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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
74d4f5 | diophantine_fbi2_min_v1_397696148_191 | Let $n = 4$ and $k = 55$. Let $D$ be the set of all divisors $d$ of $32842151$ such that $d \geq 2$. Let $M$ be the smallest element of $D$, and let $\pi(M)$ denote the number of prime numbers $p$ such that $2 \leq p \leq M$. Let $u = \pi(M)$. Let $E$ be the set of all integers $d$ such that $5 \leq d \leq u$, $d$ divi... | 20,731 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(55),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), div... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_PRIMES"
] | 56ea03 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 2 | 0.006 | 2026-02-08T11:21:39.761514Z | {
"verified": true,
"answer": 20731,
"timestamp": "2026-02-08T11:21:39.767823Z"
} | c9592b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 6253
},
"timestamp": "2026-02-14T12:27:53.260Z",
"answer": 20731
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"le... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
247046 | nt_count_divisors_in_range_v1_349078426_1921 | Let $n = 25200$ and $a = 15$. Let $b$ be the sum of all real solutions $x$ to the equation $x^2 - 1270x - 1271 = 0$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let this count be $r$. Compute the remainder when $44121 \cdot r$ is divided by $82834$. | 46,101 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(25200),
"a": Const(15),
"b": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-1270), Var("x")), Const(-1271)), Const(0)))),
"result": CountOverSet(set... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.029 | 2026-02-08T14:00:50.384476Z | {
"verified": true,
"answer": 46101,
"timestamp": "2026-02-08T14:00:50.413196Z"
} | 13343c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 2440
},
"timestamp": "2026-02-15T23:12:27.736Z",
"answer": 46101
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"st... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
afc5ec | nt_num_divisors_compute_v1_1125832087_1120 | Let $n_2 = 1$ and define $f = \omega(n_2)$, where $\omega(n)$ denotes the number of distinct prime factors of $n$. Let $n_1$ be the number of positive integers $n \leq 1083$ such that the $n$-th Fibonacci number is even. Define $h = \lambda(n_1)$, where $\lambda$ denotes the Liouville function. Let $n = (11 + f) \cdot ... | 2 | graphs = [
Graph(
let={
"_n": Const(11),
"n2": Const(1),
"f": SmallOmega(n=Ref(name='n2')),
"n1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1083)), Divides(divisor=Const(2), dividend=Fibonacci(arg=Va... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/LIOUVILLE_ONE",
"OMEGA_ZERO"
] | 291f90 | nt_num_divisors_compute_v1 | null | 6 | 2 | [
"COUNT_FIB_DIVISIBLE",
"LIOUVILLE_ONE",
"OMEGA_ZERO"
] | 3 | 0.002 | 2026-02-08T03:32:58.616316Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T03:32:58.618419Z"
} | 1291fc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 451
},
"timestamp": "2026-02-18T02:31:30.896Z",
"answer": 2
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "OMEGA_ZERO",
"status... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
bf6fe4 | modular_sum_quadratic_residues_v1_1742523217_812 | Let $n = 1274390773$. Let $p$ be the smallest prime divisor of $n$. Compute the value of $\frac{p(p-1)}{4}$. | 8,145 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1274390773))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
},
goa... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-02-08T03:16:00.874784Z | {
"verified": true,
"answer": 8145,
"timestamp": "2026-02-08T03:16:00.878450Z"
} | 5c4053 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 8042
},
"timestamp": "2026-02-09T07:22:20.299Z",
"answer": 8145
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
706fe6 | algebra_quadratic_discriminant_v1_1125832087_52 | Let $b = \sum_{k=1}^{2} k$. Define $\Delta = b^2 - 4(-1)(-2)$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|\Delta| + 2$. | 4 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"c": Const(-2),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": FibonacciEntr... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T02:51:09.321849Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T02:51:09.323101Z"
} | 92f9ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 710
},
"timestamp": "2026-02-10T11:40:58.904Z",
"answer": 4
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
... | {
"lo": -9.16,
"mid": -6.07,
"hi": -3.82
} | ||
ade7a7 | nt_count_primes_v1_1439011603_2644 | Let $\pi(50000)$ denote the number of prime numbers $n$ such that $2 \leq n \leq 50000$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $537251$. Compute the Bell number $B_r$, where $r$ is the remainder when $|\pi(50000)|$ is divided by $d_{\text{min}}$. | 877 | graphs = [
Graph(
let={
"upper": Const(50000),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=Solutions... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_primes_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.728 | 2026-02-08T16:53:40.788769Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T16:53:43.516961Z"
} | c1eefa | 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": 922
},
"timestamp": "2026-02-17T14:22:05.347Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5ad01b | comb_count_partitions_v1_1248542787_237 | Let $m = 44$. Let $n_0$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = m$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n_0$. Compute the number of integer partitions of $n$. | 75,175 | graphs = [
Graph(
let={
"_m": Const(44),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_count_partitions_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T03:02:01.484807Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T03:02:01.487265Z"
} | fbd8bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 869
},
"timestamp": "2026-02-09T01:46:27.878Z",
"answer": 75175
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status... | {
"lo": 0.52,
"mid": 2,
"hi": 3.36
} | ||
39d3d7 | nt_count_primes_v1_124444284_3105 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the value of $m$. Now consider the set of all prime numbers $n$ such that $m \leq n \leq 15120$. Compute the number... | 1,765 | graphs = [
Graph(
let={
"upper": Const(15120),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.135 | 2026-02-08T05:15:04.245746Z | {
"verified": true,
"answer": 1765,
"timestamp": "2026-02-08T05:15:06.380249Z"
} | 7332f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1381
},
"timestamp": "2026-02-12T05:41:03.134Z",
"answer": 1765
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5aaa91 | comb_count_partitions_v1_2051736721_1530 | Let $n$ be the number of integers $t$ with $7 \le t \le 52$ such that there exist integers $a$ and $b$ satisfying $1 \le a \le 4$, $1 \le b \le 10$, and $t = 3a + 4b$. Determine the value of $p(n)$, the number of integer partitions of $n$. | 37,338 | 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=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:05:37.394207Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T16:05:37.397219Z"
} | b123c5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 2336
},
"timestamp": "2026-02-24T19:48:09.610Z",
"answer": 37338
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
10cac2 | alg_qf_psd_sum_v1_1218484723_1371 | Let $S$ be the sum over all ordered quadruples $(a, b, c, d)$ with $1 \le a, c, d \le 7$ and $1 \le b \le \min\{ d_1 : d_1 \ge 2, d_1 \mid 13013 \}$ of the expression $$ 28b \cdot d + 34 \cdot d^{2} + 32a \cdot c + \sum_{k=0}^{2} 4^{k} \cdot b^{2} + 74 \cdot c \cdot d + 26b \cdot c + 42a \cdot b + 26 \cdot a^{2} + 47 \... | 34,412 | graphs = [
Graph(
let={
"_m": Const(74),
"_n": Const(34),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(7)), Geq(Var("b"), Const(1)), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"SUM_GEOM"
] | 6cc952 | alg_qf_psd_sum_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_GEOM"
] | 2 | 0.027 | 2026-02-25T03:04:56.550489Z | {
"verified": true,
"answer": 34412,
"timestamp": "2026-02-25T03:04:56.577521Z"
} | 31e233 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 3987
},
"timestamp": "2026-03-10T06:43:21.167Z",
"answer": 34412
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "... | {
"lo": 0.8,
"mid": 3.7,
"hi": 5.71
} | ||
b76e93 | antilemma_cartesian_v1_1874849503_496 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 19$ and $1 \leq b \leq 20$. Compute the remainder when $x^2 + 47x + 64$ is divided by $52786$. | 3,966 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(19)), right=IntegerRange(start=Const(1), end=Const(20)))),
"_c": Const(64),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(47), Ref("x")), Ref("_c")), modulus... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T13:07:41.489064Z | {
"verified": true,
"answer": 3966,
"timestamp": "2026-02-08T13:07:41.489612Z"
} | e78ae4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 486
},
"timestamp": "2026-02-09T17:40:50.846Z",
"answer": 3966
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
f15eef | lte_diff_endings_v1_677425708_491 | Let $a = 44$, $b = 8$, $p = 3$, and $T = 9$. Define $\text{diff} = a - b$, and let $v_p(\text{diff})$ be the largest integer $k$ such that $p^k$ divides $\text{diff}$. Let $\text{exp} = T - v_p(\text{diff})$. Compute $p^{\text{exp}}$. | 2,187 | graphs = [
Graph(
let={
"a_val": Const(44),
"b_val": Const(8),
"p_val": Const(3),
"T_val": Const(9),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T_v... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:34:23.126530Z | {
"verified": true,
"answer": 2187,
"timestamp": "2026-02-08T03:34:23.127269Z"
} | a020ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 174
