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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
dbadf6 | lin_form_endings_v1_677425708_3237 | Let $a = 21$ and $b = 6$. Define $g = \gcd(a, b)$, and let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let
$$
S = a' \cdot 44 + b' \cdot 56 - a' \cdot b'.
$$
Multiply $S$ by 5040, and let $T$ be the result. Compute the remainder when $T$ is divided by 58210. | 8,890 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(6),
"A_val": Const(44),
"B_val": Const(56),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:33:23.414184Z | {
"verified": true,
"answer": 8890,
"timestamp": "2026-02-08T05:33:23.415015Z"
} | 9bb27a | 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": 713
},
"timestamp": "2026-02-12T11:30:29.389Z",
"answer": 8890
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
386ae6 | algebra_poly_eval_v1_865884756_573 | Let $y$ be the number of positive integers $n$ such that $1 \leq n \leq 144$ and $9$ divides the $n$th Fibonacci number. Compute $3y^4 - 10y^3 + 4y^2 - 5y - 10$. | 45,434 | graphs = [
Graph(
let={
"_n": Const(4),
"y": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(144)), Divides(divisor=Const(9), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Sum(Mul(Const(3), Pow(Ref("y"), Ref("_... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | algebra_poly_eval_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T15:31:02.278932Z | {
"verified": true,
"answer": 45434,
"timestamp": "2026-02-08T15:31:02.282197Z"
} | ca56c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1557
},
"timestamp": "2026-02-16T07:41:07.223Z",
"answer": 45434
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
16c9af | antilemma_v7_kummer_1520064083_2987 | Let $ n = 380 $. Let $ x $ be the largest integer $ k $ such that $ 3^k $ divides $ \binom{n}{152} $. Compute $ x $. | 4 | graphs = [
Graph(
let={
"_n": Const(380),
"x": MaxKDivides(target=Binom(n=Ref("_n"), k=Const(152)), base=Const(3)),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"V7"
] | 2 | 0.012 | 2026-02-08T05:23:21.895056Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T05:23:21.907084Z"
} | 041466 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 506
},
"timestamp": "2026-02-18T16:00:35.173Z",
"answer": 4
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"st... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
1b0dcb | alg_poly4_sum_v1_1218484723_2111 | Let $V = \left|\left\{ v : 4 \le v \le 5165,\ \exists\text{ integers } a, b \in [1,14] \text{ such that } 13b^2 + 29a^2 - 38ab = v \right\}\right|$. Find the remainder when
\[
\sum_{\substack{a=1 \\ b=1}}^{155, V} \left( 97a^4 - 32a^3b + 24a^2b^2 - 8ab^3 + b^4 \right)
\]
is divided by $77506€. | 12,974 | graphs = [
Graph(
let={
"_n": Const(24),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(155)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly4_sum_v1 | null | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.063 | 2026-02-25T03:50:16.609710Z | {
"verified": true,
"answer": 12974,
"timestamp": "2026-02-25T03:50:16.672383Z"
} | fbd62f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T03:07:00.452Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 4.43,
"mid": 6.62,
"hi": 9.7
} | ||
717fc3 | nt_count_divisors_in_range_v1_655260480_1287 | Let $n_0 = 1089$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 176400$. Define $n$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $a = 1$. Let $T$ be the set of all ordered pairs $(x_1,y_1)$ of positive integers such that $x_1 y_1 = n_0$. Define $b$ to be th... | 22 | graphs = [
Graph(
let={
"_n": Const(1089),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T16:03:11.638199Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T16:03:11.643206Z"
} | 9eabc0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 2455
},
"timestamp": "2026-02-16T20:26:46.577Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d88233 | modular_count_residue_v1_124444284_1646 | Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 450$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq 80089$ such that $n \equiv r \pmod{6}$. Compute $60025$ minus the number of elements in $S$. | 46,677 | graphs = [
Graph(
let={
"upper": Const(80089),
"m": Const(6),
"r": 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=450)), Eq(left=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_count_residue_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.597 | 2026-02-08T04:03:59.127013Z | {
"verified": true,
"answer": 46677,
"timestamp": "2026-02-08T04:04:03.723777Z"
} | 2759c3 | 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": 1918
},
"timestamp": "2026-02-10T15:21:21.596Z",
"answer": 46677
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
db9edf | comb_count_derangements_v1_655260480_905 | Let $n$ be the largest prime number such that $2 \le n \le 8$. Define $r$ to be the number of derangements of $n$ elements. Let $Q$ be the remainder when $44121 \cdot r$ is divided by $76765$.
