{102},
$$
and then find the remainder when $800$ minus this result is divided by $57503$. | 46,262 | graphs = [
Graph(
let={
"_n": Const(57),
"b": Const(13),
"result": Div(Sum(Mul(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")), Cons... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T03:22:37.027468Z | {
"verified": true,
"answer": 46262,
"timestamp": "2026-02-08T03:22:37.030816Z"
} | fbc037 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 5440
},
"timestamp": "2026-02-10T13:26:35.479Z",
"answer": 46262
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
edf39e | antilemma_k3_v1_865884756_6719 | Let $n = 88330$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. Multiply this sum by $62129$, and find the remainder when the result is divided by $67572$. | 62,162 | graphs = [
Graph(
let={
"_n": Const(88330),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(62129),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(67572)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T19:21:59.497531Z | {
"verified": true,
"answer": 62162,
"timestamp": "2026-02-08T19:21:59.498435Z"
} | 53b563 | 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": 3076
},
"timestamp": "2026-02-18T22:11:53.526Z",
"answer": 62162
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a40436 | sequence_lucas_compute_v1_601307018_4078 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 35$ such that $2b^2 - 4ab + 2a^2 = 1152$. Let $n$ be the minimum value of $4a1^2 + 16b1^2$ over all ordered pairs $(a1, b1)$ of positive integers with $1 \leq a1 \leq M$ and $1 \leq b1 \leq 11$. Compute $L_n$, the $n$-th Luc... | 15,127 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Ref("_m"), Pow... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/QF_PSD_MIN"
] | 92e4bc | sequence_lucas_compute_v1 | null | 6 | 0 | [
"QF_PSD_MIN",
"QF_PSD_ORBIT"
] | 2 | 0.003 | 2026-03-10T04:41:45.074272Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-03-10T04:41:45.077309Z"
} | c42b2b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 1192
},
"timestamp": "2026-03-29T10:55:23.950Z",
"answer": 15127
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
7ea51e | diophantine_fbi2_min_v1_655260480_3722 | Let $k = 180$ and define the upper bound to be $190$. Determine the smallest positive integer $d$ such that $4 \leq d \leq 190$, $d$ divides $180$, and the quotient $\frac{180}{d}$ is at least $7$. Compute this value. | 4 | graphs = [
Graph(
let={
"k": Const(180),
"a": Const(3),
"b": Const(6),
"upper": Const(190),
"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 | COPRIME_PAIRS | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.259 | 2026-02-08T17:30:50.053025Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T17:30:50.311981Z"
} | ea7782 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 487
},
"timestamp": "2026-02-16T10:47:49.218Z",
"answer": 4
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
4129a5 | comb_count_permutations_fixed_v1_1125832087_103 | Define $$v = \sum_{k=0}^{1} (-1)^k \binom{1}{k}, \quad t = \sum_{k=0}^{4} (-1)^k \binom{4}{k}.$$ Let $k = \binom{4}{0} + v + t$, and let $n = 6$. Compute the value of $$\binom{n}{k} \cdot !(n - k),$$ where $!m$ denotes the number of derangements of $m$ elements. Find the value of this expression. | 264 | graphs = [
Graph(
let={
"n2": Const(1),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(4),
"t": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_0"
] | 04f128 | comb_count_permutations_fixed_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_0"
] | 2 | 0.003 | 2026-02-08T02:52:14.351052Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T02:52:14.353584Z"
} | 843205 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 970
},
"timestamp": "2026-02-10T11:43:11.777Z",
"answer": 264
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.98
} | ||
d104d0 | antilemma_sum_equals_v1_397696148_2422 | Let $x$ be the number of ordered pairs $(i,j)$ of integers such that $1 \le i \le 6$, $1 \le j \le 6$, and $i + j = 7$. Compute the value of $$Q = \left(353702 \cdot (|x| \bmod 97) + 329703 \cdot (|x|^2 + 1) \bmod 101 + 215534 \cdot (|x| + 16) \bmod 103\right) \bmod 1009091 \bmod 91926.$$ | 71,999 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6))))),
"Q": Mod... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T13:19:34.963542Z | {
"verified": true,
"answer": 71999,
"timestamp": "2026-02-08T13:19:34.974603Z"
} | 7f653c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1857
},
"timestamp": "2026-02-24T17:46:04.674Z",
"answer": 12173
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
98c0d8 | geo_count_lattice_rect_v1_1874849503_727 | Let $a = 81$ and $b = 171$. Define $r$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Compute the value of $Q = |r|$. | 14,104 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(171),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T13:16:21.788606Z | {