},
"timestamp": "2026-02-08T20:39:05.276Z",
"answer": 2187
},
{
"id... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
95581f_n | alg_sym_quad_system_v1_1218484723_5752 | An engineer is cataloging sensor settings. First, she counts how many ordered pairs of settings $(a_1, b_1)$ with $1 \le a_1, b_1 \le 40$ satisfy the safety constraint
$$2b_1^{2} - 2a_1b_1 + 13a_1^{2} \le 877;$$
call this count $N$. Next, she looks at triples of settings $(a, b, c)$ (all positive integers) that form a ... | 5,889 | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | e34ff7 | alg_sym_quad_system_v1 | quadratic_mod | 7 | null | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.016 | 2026-02-25T07:19:16.275167Z | null | fa6e93 | 95581f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 349,
"completion_tokens": 4635
},
"timestamp": "2026-03-31T00:04:12.521Z",
"answer": 5889
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
6847bb | alg_telescope_v1_1419126231_523 | Find the remainder when $\sum_{k=0}^{1795} \left( (k+1)^2 - k^2 \right)$ is divided by the number of pairs $(a,b)$ with $1 \le a \le 35$, $1 \le b \le N$, and $18a^2 + 32b^2 \le 42050$, where $N$ is the number of pairs $(a_1,b_1)$ with $1 \le a_1,b_1 \le 35$ such that $17b_1^4 = 4352$. | 499 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(35),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(1795), expr=Sub(Pow(Sum(Var("k"), Const(1)), Const(2)), Pow(Var("k"), Const(2)))), modulus=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a")... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_COUNT_LEQ"
] | 94cd2a | alg_telescope_v1 | null | 4 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.1 | 2026-02-25T10:03:03.030423Z | {
"verified": true,
"answer": 499,
"timestamp": "2026-02-25T10:03:03.130689Z"
} | 2faac9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 4601
},
"timestamp": "2026-03-30T08:50:47.536Z",
"answer": 241
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
0b8f91_n | alg_qf_psd_sum_v1_1218484723_5227 | A game designer is balancing a four-character team. Each team is described by four integers $(a, b, c, d)$ between $1$ and $13$, representing different stats. For each team, its total power is
$$44c d + 40ab - 2ad - 10bd + 50b^{2} + 68c^{2} + 52bc + K a c + 18d^{2} + 42a^{2},$$
where $K$ is a fixed integer defined as f... | 45,162 | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/QF_PSD_COUNT",
"B1/QF_PSD_COUNT"
] | 23adb5 | alg_qf_psd_sum_v1 | null | 7 | null | [
"B1",
"QF_PSD_COUNT"
] | 2 | 0.204 | 2026-02-25T06:50:56.429295Z | null | 4a342a | 0b8f91 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 442,
"completion_tokens": 5213
},
"timestamp": "2026-03-30T23:03:58.749Z",
"answer": 45162
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
0cac1a | nt_min_phi_inverse_v1_717093673_247 | Let $\text{upper} = \sum_{k_1=1}^{4} \phi(k_1) \left\lfloor \frac{4}{k_1} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k = 2$. Define $\text{result}$ to be the smallest positive integer $n$ such that $1 \le n \le \text{upper}$ and $\phi(n) = k$. Find the value of $\text{result}$. | 3 | graphs = [
Graph(
let={
"upper": Summation(var="k1", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(4), Var("k1"))))),
"k": Const(2),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Re... | NT | null | EXTREMUM | sympy | B3 | [
"K2"
] | 6897ab | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"B3",
"K2"
] | 2 | 0.028 | 2026-02-08T15:15:51.846275Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T15:15:51.873835Z"
} | c7d22a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 875
},
"timestamp": "2026-02-16T03:34:04.051Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a133c6 | sequence_count_fib_divisible_v1_2051736721_1153 | Let $S$ be the set of positive integers $n \leq 486$ such that $5$ divides the $n$-th Fibonacci number, where $F_1 = F_2 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 3$. Let $r = |S|$. Compute the value of
$$
r + \phi(r+1) + \tau(r+1),
$$
where $\phi(n)$ is Euler's totient function and $\tau(n)$ is the number of posi... | 145 | graphs = [
Graph(
let={
"upper": Const(486),
"d": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"Q": Sum(... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"LIN_FORM",
"ONE_PHI_1"
] | e67fb6 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 3 | 0.075 | 2026-02-08T15:52:07.124604Z | {
"verified": true,
"answer": 145,
"timestamp": "2026-02-08T15:52:07.199294Z"
} | 72f22a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 904
},
"timestamp": "2026-02-16T14:41:40.328Z",
"answer": 145
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9c0ac3 | nt_count_divisible_v1_124444284_4366 | Compute the number of positive integers $n \leq 49729$ such that $$ n \equiv \sum_{k=\binom{16}{16}-1}^{2} (-1)^k \binom{2}{k} \pmod{8}. $$ | 6,216 | graphs = [
Graph(
let={
"upper": Const(49729),
"divisor": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Sub(Binom... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | nt_count_divisible_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 1.706 | 2026-02-08T05:57:43.797982Z | {
"verified": true,
"answer": 6216,
"timestamp": "2026-02-08T05:57:45.503745Z"
} | 29cdda | 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": 742
},
"timestamp": "2026-02-24T05:06:53.204Z",
"answer": 6216
},
{
"id... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
207b3b | lte_diff_endings_v1_458359167_628 | Let $a = 89$, $b = 9$, $p = 2$, and $T = 17$. Compute the value of $p^{T - v_p(a - b)}$, where $v_p(m)$ denotes the largest integer $k$ such that $p^k$ divides $m$. | 8,192 | graphs = [
Graph(
let={
"a_val": Const(89),
"b_val": Const(9),
"p_val": Const(2),
"T_val": Const(17),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:26:41.946500Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T03:26:41.947154Z"
} | 09976b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 355
},
"timestamp": "2026-02-18T00:18:04.315Z",
"answer": 8192
}
] | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
8fa7ab | alg_sym_quad_system_v1_1218484723_112 | Let $M$ be the smallest positive divisor of $1876891$. Find the remainder when $$\sum_{\substack{a,b,c \geq 1 \\ a^2 + b^2 + c^2 = ab + bc + ca \\ 6a + 3b + 4c = \min\{x+y : x,y > 0,\, xy = 5116644\}}} (a^5 + b^5 + c^5)$$ is divided by $M$. | 1,082 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1876891))))),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/B3"
] | 5a1a4d | alg_sym_quad_system_v1 | null | 7 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.04 | 2026-02-25T01:49:48.993942Z | {
"verified": true,
"answer": 1082,
"timestamp": "2026-02-25T01:49:49.033493Z"
} | bf51ce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 17641
},
"timestamp": "2026-03-28T21:44:58.823Z",
"answer": 1082
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
09e319 | antilemma_k2_v1_1742523217_3752 | Compute the value of
$$
\left( 20814 \cdot \sum_{k=1}^{333} \phi(k) \left\lfloor \frac{333}{k} \right\rfloor \right) \bmod 52525.
$$ | 46,454 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(333), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(333), Var("k"))))),
"Q": Mod(value=Mul(Const(20814), Ref("x")), modulus=Const(52525)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2"
] | 2 | 0.001 | 2026-02-08T06:05:00.605409Z | {
"verified": true,
"answer": 46454,
"timestamp": "2026-02-08T06:05:00.606827Z"
} | ff5fe0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1438
},
"timestamp": "2026-02-12T19:19:55.094Z",
"answer": 46454
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f7c21e | geo_count_lattice_rect_v1_1439011603_2508 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 240$ and $0 \leq y \leq 312$. | 75,433 | graphs = [
Graph(
let={
"a": Const(240),
"b": Const(312),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T16:50:20.844818Z | {
"verified": true,
"answer": 75433,
"timestamp": "2026-02-08T16:50:20.845499Z"
} | 48c688 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 413
},
"timestamp": "2026-02-17T13:30:33.810Z",
"answer": 75433
},
{
... | 1 | [] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||||
de12a0 | antilemma_cartesian_v1_1125832087_2394 | Compute the number of ordered pairs $(x, y)$ where $x$ is an integer between 1 and 29, inclusive, and $y$ is an integer between 1 and 44, inclusive. | 1,276 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=Const(44)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:34:55.465807Z | {
"verified": true,
"answer": 1276,
"timestamp": "2026-02-08T04:34:55.466505Z"
} | c12018 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 121
},
"timestamp": "2026-02-24T01:00:58.172Z",
"answer": 1276
},
{
"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",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
9dc727 | comb_sum_binomial_mod_v1_1742523217_3567 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 34$. Define $P$ to be the set of all values of $xy$ as $(x,y)$ ranges over $S$. Let $m$ be the maximum element of $P$. Compute $$\sum_{k=28}^{270} \binom{m}{k}.$$ Then find the remainder when this sum is divided by $11503$. Determin... | 11,290 | graphs = [
Graph(
let={
"_n": Const(270),
"sum": Summation(var="k", start=Const(28), end=Ref("_n"), expr=Binom(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... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.046 | 2026-02-08T05:56:54.673043Z | {
"verified": true,
"answer": 11290,
"timestamp": "2026-02-08T05:56:54.719484Z"
} | 50acde | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T05:05:21.424Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
c65fef | comb_count_surjections_v1_655260480_3712 | Let $n = 7$ and $k = 4$. Define $a$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 6000$. Define $b = 4! \cdot S(7, 4)$, where $S(7, 4)$ is the Stirling number of the second kind. Compute the remainder when $a - b$ is divided by $70358$. | 64,958 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')),... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_count_surjections_v1 | negation_mod | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T17:30:46.030760Z | {
"verified": true,
"answer": 64958,
"timestamp": "2026-02-08T17:30:46.032024Z"
} | 84ae0e | 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": 1228
},
"timestamp": "2026-02-18T03:23:58.467Z",
"answer": 64958
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
5d7bbc | modular_mod_compute_v1_784195855_1098 | Let $n = 40000$. Define $s$ as the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Let $a$ be the minimum value of $x + y$ as $(x,y)$ ranges over $s$. Find the remainder when $a$ is divided by $19321$. | 400 | graphs = [
Graph(
let={
"_n": Const(40000),
"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")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:51:39.228422Z | {
"verified": true,
"answer": 400,
"timestamp": "2026-02-08T04:51:39.230182Z"
} | 32ee42 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 826
},
"timestamp": "2026-02-11T22:15:28.345Z",
"answer": 400
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
af6d7d | geo_visible_lattice_v1_1431428450_885 | Let $ n = 128 $. Define a lattice point $ (x, y) $ to be visible from the origin if $ \gcd(x, y) = 1 $. Let $ V(n) $ be the number of visible lattice points in the square $ 1 \leq x, y \leq n $. Given that $ c = 576 $, compute the remainder when $ c - V(n) $ is divided by $ 84443 $. | 74,976 | graphs = [
Graph(
let={
"n": Const(128),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(576),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(84443)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.724 | 2026-02-08T13:46:07.877461Z | {
"verified": true,
"answer": 74976,
"timestamp": "2026-02-08T13:46:08.600974Z"
} | 1bf958 | 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": 15400
},
"timestamp": "2026-02-24T19:03:51.268Z",
"answer": 74976
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
6733b5 | comb_count_permutations_fixed_v1_1742523217_2546 | Let $p_0$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 108$ and $\gcd(p, q) = 1$. Let $n$ be the largest prime number not exceeding $12$ that is at least $p_0$. Let $k$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $p... | 11,998 | graphs = [
Graph(
let={
"_n": Const(12),
"n": 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'), Var(name='q'... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T04:50:07.686772Z | {
"verified": true,
"answer": 11998,
"timestamp": "2026-02-08T04:50:07.691577Z"
} | 4e7989 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 2517
},
"timestamp": "2026-02-11T22:06:23.556Z",
"answer": 11998
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ea80d5 | modular_min_linear_v1_784195855_2907 | Let $a = 70673$, $b = 81444$, and $m = 88266$. Let $\text{result}$ be the smallest positive integer $x$ such that $1 \leq x \leq m$ and $ax \equiv b \pmod{m}$. Let $c' = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Compute the remainder when $c' - \text{resul... | 7,095 | graphs = [
Graph(
let={
"a": Const(70673),
"b": Const(81444),
"m": Const(88266),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Ref("b... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 9468ae | modular_min_linear_v1 | negation_mod | 4 | 0 | [
"K2"
] | 1 | 4.199 | 2026-02-08T06:07:18.326934Z | {
"verified": true,
"answer": 7095,
"timestamp": "2026-02-08T06:07:22.525572Z"
} | a7a73b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 2873
},
"timestamp": "2026-02-12T19:47:19.579Z",
"answer": 7095
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d40905 | geo_count_lattice_rect_v1_124444284_7085 | Compute the number of lattice points in the rectangle $[0, 196] \times [0, 59]$. | 11,820 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(59),
"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 | 0.001 | 2026-02-08T08:50:24.015998Z | {
"verified": true,
"answer": 11820,
"timestamp": "2026-02-08T08:50:24.017009Z"
} | e13606 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 269
},
"timestamp": "2026-02-24T10:04:04.567Z",
"answer": 11820
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
d392ac | diophantine_fbi2_count_v1_458359167_1533 | Let $ k = 120 $. Define $ d_0 $ to be the number of positive divisors $ d $ of $ k $ such that $ 4 \leq d \leq 67 $, $ 2 \leq \frac{k}{d} \leq 65 $. Let $ a $ be the number of ordered pairs $ (p, q) $ of positive integers such that $ p < q $, $ \gcd(p, q) = 1 $, and $ p \cdot q = 24 $. Let $ b $ be the number of ordere... | 4,108 | graphs = [
Graph(
let={
"_n": Const(60216),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(67)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Di... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | diophantine_fbi2_count_v1 | mod_exp | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.122 | 2026-02-08T04:42:11.204731Z | {
"verified": true,
"answer": 4108,
"timestamp": "2026-02-08T04:42:11.326247Z"
} | ad2d36 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 2370
},
"timestamp": "2026-02-11T21:52:03.964Z",
"answer": 4108
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
f64ed6 | modular_sum_quadratic_residues_v1_151522320_727 | Let $p$ be the largest prime number less than or equal to 433. Define $r = \frac{p(p-1)}{4}$. Compute the remainder when $70253r$ is divided by 75420. | 16,092 | graphs = [
Graph(
let={
"_n": Const(433),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=Mul(... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T03:28:27.585102Z | {
"verified": true,
"answer": 16092,
"timestamp": "2026-02-08T03:28:27.587951Z"
} | 6b462e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2398
},
"timestamp": "2026-02-10T14:34:22.672Z",
"answer": 16092
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
c5e21d | nt_count_gcd_equals_v1_677425708_2444 | Let $N$ be the number of positive integers $n \leq 3992$ that are even and relatively prime to 35. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = N$. Compute the number of positive integers $n \leq 39601$ such that $\gcd(n, k) = 74$. | 535 | graphs = [
Graph(
let={
"upper": Const(39601),
"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")), CountOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | COUNT | sympy | C5 | [
"C5/B3"
] | 6843bc | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"C5"
] | 2 | 3.474 | 2026-02-08T05:03:36.003227Z | {
"verified": true,
"answer": 535,
"timestamp": "2026-02-08T05:03:39.477586Z"
} | 859778 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1590
},
"timestamp": "2026-02-11T22:48:50.878Z",
"answer": 535
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
32f89c | geo_count_lattice_triangle_v1_124444284_10306 | Let $A = (0, 0)$, $B = (128, 120)$, and $C = (289, 222)$. The area of triangle $ABC$ can be expressed as $\frac{1}{2} \left| 2x \right|$, where $2x = |128 \cdot 222 - 289 \cdot 120|$. Let $b$ be the number of lattice points on the boundary of triangle $ABC$, which is given by $\gcd(128, 120) + \gcd(|289 - t|, |222 - 12... | 58,512 | graphs = [
Graph(
let={
"_n": Const(222),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=222)), Mul(Const(value=289), Sub(left=Const(value=0), right=Const(value=120))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=120))), GCD(a=Abs(ar... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T12:58:12.122182Z | {
"verified": true,
"answer": 58512,
"timestamp": "2026-02-08T12:58:12.126868Z"
} | 40891c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 2514
},
"timestamp": "2026-02-15T07:50:09.742Z",
"answer": 58512
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3d3f1e | modular_modexp_compute_v1_1125832087_1745 | Let $a$ be the number of integers $t$ with $14 \leq t \leq 62$ for which there exist positive integers $a \leq 4$ and $b \leq 5$ such that $t = 8a + 6b$. Let $e$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 40000$. Let $m = 24336$ and let $r = a^e \bmod m$. Find the remai... | 42,623 | graphs = [
Graph(
let={
"_n": Const(71835),
"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=4)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | modular_modexp_compute_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T03:54:37.687957Z | {
"verified": true,
"answer": 42623,
"timestamp": "2026-02-08T03:54:37.691239Z"
} | 244981 | 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": 4567
},
"timestamp": "2026-02-10T16:08:43.929Z",
"answer": 42623
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e75d93 | diophantine_fbi2_min_v1_2051736721_2142 | Let $k = 360$. Consider the set of all integers $d$ such that $3 \leq d \leq 370$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Determine the value of the smallest such $d$. | 3 | graphs = [
Graph(
let={
"k": Const(360),
"a": Const(2),
"b": Const(5),
"upper": Const(370),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | null | EXTREMUM | sympy | B3 | [
"B3/COUNT_CARTESIAN"
] | b198a7 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 0.049 | 2026-02-08T16:30:04.070171Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T16:30:04.119298Z"
} | fd66be | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 699
},
"timestamp": "2026-02-17T05:22:10.485Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d24d05 | nt_count_coprime_v1_1440796553_640 | Let $P$ be the number of prime numbers between 2 and 151, inclusive. Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = P$. Compute the number of positive integers $n \le 33333$ such that $\gcd(n, k) = 1$. | 11,111 | graphs = [