"verified": true,
"answer": 14104,
"timestamp": "2026-02-08T13:16:21.789324Z"
} | 12a5e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 618
},
"timestamp": "2026-02-09T20:18:12.931Z",
"answer": 14104
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
9f7fb2 | modular_modexp_compute_v1_1918700295_4174 | Let $a = 29$. Let $e$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 1048576$. Let $r$ be the remainder when $a^e$ is divided by $10000$. Compute the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $r + 2$. | 220 | graphs = [
Graph(
let={
"a": Const(29),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1048576)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T09:12:22.460339Z | {
"verified": true,
"answer": 220,
"timestamp": "2026-02-08T09:12:22.461743Z"
} | ef44e8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 2907
},
"timestamp": "2026-02-14T01:46:44.032Z",
"answer": 220
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2fe534 | algebra_poly_eval_v1_677425708_3514 | Let $n = 17$. Let $a$ be the sum of all real solutions to the equation $x^2 - 6165x - 537586 = 0$. Compute the value of
$$
\frac{54n^5 + 183n^4 - 559n^3 + 436n^2 + 117n - 1232}{a}.
$$ | 14,491 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Const(17),
"result": Div(Sum(Mul(Const(54), Pow(Ref("n"), Const(5))), Mul(Const(183), Pow(Ref("n"), Ref("_n"))), Mul(Const(-559), Pow(Ref("n"), Const(3))), Mul(Const(436), Pow(Ref("n"), Const(2))), Mul(Const(117), Ref("n")), Co... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | algebra_poly_eval_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.003 | 2026-02-08T05:47:20.635813Z | {
"verified": true,
"answer": 14491,
"timestamp": "2026-02-08T05:47:20.639182Z"
} | abe7d7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1444
},
"timestamp": "2026-02-12T15:02:50.390Z",
"answer": 14491
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cc4084 | comb_sum_binomial_row_v1_458359167_2897 | Let $ u = 4 $ and $ n_2 = u + 1 $. Define $ e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k} $. Let $ n_1 = 0 $ and define $ s = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k} $. Let $ n = 14s $. Compute $ (2 + e)^n $. Find the value of this result. | 16,384 | graphs = [
Graph(
let={
"u": Const(4),
"n2": Sum(Ref("u"), Const(1)),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"s": Summation(var="k", start=Const(0)... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T06:49:37.717624Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T06:49:37.718677Z"
} | 7a6b06 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 371
},
"timestamp": "2026-02-24T07:08:59.296Z",
"answer": 16384
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
7cab2c | nt_sum_divisors_mod_v1_1125832087_479 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 3360$ and $3$ divides the $k$-th Fibonacci number. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $10093$. | 2,880 | graphs = [
Graph(
let={
"_n": Const(3360),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(3), dividend=Fibonacci(arg=Var(name='n')))))),
"M": Const(10093),
"sigma": SumDiv... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T03:07:05.182444Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T03:07:05.183950Z"
} | f43c7a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 1253
},
"timestamp": "2026-02-10T13:02:00.707Z",
"answer": 2880
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
330a7a | lin_form_endings_v1_458359167_3398 | Let $a = 6$, $b = 15$, $A = 47$, and $B = 12$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $$
abla = \left\lfloor \frac{aA + bB - (a + b)}{g} \right\rfloor + 1.$$ Compute the remainder when $11942 \cdot \nabla$ is divided by $82632$. | 32,144 | graphs = [
Graph(
let={
"a_coeff": Const(6),
"b_coeff": Const(15),
"A_val": Const(47),
"B_val": Const(12),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), Re... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:20:06.032510Z | {
"verified": true,
"answer": 32144,
"timestamp": "2026-02-08T08:20:06.033586Z"
} | b77f02 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1034
},
"timestamp": "2026-02-13T17:08:25.054Z",
"answer": 32144
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fd20e4 | alg_qf_psd_orbit_v1_601307018_10197 | Find the number of ordered triples $(a, b, c)$ of positive integers such that $1 \leq a \leq b \leq c \leq 42$ and $$22ac + 22ab + 42b^2 + 42c^2 + 42a^2 + \left|\left\{ v : 5 \leq v \leq 333,\ \text{there exist integers } a, b \text{ with } 1 \leq a \leq 5,\ 1 \leq b \leq 5\ \text{such that } -20ab + 17b^2 + 8a^2 = v \... | 5 | graphs = [
Graph(
let={
"_n": Const(22),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(42)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(42)), Geq(Var("c"), Const(1)), Leq(Var("c... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_orbit_v1 | null | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.509 | 2026-03-10T10:43:08.923718Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T10:43:09.432675Z"