Graph(
let={
"upper": Const(33333),
"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")), CountOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/B3"
] | 3caaca | nt_count_coprime_v1 | null | 5 | 0 | [
"B3",
"COUNT_PRIMES"
] | 2 | 9.05 | 2026-02-08T11:54:46.711810Z | {
"verified": true,
"answer": 11111,
"timestamp": "2026-02-08T11:54:55.762286Z"
} | 41afb9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 849
},
"timestamp": "2026-02-14T20:28:48.731Z",
"answer": 11111
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemm... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
613100 | antilemma_k2_v1_1520064083_5728 | Let $m$ be the sum $1 + 2 + 3 + 4 + 5 + 6 + 7$, and let $n = 406$. Compute
$$
\sum_{k=1}^{1 + 2 + \cdots + m} \varphi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\varphi(k)$ denotes Euler's totient function and $\left\lfloor \cdot \right\rfloor$ denotes the floor function. | 82,621 | graphs = [
Graph(
let={
"_m": Summation(var="k", start=Const(1), end=Const(7), expr=Var("k")),
"_n": Const(406),
"x": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"... | NT | COMB | COMPUTE | sympy | K13 | [
"SUM_ARITHMETIC/SUM_ARITHMETIC/K2",
"K2"
] | bb97a6 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.005 | 2026-02-08T07:33:53.261688Z | {
"verified": true,
"answer": 82621,
"timestamp": "2026-02-08T07:33:53.266361Z"
} | a55f25 | 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": 669
},
"timestamp": "2026-02-13T11:04:32.257Z",
"answer": 82621
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
003104_n | alg_poly4_min_v1_1218484723_7652 | An engineer designs rectangular frames where side lengths are integers $a$ and $b$ (between 1 and 155). The stability score of a frame is given by $4320a^2b^2 + 1280a^4 + 3840a^3b + D\cdot ab^3 + 410b^4$, where $D$ is the largest divisor of $4758480$ not exceeding $2160$. What is the minimum possible stability score ac... | 12,010 | ALG | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | alg_poly4_min_v1 | null | 5 | null | [
"MAX_DIVISOR"
] | 1 | 0.062 | 2026-02-25T09:06:34.925011Z | null | 3fbea0 | 003104 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 2569
},
"timestamp": "2026-03-31T02:46:04.497Z",
"answer": 12010
},
{
"... | 1 | [
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
a018b6 | antilemma_k2_v1_168721529_281 | Compute $\sum_{k=1}^{93} \phi(k) \left\lfloor \frac{93}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. | 4,371 | graphs = [
Graph(
let={
"_n": Const(93),
"x": Summation(var="k", start=Const(1), end=Const(93), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T12:56:41.195482Z | {
"verified": true,
"answer": 4371,
"timestamp": "2026-02-08T12:56:41.196165Z"
} | 5553de | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 945
},
"timestamp": "2026-02-09T03:13:30.258Z",
"answer": 4371
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.05,
"mid": 1.74,
"hi": 4.86
} | ||
3d490c | diophantine_sum_product_min_v1_1874849503_1618 | Let $S = 61$. Define $P$ to be the number of positive integers $n \le 6510$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $x$ be the smallest positive integer such that $1 \le x \le 60$ and $x(S - x) = P$. Compute the remainder when $80369 \cdot x$ is divided by $56112$. | 54,366 | graphs = [
Graph(
let={
"S": Const(61),
"P": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6510)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
"... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.019 | 2026-02-08T14:00:15.087066Z | {
"verified": true,
"answer": 54366,
"timestamp": "2026-02-08T14:00:15.106278Z"
} | 1d625d | 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": 1630
},
"timestamp": "2026-02-10T05:50:23.702Z",
"answer": 54366
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
f5116d | antilemma_sum_primes_v1_168721529_1336 | Let $\_m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
\[
pq = 72, \quad \gcd(p,q) = 1, \quad p < q.
\]
Let $\_n = 2$. Let $C$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying
\[
1 \le a \le 19, \quad 1 \le b \le 10, \quad 7 \le t \le... | 5 | 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=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM/MIN_PRIME_FACTOR/SUM_PRIMES",
"SUM_PRIMES"
] | 3e5dcd | antilemma_sum_primes_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MIN_PRIME_FACTOR",
"SUM_PRIMES"
] | 4 | 0.01 | 2026-02-08T13:37:55.715415Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T13:37:55.725525Z"
} | 0d34d7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 333,
"completion_tokens": 3939
},
"timestamp": "2026-02-09T15:51:05.972Z",
"answer": 5
},
{
"id":... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIA... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
131332 | algebra_vieta_sum_v1_124444284_9238 | Let $n=4$. Let $k$ be the smallest positive integer $d$ such that
\begin{itemize}
\item $d\ge r$, where $r$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=72,\qquad \gcd(p,q)=1,\qquad p<q,$$
\item and $d$ divides $15$.
\end{itemize}
Consider all real numbers $x$ sat... | 0 | graphs = [
Graph(
let={
"_n": Const(4),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Ref(name='_n')), Mul(Const(value=-1), Pow(base=Var(name='x'), exp=MinOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(le... | NT | null | COMPUTE | sympy | K14 | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | algebra_vieta_sum_v1 | null | 8 | 0 | [
"COPRIME_PAIRS",
"K14",
"MIN_PRIME_FACTOR"
] | 3 | 0.017 | 2026-02-08T12:19:48.740879Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T12:19:48.757966Z"
} | 711109 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 522
},
"timestamp": "2026-02-16T03:34:29.577Z",
"answer": -2
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status":... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
6ef2d7 | diophantine_product_count_v1_898971024_1498 | Let $k = 840$ and $u = 298$. Let $r$ be the number of positive integers $x$ with $1 \leq x \leq u$ such that $x$ divides $k$ and $\frac{k}{x} \leq u$. Let $m$ be the largest prime number less than or equal to $2028$. Compute $m - r$. | 1,999 | graphs = [
Graph(
let={
"k": Const(840),
"upper": Const(298),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | diophantine_product_count_v1 | negation_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.023 | 2026-02-08T16:10:44.542988Z | {
"verified": true,
"answer": 1999,
"timestamp": "2026-02-08T16:10:44.565962Z"
} | 7b6f8e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1979
},
"timestamp": "2026-02-16T21:56:11.557Z",
"answer": 1999
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a6055e | diophantine_product_count_v1_458359167_1571 | Let $k = 480$. Let $n$ be a positive integer such that $1 \leq n \leq 3300$ and $24$ divides the $n$th Fibonacci number. Define $\text{upper}$ to be the number of such integers $n$. Now, let $x$ be a positive integer such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$. Compute t... | 22 | graphs = [
Graph(
let={
"k": Const(480),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(3300)), Divides(divisor=Const(24), dividend=Fibonacci(arg=Var(name='n')))))),
"result": CountOverSet(set=SolutionsSet(v... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 0.123 | 2026-02-08T04:45:30.403479Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T04:45:30.526863Z"
} | d150e1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 3047
},
"timestamp": "2026-02-11T21:53:49.992Z",
"answer": 22
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
912c11 | modular_product_range_v1_601307018_1482 | Let $R = \prod_{i=3}^{N} i$, where $N$ is the number of ordered pairs $(a,b)$ of positive integers with $1 \le a, b \le 30$ satisfying $20b^2 + 41a^2 - 12ab \le 8665$. Let $S = R \bmod 11701$. Find the remainder when $46395S$ is divided by $80306$. | 72,258 | graphs = [
Graph(
let={
"_n": Const(11701),
"prod": MathProduct(expr=Var("i"), var="i", start=Const(3), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), ... | NT | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | modular_product_range_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.008 | 2026-03-10T02:12:54.152244Z | {
"verified": true,
"answer": 72258,
"timestamp": "2026-03-10T02:12:54.160583Z"
} | 207421 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T02:24:21.286Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
29388e | comb_factorial_compute_v1_1218484723_4031 | Let $N = \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 10,\ 510a_1^2b_1^2 - 292a_1^3b_1 + 82b_1^4 + 97a_1^4 - 316a_1b_1^3 = 111537 \}\right|$. Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that
$$
91a^3 + 48ab^2 - 96a^2b - 8b^N = 120744.
$$Let $n$ be the number of integer... | 40,320 | graphs = [
Graph(
let={
"_c": Const(510),
"_m": Const(15),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_m")), Eq(Sum(Mul(Const(48... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/POLY3_COUNT/QF_PSD_DISTINCT"
] | 9f9181 | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 0.007 | 2026-02-25T05:38:30.141159Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T05:38:30.148050Z"
} | 67e58d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 329,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T13:29:45.051Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY4_C... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
0f989a | antilemma_k2_v1_655260480_5236 | Let $m = 144$. Compute the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $m$. Let this sum be $A$. Then compute the sum of $\phi(d)$ over all positive divisors $d$ of $A$. Let this sum be $B$. Now compute the sum
$$
\sum_{k=1}^{B} \phi(k) \left\lfloor \frac{144}{k} \right\rfloor.
$$
Determ... | 10,440 | graphs = [
Graph(
let={
"_m": Const(144),
"_n": Const(50),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=SumOverDivisors(n=Ref(name='_m'), var='d1', expr=EulerPhi(n=Var(name='d1'))), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), ... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3/K2",
"IDENTITY_POW_ZERO",
"K2"
] | fff36e | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_POW_ZERO",
"K2",
"K3"
] | 3 | 0.002 | 2026-02-08T18:22:31.790682Z | {
"verified": true,
"answer": 10440,
"timestamp": "2026-02-08T18:22:31.792556Z"
} | 80eef1 | 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": 1309
},
"timestamp": "2026-02-18T16:31:28.603Z",
"answer": 10440
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c5bd1 | comb_count_derangements_v1_1978505735_6969 | Let $n = 8$. Define $result = !n$, the number of derangements of $n$ elements. Let $N = 9409$. Consider the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = N$. Let $s_{\min}$ be the minimum value of $x_1 + y_1$ over all such pairs. Now consider the set of all ordered pairs $(x, y)$ of po... | 76,861 | graphs = [
Graph(
let={
"_n": Const(9409),
"n": Const(8),
"result": Subfactorial(arg=Ref(name='n')),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name... | COMB | null | COUNT | sympy | B3 | [
"B3/B1"
] | 6cdf3d | comb_count_derangements_v1 | negation_mod | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T19:55:53.538654Z | {
"verified": true,
"answer": 76861,
"timestamp": "2026-02-08T19:55:53.540923Z"
} | f6a2ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1816
},
"timestamp": "2026-02-18T23:45:24.621Z",
"answer": 76861
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"st... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
c45703 | nt_max_prime_below_v1_784195855_9919 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $n$ be the largest prime number such that $m \leq n \leq 15876$. Compute the remainder when $88327n$ is divided by $84804$. | 70,225 | graphs = [
Graph(
let={
"upper": Const(15876),
"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 | 0.373 | 2026-02-08T17:18:41.342028Z | {
"verified": true,
"answer": 70225,
"timestamp": "2026-02-08T17:18:41.714948Z"
} | 098077 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 3967
},
"timestamp": "2026-02-18T00:17:45.732Z",
"answer": 70225
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
945e8e_n | alg_qf_psd_count_leq_v1_1218484723_6166 | A rectangular garden is to be enclosed with a perimeter of 60 meters, where the side lengths are positive real numbers. Among all such rectangles, let $M$ be the maximum possible area. A landscape artist considers all grid positions $(a, b)$ where $a$ is an integer from 1 to $M$ and $b$ is an integer from 1 to 225. She... | 47,052 | ALG | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | alg_qf_psd_count_leq_v1 | null | 5 | null | [
"B1"
] | 1 | 0.089 | 2026-02-25T07:46:42.821643Z | null | 253432 | 945e8e | narrative | 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": 7734
},
"timestamp": "2026-03-31T00:46:38.657Z",
"answer": 47052
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
e21fc2 | comb_binomial_compute_v1_1742523217_478 | Let $n_0$ be the number of integers $n$ with $1 \leq n \leq 99$ such that the sum of the digits of $n$ is even. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n_0$. Let $r = \binom{n}{6}$. Find the value of $r$. | 3,003 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(99)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), V... | ALG | COMB | COMPUTE | sympy | L3B | [
"L3B/B3"
] | f2ec8b | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3",
"L3B"
] | 2 | 0.003 | 2026-02-08T03:04:36.551992Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T03:04:36.555115Z"
} | 5b6082 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 985
},
"timestamp": "2026-02-09T18:29:03.982Z",
"answer": 3003
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
a57ade | comb_catalan_compute_v1_1742523217_96 | Let $m = 25$. Let $s$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = m$ and $1 \leq i, j \leq 23$. Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = s$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $44121 \cdot ... | 18,826 | graphs = [
Graph(
let={
"_m": Const(25),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T02:52:46.947560Z | {
"verified": true,
"answer": 18826,
"timestamp": "2026-02-08T02:52:46.959124Z"
} | c8e20a | 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": 2122
},
"timestamp": "2026-02-09T13:44:22.446Z",
"answer": 18826
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_... | {
"lo": 1.01,
"mid": 2.46,
"hi": 3.79
} | ||
97d0d5 | nt_count_divisible_and_v1_1520064083_2238 | Let $T$ be the set of all integers $t$ such that $13 \leq t \leq 150$ and there exist positive integers $a \leq 10$ and $b \leq 38$ satisfying $t = 7a + 2b + 4$. Let $m$ be the number of elements in $T$. Let $d$ be the number of positive integers $n \leq m$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pm... | 193 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/L3C"
] | cf7f86 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.777 | 2026-02-08T04:35:35.298670Z | {
"verified": true,
"answer": 193,
"timestamp": "2026-02-08T04:35:36.075623Z"
} | 0e5354 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 4861
},
"timestamp": "2026-02-10T17:09:18.064Z",
"answer": 193
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
dfef64 | diophantine_fbi2_min_v1_238844314_118 | Let $n = 720$. Define $k$ to be the number of positive integers from $1$ to $n$ that are divisible by $30$. Let $S$ be the set of all integers $d$ such that $2 \leq d \leq 34$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Determine the value of the smallest element in $S$. | 2 | graphs = [
Graph(
let={
"_n": Const(720),
"k": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(30), dividend=Var("k"))), domain='positive_integers')),
"upper": Const(34),
"resul... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"C2"
] | 9685eb | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C2",
"MOBIUS_COPRIME"
] | 2 | 0.079 | 2026-02-08T13:07:48.687152Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:07:48.765991Z"
} | 9466b2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 458
},
"timestamp": "2026-02-16T04:26:10.829Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
81b09f | comb_count_derangements_v1_458359167_1620 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Define $n$ to be the largest prime number that is less than or equal to $8$ and at least $m$. Compute $!n$, the number of derangeme... | 1,854 | graphs = [
Graph(
let={
"_n": Const(8),
"n": 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'), Var(name='q')... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T04:46:58.251733Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T04:46:58.253441Z"
} | 14d9e8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1674
},
"timestamp": "2026-02-11T21:57:22.976Z",
"answer": 1854
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
63300c | nt_euler_phi_compute_v1_1353956133_301 | Let $n = 32761$ and define $\varphi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $c$ be the number of positive integers $k$ such that $1 \leq k \leq 19494$ and the $k$-th Fibonacci number is divisible by 4. Compute the value of $$
+ \sum_{i=0}^{d-1} a_i (i+1... | 3,433 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(32761),
"result": EulerPhi(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19494)), Divides(divisor=Const(4), dividend=Fibonacci(arg=Va... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 926637 | nt_euler_phi_compute_v1 | digits_weighted_mod | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T11:23:25.123745Z | {
"verified": true,
"answer": 3433,
"timestamp": "2026-02-08T11:23:25.125740Z"
} | ab8808 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1459
},
"timestamp": "2026-02-14T13:20:31.577Z",
"answer": 3433
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
28d53c | modular_modexp_compute_v1_865884756_921 | Let $a = 47$, and let $e = \sum_{k=1}^{129} k$. Compute the remainder when $a^e$ is divided by $75025$. | 49,832 | graphs = [
Graph(
let={
"a": Const(47),
"e": Summation(var="k", start=Const(1), end=Const(129), expr=Var("k")),
"m": Const(75025),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_modexp_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T15:41:21.676814Z | {
"verified": true,
"answer": 49832,
"timestamp": "2026-02-08T15:41:21.678766Z"
} | 238dcb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 4516
},
"timestamp": "2026-02-16T11:01:16.352Z",
"answer": 49832
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
226ffa | comb_catalan_compute_v1_898971024_2623 | Let $n$ be the number of integers $t$ with $16 \leq t \leq 29$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 5a + 2b + 9$. Compute the $n$-th Catalan number. Find the value of this Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.028 | 2026-02-08T16:53:06.023421Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T16:53:06.050979Z"
} | 9992c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1017
},
"timestamp": "2026-02-17T14:09:09.570Z",
"answer": 16796
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