} | 24c565 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 8725
},
"timestamp": "2026-04-19T13:10:08.923Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
05e7b3 | diophantine_fbi2_min_v1_153355830_1495 | Let $k = 55$ and let $d$ be an integer satisfying $6 \leq d \leq 65$ such that $d$ divides $k$ and $\frac{k}{d}$ is at least the largest prime number between 2 and 6, inclusive. Determine the value of $79873d \bmod 66713$. | 11,334 | graphs = [
Graph(
let={
"k": Const(55),
"upper": Const(65),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), MaxOverSet(set=So... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.005 | 2026-02-08T06:27:26.245111Z | {
"verified": true,
"answer": 11334,
"timestamp": "2026-02-08T06:27:26.250273Z"
} | 138a36 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 713
},
"timestamp": "2026-02-13T00:15:07.998Z",
"answer": 11334
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f8e057 | modular_modexp_compute_v1_349078426_631 | Let $a = 29$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1369$. Define $s_{\min}$ to be the minimum value of $x + y$ over all $(x, y) \in S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s_{\min}$. Define $e$ to be the maximum value ... | 43,153 | graphs = [
Graph(
let={
"a": Const(29),
"e": 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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tup... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T13:10:30.699240Z | {
"verified": true,
"answer": 43153,
"timestamp": "2026-02-08T13:10:30.702535Z"
} | c3fcf7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2990
},
"timestamp": "2026-02-15T10:25:27.102Z",
"answer": 43153
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fb5ab9 | alg_poly3_min_v1_1218484723_278 | Let $T = \left| \left\{ (a_1, b_1) \mid 1 \le a_1, b_1 \le 30,\ 13a_1^2 - 2a_1b_1 + 2b_1^2 \le 673 \right\} \right| $. Find the remainder when $$\min_{\substack{1 \le a \le 102\\1 \le b \le 102}} \left( T \cdot a b^2 - 144a^2b - 27b^3 \right)$$ is divided by $78386$. | 7,154 | graphs = [
Graph(
let={
"_n": Const(102),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(102)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(Count... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_min_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.021 | 2026-02-25T01:58:23.266758Z | {
"verified": true,
"answer": 7154,
"timestamp": "2026-02-25T01:58:23.287761Z"
} | cd9333 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 9300
},
"timestamp": "2026-03-10T09:18:03.835Z",
"answer": 7154
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
abb781 | comb_sum_binomial_row_v1_601307018_7594 | Let $C = \left|\{ (a, b) : 1 \le a, b \le 35,\ -12ab + 20b^2 + 41a^2 \le 16705 \}\right|$. Let $n$ be the minimum value of $|x - y|$ over all ordered pairs of positive integers $(x, y)$ such that $xy = C$. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(2),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=Solu... | COMB | null | SUM | sympy | LIN_FORM | [
"QF_PSD_COUNT_LEQ/B3_DIFF"
] | b85ce5 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B3_DIFF",
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.121 | 2026-03-10T08:07:40.420867Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-03-10T08:07:40.542250Z"
} | 53f96f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 5596
},
"timestamp": "2026-04-19T07:04:27.806Z",
"answer": 8192
},
{
"... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
9544d9 | nt_sum_over_divisible_v1_1470522791_869 | Let $n = 44121$ and let $u = 73441$. Let $d$ be the smallest divisor of $343835282311$ that is at least $2$. Define $S$ to be the set of all positive integers $k$ such that $k \leq u$ and $k$ is divisible by $d$. Let $R$ be the sum of all elements in $S$. Compute the remainder when $n \cdot R$ is divided by $99832$. | 49,546 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(73441),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(343835282311))))),
"result": SumOverSet(set=SolutionsSet(var... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.517 | 2026-02-08T13:17:36.708843Z | {
"verified": true,
"answer": 49546,
"timestamp": "2026-02-08T13:17:39.225915Z"
} | 765063 | 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": 3760
},
"timestamp": "2026-02-15T13:08:41.769Z",
"answer": 49546
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
171259 | sequence_count_fib_divisible_v1_1742523217_1288 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 51984$. Define $s_{\text{min}}$ to be the minimum value of $x + y$ over all pairs in $S$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq s_{\text{min}}$ and $7$ divides the $n$th Fibonacci number.