c7de96 | antilemma_k3_v1_168721529_1087 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $82490$, where $\phi$ is Euler's totient function. Compute the remainder when $$ x + \phi(|x| + 1) + \tau(|x| + 1) $$ is divided by $56133$, where $\tau(k)$ denotes the number of positive divisors of $k$. | 23,392 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=82490), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Div(Const(86), Const(86)))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Pow(Const(97), Const(0))))), modulus... | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"IDENTITY_DIV_SELF",
"K3"
] | 363658 | antilemma_k3_v1 | null | 3 | 0 | [
"IDENTITY_DIV_SELF",
"IDENTITY_POW_ZERO",
"K3"
] | 3 | 0.001 | 2026-02-08T13:27:41.582423Z | {
"verified": true,
"answer": 23392,
"timestamp": "2026-02-08T13:27:41.583910Z"
} | b073af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 4503
},
"timestamp": "2026-02-09T13:39:40.723Z",
"answer": 23392
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
0ac144 | sequence_count_fib_divisible_v1_1742523217_4704 | Let $p$ be the largest prime number less than or equal to 104. Determine the number of positive integers $n$ such that $n \leq p$ and the $n$th Fibonacci number is divisible by 19. Let this count be $c$. Compute the remainder when $66707 \cdot c$ is divided by 55117. | 2,833 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(104)), IsPrime(Var("n"))))),
"d": Const(19),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), ... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.008 | 2026-02-08T09:05:45.734362Z | {
"verified": true,
"answer": 2833,
"timestamp": "2026-02-08T09:05:45.741951Z"
} | c483a7 | 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": 1878
},
"timestamp": "2026-02-14T00:18:56.533Z",
"answer": 2833
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6609c2 | alg_qf_psd_min_v1_1218484723_863 | Let $M = \min\{54a_1^2b_1 + 2b_1^3 : 1 \le a_1, b_1 \le 26\}$. Find the minimum value $Q$ of the expression $$58276a^2 - 95984ac + 6856ab - 47992bc + 87414c^2 + 61704b^2$$ over all positive integers $a, b, c$ with $1 \le a \le M$, $1 \le b \le 56$, and $1 \le c \le 56$. | 70,274 | graphs = [
Graph(
let={
"_n": Const(87414),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1"... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"POLY3_MIN"
] | 1 | 0.386 | 2026-02-25T02:33:53.806734Z | {
"verified": true,
"answer": 70274,
"timestamp": "2026-02-25T02:33:54.192587Z"
} | cf471d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 17731
},
"timestamp": "2026-03-10T02:26:44.833Z",
"answer": 70274
},
{
... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
d6c57d | lin_form_endings_v1_1440796553_1068 | Let $a = 8$ and $b = 28$. Compute the value of $$\left\lfloor \frac{28}{\gcd(a, b)} \right\rfloor,$$ multiply the result by $11238$, and then compute the remainder when this product is divided by $88545$. Determine the value of this remainder. | 78,666 | graphs = [
Graph(
let={
"a_coeff": Const(8),
"b_coeff": Const(28),
"_inner_result": Floor(Div(Const(28), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(11238),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:10:02.665844Z | {
"verified": true,
"answer": 78666,
"timestamp": "2026-02-08T12:10:02.666625Z"
} | eeec82 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 265
},
"timestamp": "2026-02-16T03:32:07.502Z",
"answer": 78666
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
5bae38 | v1_endings_v1_1116507919_241 | Let $n = 785$. Define $v_p(n!)$ to be the largest integer $k$ such that $p^k$ divides $n!$. Compute the value of $v_7(n!) \bmod 100$, multiply the result by 1000, then add $100 \times \left(v_5(n!) \bmod 10\right)$ and $v_2(n!) \bmod 100$. Find the resulting sum. | 30,581 | graphs = [
Graph(
let={
"n_val": Const(785),
"p1_val": Const(7),
"p2_val": Const(5),
"p3_val": Const(2),
"n_fact": Factorial(Ref("n_val")),
"vp1": MaxKDivides(target=Ref("n_fact"), base=Ref("p1_val")),
"vp2": MaxKDivides(tar... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 6 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T02:29:35.638031Z | {
"verified": true,
"answer": 30581,
"timestamp": "2026-02-08T02:29:35.638782Z"
} | 2ecbc3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1392
},
"timestamp": "2026-02-08T19:16:27.828Z",
"answer": 30581
},
{
"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -4.6,
"mid": 0.15,
"hi": 4.61
} | ||
76d76d | antilemma_coprime_grid_v1_677425708_96 | Let $\phi$ denote Euler's totient function and $\mu$ the M\"obius function. Define $k = \sum_{d\mid \gcd(7,11)} \mu(d)$. Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 54$ and $1 \leq j \leq 72$ such that $\gcd(i,j) = \phi(k)$. Compute the remainder when $31981x$ is divided by $69669$. | 7,697 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=SumOverDivisors(n=GCD(a=Const(value=7), b=Const(value=11)), var='d', expr=MoebiusMu(n=Var(name='d'))))), domain=CartesianProduct(left=IntegerR... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"MOBIUS_COPRIME",
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2c7d49 | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"COUNT_COPRIME_GRID",
"MOBIUS_COPRIME",
"ONE_PHI_1"
] | 4 | 0.011 | 2026-02-08T03:04:07.974030Z | {
"verified": true,
"answer": 7697,
"timestamp": "2026-02-08T03:04:07.985371Z"
} | fc24f5 | 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": 2862
},
"timestamp": "2026-02-10T04:03:54.523Z",
"answer": 7697
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -6.5,
"mid": 0,
"hi": 6.5
} | ||
3b16b3 | modular_sum_quadratic_residues_v1_865884756_136 | Let $p$ be the largest prime number less than or equal to 102. Define $r = \frac{p(p-1)}{4}$. Find the remainder when $15553 \cdot r$ is divided by 79392. | 51,677 | graphs = [
Graph(
let={
"_n": Const(15553),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(102)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:12:08.349686Z | {
"verified": true,
"answer": 51677,
"timestamp": "2026-02-08T15:12:08.352080Z"
} | cc389a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1514
},
"timestamp": "2026-02-10T04:37:29.184Z",
"answer": 51677
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
a09ae3 | nt_count_divisors_in_range_v1_1874849503_81 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 46620$ and $37$ divides $k$. Let $a = 5$. Let $b$ be the number of positive integers $t$ such that $33 \leq t \leq 654$ and there exist positive integers $a'$, $b'$ with $1 \leq a' \leq 6$, $1 \leq b' \leq 44$, and $t = 21a' + 12b'$. Determine the ... | 26 | graphs = [
Graph(
let={
"_n": Const(46620),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(37), dividend=Var("k"))), domain='positive_integers')),
"a": Const(5),
"b": Coun... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM",
"C2"
] | c556ae | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"C2",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.277 | 2026-02-08T12:47:43.463998Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T12:47:43.740678Z"
} | edea08 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 4822
},
"timestamp": "2026-02-09T13:43:48.865Z",
"answer": 26
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}... | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
16d9fc | comb_count_permutations_fixed_v1_1978505735_5749 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 7560$. Define $k = 3$. Compute the sum of the number of positive divisors of each integer from 1 to $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of ... | 19,635 | 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=7560)), 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 | 7 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T19:12:21.043540Z | {
"verified": true,
"answer": 19635,
"timestamp": "2026-02-08T19:12:21.045622Z"
} | 8f3183 | 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": 6209
},
"timestamp": "2026-02-18T21:36:15.908Z",
"answer": 19635
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a43bf2 | comb_catalan_compute_v1_1218484723_2218 | Let $C_n$ denote the $n$-th Catalan number. Let $n = \left|\{ (x_1, x_2) : x_1 > 0, x_2 > 0, x_1 \text{ is odd}, x_2 \text{ is odd}, x_1 + x_2 = 22 \}\right| \cdot \sum_{k_1=0}^{\binom{10}{0}-1} (-1)^{k_1} \binom{\binom{10}{0}-1}{k_1} \cdot \sum_{k_2=\binom{1}{0}-1}^{\sum_{k=0}^{4} (-1)^k \binom{4}{k}} (-1)^{k_2} \bino... | 58,786 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(1),
"n3": Sum(Ref("a"), Ref("b")),
"u": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n2": Sub(Binom(n=Const(10), k=Const(0)... | COMB | null | COMPUTE | sympy | HALFPLANE_COUNT | [
"COMB1/BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2842f4 | comb_catalan_compute_v1 | null | 5 | 3 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"HALFPLANE_COUNT",
"ZERO_BINOM_0"
] | 4 | 0.149 | 2026-02-25T03:59:51.576267Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-25T03:59:51.725640Z"
} | 43c951 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 1522
},
"timestamp": "2026-03-29T03:35:53.509Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT... | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.88
} | ||
db4bd2 | nt_count_gcd_equals_v1_1918700295_3986 | Let $n = 16129$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = n$.
Let $d$ be the number of integers $t$ in the range $14 \leq t \leq 273$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 18$, $1 \leq b \leq 71$, and $t = 7a + 2b + 5$.
Let ... | 30,504 | graphs = [
Graph(
let={
"_n": Const(16129),
"upper": Const(32768),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 2.593 | 2026-02-08T09:04:43.907487Z | {
"verified": true,
"answer": 30504,
"timestamp": "2026-02-08T09:04:46.500957Z"
} | 75e4a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3407
},
"timestamp": "2026-02-14T00:03:08.373Z",
"answer": 30504
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c9f97a | nt_sum_divisors_compute_v1_1456120455_61 | Let $p$ be the largest prime number satisfying $2 \leq p \leq 8$. Define $w = (p-1)! + 1 \pmod{p}$. Let $g$ be the largest prime number satisfying $2 \leq g \leq 22$. Let $m = 14 + w$ and $n_1 = 11$. Let $a = g \cdot m$ and $b = g \cdot n_1$. Let $v = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ is the M\"obius functio... | 86,143 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(14),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"w": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), mod... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MOBIUS_COPRIME",
"MAX_PRIME_BELOW/WILSON"
] | f4ba55 | nt_sum_divisors_compute_v1 | null | 6 | 2 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME",
"WILSON"
] | 3 | 0.005 | 2026-02-08T02:52:29.018752Z | {
"verified": true,
"answer": 86143,
"timestamp": "2026-02-08T02:52:29.023576Z"
} | d286d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1054
},
"timestamp": "2026-02-08T19:57:41.705Z",
"answer": 86143
},
{
"... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later... | {
"lo": -6.52,
"mid": -0.57,
"hi": 4.59
} | ||
e80362 | alg_poly4_count_v1_601307018_5238 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 35$ such that $10a_1^2 - 18a_1b_1 + 25b_1^2 \le 4057$, and let $k = |S|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le k$, $1 \le b \le 326$, satisfying $16a^4 + 81b^4 + 216a^2b^2 - 216ab^3... | 106 | graphs = [
Graph(
let={
"_n": Const(16),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_count_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 2.74 | 2026-03-10T05:55:06.313919Z | {
"verified": true,
"answer": 106,
"timestamp": "2026-03-10T05:55:09.054285Z"
} | e22e5f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 7773
},
"timestamp": "2026-04-19T01:36:18.537Z",
"answer": 7
},
{
"... | 0 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
6febcb | alg_telescope_v1_601307018_567 | Find the remainder when $$\sum_{k=0}^{508} \left(4k^3 + 6k^2 + 4k + 1\right)$$ is divided by $$\max\left\{ d \geq 1 : d \mid 74995591,\; d^2 \leq 74995591 \right\}.$$ | 6,076 | graphs = [
Graph(
let={
"_n": Const(4),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(508), expr=Sum(Mul(Const(4), Pow(Var("k"), Const(3))), Mul(Const(6), Pow(Var("k"), Const(2))), Mul(Ref("_n"), Var("k")), Const(1))), modulus=MaxOverSet(set=SolutionsSet(var=Var("d... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | alg_telescope_v1 | null | 4 | 0 | [
"B3_CLOSEST"
] | 1 | 0.064 | 2026-03-10T01:05:44.710302Z | {
"verified": true,
"answer": 6076,
"timestamp": "2026-03-10T01:05:44.774189Z"
} | c015d1 | 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": 22584
},
"timestamp": "2026-03-28T23:26:37.007Z",
"answer": 6076
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": 2.84,
"mid": 4.95,
"hi": 7.12
} | ||
73ac74 | comb_count_derangements_v1_898971024_1556 | Let $m = 2$. Let $S$ be the set of all prime numbers $n_2$ such that $m \leq n_2 \leq 10$. Let $n$ be the largest prime number $n_1$ such that $n_1 \in S$. Define $\text{result} = !n$, the subfactorial of $n$. Let $N = 44121$. Compute the remainder when $N \cdot \text{result}$ is divided by $52007$. | 45,330 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(44121),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Ref("_m")), Leq(Var("n2"), Const(10))... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | comb_count_derangements_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T16:11:40.157422Z | {
"verified": true,
"answer": 45330,
"timestamp": "2026-02-08T16:11:40.160946Z"
} | 70602a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1542
},
"timestamp": "2026-02-16T22:28:58.404Z",
"answer": 45330
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f68537 | sequence_lucas_compute_v1_1520064083_3828 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 29$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 7$, and $t = 5a + 2b$. Let $n$ be the number of elements in $T$. Compute the $n$-th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k... | 9,349 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:55:30.344321Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T05:55:30.345549Z"
} | 3dd9da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1779
},
"timestamp": "2026-02-12T17:24:40.930Z",
"answer": 9349
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
35f3a2 | alg_sym_quad_system_v1_601307018_3141 | Let $M = \max\{ d \geq 1 : d \mid 3655743 \text{ and } d^2 \leq 3655743 \}$. Find the remainder when $$\sum_{\substack{a,b,c \geq 1 \\ a^2 + b^2 + c^2 = ab + bc + ca \\ 5a + b + 7c = M}} (a^3 + b^3 + c^3)$$ is divided by $3125$. | 1,444 | graphs = [
Graph(
let={
"_n": Const(7),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | alg_sym_quad_system_v1 | null | 7 | 0 | [
"B3_CLOSEST"
] | 1 | 0.016 | 2026-03-10T03:43:26.227215Z | {
"verified": true,
"answer": 1444,
"timestamp": "2026-03-10T03:43:26.242855Z"
} | a29c6c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:37:19.077Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
4c45ec | comb_factorial_compute_v1_677425708_193 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 8$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_factorial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T03:07:00.315089Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T03:07:00.316392Z"
} | 2ad7b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 139
},
"timestamp": "2026-02-08T20:23:58.550Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
9fd7cd | algebra_quadratic_discriminant_v1_677425708_3495 | Let $m = 2$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $n = |S|$. Let $a$ be the largest prime number between 2 and 3, inclusive. Let $D = b^2 - 4ac$, where $b = -5$ and $c = 13$. Define $r = n$ if $D > 0$, $r =... | 0 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.006 | 2026-02-08T05:45:24.508765Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T05:45:24.515024Z"
} | 2a5bf4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1801
},
"timestamp": "2026-02-12T14:06:38.215Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
47fec3 | comb_catalan_compute_v1_784195855_5966 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 13$, $1 \le i \le 11$, and $1 \le j \le 11$. Let $C_n$ denote the $n$th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by $82700$. | 64,316 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(13)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.014 | 2026-02-08T08:13:57.768397Z | {
"verified": true,
"answer": 64316,
"timestamp": "2026-02-08T08:13:57.781929Z"
} | fa8a34 | 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": 1368
},
"timestamp": "2026-02-24T09:01:56.349Z",
"answer": 64316
},
{
"... | 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": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
66855a | sequence_fibonacci_compute_v1_865884756_1932 | Let $d$ be the smallest integer greater than or equal to 2 that divides 667. Let $F_d$ denote the $d$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_n = F_{n-1} + F_{n-2}$ for $n \ge 3$. Let $m = |F_d| + 2$. Find the smallest positive integer $k$ such that $F_k$ is divisible by $m$. | 260 | 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(667))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(a... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T16:24:09.892345Z | {
"verified": true,
"answer": 260,
"timestamp": "2026-02-08T16:24:09.894549Z"
} | 1395e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1803
},
"timestamp": "2026-02-17T03:22:16.993Z",
"answer": 260
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a00a82 | nt_count_divisible_and_v1_1248542787_370 | Let $u$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 10692900$.\\
Let $d_1 = 1 + 2 + 3$ and $d_2 = 10$. Define $N$ to be the number of positive integers $n$ such that $1 \leq n \leq u$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$.\\
Compute the rema... | 9,257 | graphs = [
Graph(
let={
"_n": Const(3),
"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(10692900)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | dee757 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.251 | 2026-02-08T03:05:04.817541Z | {
"verified": true,
"answer": 9257,
"timestamp": "2026-02-08T03:05:05.068841Z"
} | e7c77a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 3638
},
"timestamp": "2026-02-09T03:22:36.856Z",
"answer": 9257
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
d5964c | nt_max_prime_below_v1_1520064083_6226 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $A$. Determine the largest prime number $n$ such that $n \geq m$ and $n \leq 15129$. | 15,121 | graphs = [
Graph(
let={
"upper": Const(15129),
"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 | 0.807 | 2026-02-08T07:55:48.409270Z | {
"verified": true,
"answer": 15121,
"timestamp": "2026-02-08T07:55:49.216122Z"
} | c13c65 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 2151
},
"timestamp": "2026-02-13T13:54:34.333Z",
"answer": 15121
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
71d3cf | comb_count_surjections_v1_1915831931_162 | Let $n = 4$ and $N = 6$. Let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = N$, $1 \leq i \leq 4$, and $1 \leq j \leq 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Let $C$ be the tot... | 1,999 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(4),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRang... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | b5abab | comb_count_surjections_v1 | negation_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.016 | 2026-02-08T15:12:45.352733Z | {
"verified": true,
"answer": 1999,
"timestamp": "2026-02-08T15:12:45.369100Z"
} | c5c59e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 754
},
"timestamp": "2026-02-24T20:10:32.490Z",
"answer": 1999
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
9dbfd8 | comb_sum_binomial_row_v1_1520064083_1824 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = \sum_{k=1}^{8} \phi(k) \left\lfloor \frac{8}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. For each such pair, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_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")), Summation(var="k", start=Const(1), end=Const(8), e... | NT | null | SUM | sympy | K2 | [
"K2/B3"
] | 56e545 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.004 | 2026-02-08T04:19:08.001069Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T04:19:08.004896Z"
} | c4e26f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 916
},
"timestamp": "2026-02-10T16:19:34.530Z",
"answer": 4096
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f12bc9 | nt_count_gcd_equals_v1_1978505735_687 | Let $k$ be the number of positive integers $n \leq 1752$ such that the $n$-th Fibonacci number is divisible by 7. Let $d$ be the smallest prime divisor of $2760437987$. Let $R$ be the number of positive integers $n_1 \leq 15376$ such that $\gcd(n_1, k) = d$. Find the remainder when $84157 \cdot R$ is divided by $72387$... | 55,286 | graphs = [
Graph(
let={
"upper": Const(15376),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1752)), Divides(divisor=Const(7), dividend=Fibonacci(arg=Var(name='n')))))),
"d": MinOverSet(set=SolutionsSet(var=Var... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | d4f327 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 1.263 | 2026-02-08T15:32:37.787526Z | {