Compute the... | 2,105 | graphs = [
Graph(
let={
"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(51984)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(7)... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.021 | 2026-02-08T03:35:45.339154Z | {
"verified": true,
"answer": 2105,
"timestamp": "2026-02-08T03:35:45.359966Z"
} | b63b6d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2737
},
"timestamp": "2026-02-10T06:12:08.386Z",
"answer": 2105
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
65cf94 | antilemma_k3_v1_349078426_1889 | Let $n = 24457$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, and then find the remainder when the absolute value of this sum is divided by $55286$. | 24,457 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=24457), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Abs(arg=Ref(name='x')), modulus=Const(55286)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.006 | 2026-02-08T13:59:02.409678Z | {
"verified": true,
"answer": 24457,
"timestamp": "2026-02-08T13:59:02.415400Z"
} | ac8881 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 843
},
"timestamp": "2026-02-15T22:45:20.662Z",
"answer": 24457
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b89418 | nt_count_digit_sum_v1_349078426_1286 | Let $s = \sum_{k=1}^{5} k$. Compute the number of positive integers $n \leq 16384$ such that the sum of the decimal digits of $n$ is equal to $s$. | 1,032 | graphs = [
Graph(
let={
"upper": Const(16384),
"target_sum": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), R... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.596 | 2026-02-08T13:32:52.108795Z | {
"verified": true,
"answer": 1032,
"timestamp": "2026-02-08T13:32:52.704479Z"
} | fc4617 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 3610
},
"timestamp": "2026-02-15T16:56:26.806Z",
"answer": 1032
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
63b579 | nt_lcm_compute_v1_1116507919_18 | Let $n = 79524$. Define $a$ to be the number of integers $t$ in the range $9 \leq t \leq 1418$ for which there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 219$, $1 \leq b' \leq 140$, and
$$
t = 2a' + 7b'.
$$
Now consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $... | 65,988 | graphs = [
Graph(
let={
"_n": Const(79524),
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=219)), Geq(left=... | NT | null | COMPUTE | sympy | B3 | [
"LIN_FORM",
"B3"
] | 688dbe | nt_lcm_compute_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T02:23:34.423113Z | {
"verified": true,
"answer": 65988,
"timestamp": "2026-02-08T02:23:34.434154Z"
} | 7ec1f1 | 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": 16510
},
"timestamp": "2026-02-23T15:10:10.020Z",
"answer": 65988
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": 1.66,
"mid": 3.2,
"hi": 4.64
} | ||
d8bcbd | geo_visible_lattice_v1_124444284_8980 | Let $n = 78$. A visible lattice point is an ordered pair $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $v$ be the number of visible lattice points. Compute the remainder when $88251 \cdot v$ is divided by $84355$. | 33,351 | graphs = [
Graph(
let={
"n": Const(78),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(88251),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(84355)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.131 | 2026-02-08T12:06:46.003961Z | {
"verified": true,
"answer": 33351,
"timestamp": "2026-02-08T12:06:46.134642Z"
} | 010ee4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 4407
},
"timestamp": "2026-02-24T15:12:32.148Z",
"answer": 33351
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
abb6d5 | nt_count_intersection_v1_601307018_353 | Let $N$ be the number of positive integers $n$ with $1 \le n \le 20001$ such that the sum of the digits of $n$, denoted $S(n)$, is even. Let $R$ be the number of positive integers $n_1$ with $1 \le n_1 \le N$ such that $\gcd(n_1, 15) = 1$ and $11 \mid n_1$. Find the remainder when $36557R$ is divided by $91061$. | 64,311 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(20001)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"a": Const(11),
"b": Const(15),
"result": CountOverSe... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | nt_count_intersection_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 0.013 | 2026-03-10T00:54:17.681685Z | {
"verified": true,
"answer": 64311,
"timestamp": "2026-03-10T00:54:17.694504Z"
} | 22c1e2 | CC BY 4.0 | null | null | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -10,
"mid": 0,
"hi": 10
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.