"verified": true,
"answer": 55286,
"timestamp": "2026-02-08T15:32:39.050188Z"
} | 82f00d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 2382
},
"timestamp": "2026-02-16T08:13:44.181Z",
"answer": 55286
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb1ad2 | antilemma_sum_equals_v1_1978505735_1709 | Let $c = 104$. Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$. Let $n$ be the number of ordered pairs $(x_{11}, x_{21})$ of positive odd integers such that $x_{11} + x_{21} = m$. Compute the number of ordered pairs $(i, j)$ with $1 \le i \le 26$ and $1 \le j \le 2... | 25 | graphs = [
Graph(
let={
"_c": Const(104),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COMB1/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 566266 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.107 | 2026-02-08T16:21:47.074035Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T16:21:47.181063Z"
} | 7dd14d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 850
},
"timestamp": "2026-02-24T20:36:55.298Z",
"answer": 25
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
7755ea | modular_min_linear_v1_1742523217_3152 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 24880144$. Let $T$ be the set of all sums $x + y$ where $(x,y) \in S$. Let $a$ be the minimum element of $T$. Let $m = 14513$ and $b = 947$. Determine the smallest positive integer $x$ such that $1 \leq x \leq m$ and
$$
ax \equiv b \pm... | 4,814 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(24880144)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(947... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_linear_v1 | null | 6 | 0 | [
"B3"
] | 1 | 2.385 | 2026-02-08T05:41:02.133162Z | {
"verified": true,
"answer": 4814,
"timestamp": "2026-02-08T05:41:04.517890Z"
} | ab18a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2227
},
"timestamp": "2026-02-12T12:33:43.591Z",
"answer": 4814
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
648922 | comb_binomial_compute_v1_1419126231_1544 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 35$ such that $9a^2 + 30ab + 25b^2 = 10609$. Compute $\binom{15}{k}$. | 6,435 | graphs = [
Graph(
let={
"_n": Const(10609),
"n": Const(15),
"k": 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)), Eq(Sum(Mul(Const(9)... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_binomial_compute_v1 | null | 4 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.011 | 2026-02-25T11:05:13.972700Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-25T11:05:13.983216Z"
} | 901d7d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1358
},
"timestamp": "2026-03-30T12:59:08.454Z",
"answer": 6435
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
68341d | diophantine_fbi2_min_v1_1520064083_5279 | Let $k = 22$. Determine the smallest integer $d$ such that $2 \leq d \leq 32$, $d$ divides $22$, and $\frac{22}{d} \geq 4$. | 2 | graphs = [
Graph(
let={
"k": Const(22),
"a": Const(1),
"b": Const(3),
"upper": Const(32),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | B3 | [
"L3C/B3"
] | 4d8a41 | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"B3",
"L3C"
] | 2 | 0.062 | 2026-02-08T06:43:01.675064Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T06:43:01.736795Z"
} | f5f50e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 241
},
"timestamp": "2026-02-15T17:42:17.522Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lem... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
a4a484 | algebra_poly_eval_v1_1218484723_4068 | Compute $7 \cdot 7^3 - 10 \cdot 7^2 + 10 \cdot 7 + \left|\{ (a, b) : 1 \le a \le b \le 25,\ 2a^2 - 4ab + 2b^2 = 450 \}\right|$. | 1,991 | graphs = [
Graph(
let={
"_n": Const(2),
"t": Const(7),
"result": Sum(Mul(Const(7), Pow(Ref("t"), Const(3))), Mul(Const(-10), Pow(Ref("t"), Const(2))), Mul(Const(10), Ref("t")), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | algebra_poly_eval_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.004 | 2026-02-25T05:43:24.462799Z | {
"verified": true,
"answer": 1991,
"timestamp": "2026-02-25T05:43:24.466561Z"
} | 60bb3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 594
},
"timestamp": "2026-03-29T13:36:58.047Z",
"answer": 1991
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
8c9062 | nt_count_divisors_in_range_v1_2051736721_1584 | Let $n = 83160$, $a = 40$, and let $b$ be the number of integers $t$ such that $27 \leq t \leq 2598$ and there exist positive integers $a'$, $b'$ with $1 \leq a' \leq 102$, $1 \leq b' \leq 89$, and $t = 15a' + 12b'$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 62 | graphs = [
Graph(
let={
"n": Const(83160),
"a": Const(40),
"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=C... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.017 | 2026-02-08T16:06:45.028512Z | {
"verified": true,
"answer": 62,
"timestamp": "2026-02-08T16:06:45.045498Z"
} | 6f77a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 7471
},
"timestamp": "2026-02-16T21:17:46.335Z",
"answer": 62
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
326777 | antilemma_cartesian_v1_1440796553_961 | Compute the remainder when $44121$ times the number of ordered pairs $(i, j)$ with $1 \leq i \leq 30$ and $1 \leq j \leq 39$ is divided by $95285$. | 72,385 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Const(39)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(95285)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T12:04:39.050131Z | {
"verified": true,
"answer": 72385,
"timestamp": "2026-02-08T12:04:39.050642Z"
} | 76eea4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1159
},
"timestamp": "2026-02-24T15:09:08.530Z",
"answer": 72385
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6e541b | nt_lcm_compute_v1_1526740231_437 | Let $a = 1781$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 305809$. Let $b$ be the minimum value of $x + y$ over all pairs in $S$. Let $\ell = \operatorname{lcm}(a,b)$. Find the remainder when $51984 - \ell$ is divided by $78446$. | 43,348 | graphs = [
Graph(
let={
"_n": Const(78446),
"a": Const(1781),
"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(305809))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T11:30:57.538210Z | {
"verified": true,
"answer": 43348,
"timestamp": "2026-02-08T11:30:57.540916Z"
} | 60e88b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 2263
},
"timestamp": "2026-02-14T16:10:53.209Z",
"answer": 43348
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
28e486 | algebra_poly_eval_v1_971394319_1944 | Let $t = 16$ and define $\text{result} = 6t^2 + 3t + 7$. Let $c$ be the number of positive integers $n$ with $1 \le n \le 489$ such that $\gcd(n, 10) = 1$. Compute the remainder when $c - \text{result}$ is divided by $68740$. | 67,345 | graphs = [
Graph(
let={
"_n": Const(3),
"t": Const(16),
"result": Sum(Mul(Const(6), Pow(Ref("t"), Const(2))), Mul(Ref("_n"), Ref("t")), Const(7)),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(489)... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | acb85c | algebra_poly_eval_v1 | negation_mod | 3 | 0 | [
"C4"
] | 1 | 0.003 | 2026-02-08T14:00:56.898493Z | {
"verified": true,
"answer": 67345,
"timestamp": "2026-02-08T14:00:56.901798Z"
} | 1fb68a | 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": 873
},
"timestamp": "2026-02-15T23:35:17.382Z",
"answer": 67345
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
38a565 | alg_sum_ap_v1_1218484723_5619 | Find the remainder when $\sum_{k=0}^{130} (2k + 30)$ is divided by $\min\{ x + y : x > 0,\ y > 0,\ xy = 5707321 \}$. | 1,848 | graphs = [
Graph(
let={
"_n": Const(130),
"result": Mod(value=Summation(var="k", start=Const(0), end=Ref("_n"), expr=Sum(Mul(Const(2), Var("k")), Const(30))), modulus=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_ap_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.023 | 2026-02-25T07:08:09.055583Z | {
"verified": true,
"answer": 1848,
"timestamp": "2026-02-25T07:08:09.078406Z"
} | d8aa2e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 29227
},
"timestamp": "2026-03-29T22:01:44.051Z",
"answer": 1848
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
35ea86 | modular_mod_compute_v1_865884756_3145 | Let $a = 7225$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 250000$. For each such pair, compute $x + y$, and let $m$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when $a$ is divided by $m$. | 225 | graphs = [
Graph(
let={
"a": Const(7225),
"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(250000)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:12:17.677302Z | {
"verified": true,
"answer": 225,
"timestamp": "2026-02-08T17:12:17.679209Z"
} | b23f6a | 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": "2026-02-17T20:59:37.577Z",
"answer": 225
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
734533 | antilemma_cartesian_v1_784195855_1038 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 15$ and $1 \leq b \leq 20$. Let $Q$ be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|x| + 2$. Find the value of $Q$. | 150 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Const(20)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:48:08.994233Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T04:48:08.995200Z"
} | aa59c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 7722
},
"timestamp": "2026-02-24T01:50:56.665Z",
"answer": 150
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
1cb7d7 | modular_sum_quadratic_residues_v1_1431428450_237 | Let $p$ be the number of integers $t$ with $7 \leq t \leq 167$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 56$, $1 \leq b \leq 11$, and $t = 2a + 5b$. Compute $\frac{p(p-1)}{4}$. | 6,123 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=56)), Geq(left=Var(n... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:18:52.130123Z | {
"verified": true,
"answer": 6123,
"timestamp": "2026-02-08T13:18:52.131947Z"
} | b39c97 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 3397
},
"timestamp": "2026-02-15T13:52:46.628Z",
"answer": 6123
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
22c75e | nt_count_coprime_and_v1_655260480_5780 | Let $d$ be the smallest divisor of $3823963$ that is at least $2$. Let $k = 13$. Compute the number of positive integers $n$ such that $1 \leq n \leq 29946$, $\gcd(n, d) = 1$, and $\gcd(n, k) = 1$. | 25,130 | graphs = [
Graph(
let={
"upper": Const(29946),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3823963))))),
"k2": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), ... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.261 | 2026-02-08T18:39:42.151096Z | {
"verified": true,
"answer": 25130,
"timestamp": "2026-02-08T18:39:45.412385Z"
} | 02660a | 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": 1158
},
"timestamp": "2026-02-18T18:29:35.049Z",
"answer": 25130
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d1522d | modular_count_residue_v1_1520064083_1003 | Let $r = \sum_{k=0}^{9} (-1)^k \binom{t_k}{k}$, where $t_k$ is the number of integers $t$ with $10 \leq t \leq 30$ for which there exist positive integers $a, b$, each at most $3$, such that $t = 6a + 4b$. Let $m = 2$ and let the upper bound be $44521$. Determine the number of positive integers $n \leq 44521$ such that... | 22,260 | graphs = [
Graph(
let={
"upper": Const(44521),
"m": Const(2),
"r": Summation(var="k", start=Const(0), end=Const(9), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | modular_count_residue_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 7.363 | 2026-02-08T03:42:07.452944Z | {
"verified": true,
"answer": 22260,
"timestamp": "2026-02-08T03:42:14.815508Z"
} | aa5adf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1240
},
"timestamp": "2026-02-10T15:36:05.958Z",
"answer": 22260
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} |
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