Find the value of $Q$. | 45,609 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(8)), IsPrime(Var("n1"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("r... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:44:47.164790Z | {
"verified": true,
"answer": 45609,
"timestamp": "2026-02-08T15:44:47.166660Z"
} | e5ca51 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1672
},
"timestamp": "2026-02-16T12:53:21.858Z",
"answer": 45609
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MO... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dcb4bf | algebra_vieta_sum_v1_655260480_2400 | Let $m = 49$ and let $n$ be the largest prime number less than or equal to $135$. Consider the cubic equation $x^3 - 20x^2 + n x - 280 = 0$. Let $r$ be the product of all integer roots of this equation. Define $c = \sum_{k=1}^{49} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor$, where $\phi$ denotes Euler's totient fun... | 945 | graphs = [
Graph(
let={
"_m": Const(49),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(135)), IsPrime(Var("n"))))),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2",
"K2"
] | daab4c | algebra_vieta_sum_v1 | negation_mod | 6 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.015 | 2026-02-08T16:42:35.663920Z | {
"verified": true,
"answer": 945,
"timestamp": "2026-02-08T16:42:35.679185Z"
} | 52331b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1198
},
"timestamp": "2026-02-17T09:34:33.294Z",
"answer": 945
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e69911 | comb_binomial_compute_v1_238844314_618 | Let $n = 14$. Let $k$ be the smallest integer greater than or equal to 2 that divides 77. Compute $\binom{n}{k}$. | 3,432 | graphs = [
Graph(
let={
"n": Const(14),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T13:25:52.484882Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T13:25:52.486514Z"
} | 2d6cc7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 990
},
"timestamp": "2026-02-15T15:21:25.121Z",
"answer": 3432
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
3cbf1a | comb_factorial_compute_v1_655260480_2540 | Let $n_2 = \binom{11}{11} - 1$. Define $h = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = 0$ and define $e = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}$. Let $n = 8 \cdot e$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n2": Sub(Binom(n=Const(11), k=Const(11)), Const(1)),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"e": Summation(var="k1", start=Const(0), e... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | comb_factorial_compute_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 0.003 | 2026-02-08T16:49:38.661539Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T16:49:38.664391Z"
} | 209805 | 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": 407
},
"timestamp": "2026-02-24T21:59:02.525Z",
"answer": 40320
},
{... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
81b311_n | comb_count_partitions_v1_601307018_2654 | A museum has a collection of identical tiles, and they plan to arrange them into rows such that each row contains at least as many tiles as the row below it. The total number of tiles is $n = 3^0 + 3^1 + 3^2 + 3^3$. The curator counts $M$, the number of distinct non-increasing arrangements (partitions) of these tiles. ... | 24,542 | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_GEOM"
] | 04214c | comb_count_partitions_v1 | null | 4 | null | [
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM"
] | 2 | 0.02 | 2026-03-10T03:19:11.085467Z | null | a3e5ca | 81b311 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T16:32:28.603Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
145322 | nt_count_gcd_equals_v1_1520064083_4435 | Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 13689$ and $\gcd(n, 341) = 11$. Let $T$ be the set of ordered pairs $(x, y)$ of positive integers such that $xy = 7744$. Let $s_{\min}$ be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Let $P$ be the set of ordered pairs $(x, y)$ of posi... | 6,540 | graphs = [
Graph(
let={
"upper": Const(13689),
"k": Const(341),
"d": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
... | NT | null | COUNT | sympy | B3 | [
"B3/B1"
] | 6cdf3d | nt_count_gcd_equals_v1 | negation_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 4.721 | 2026-02-08T06:16:08.395424Z | {
"verified": true,
"answer": 6540,
"timestamp": "2026-02-08T06:16:13.116084Z"
} | 6f43f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1344
},
"timestamp": "2026-02-12T22:08:48.027Z",
"answer": 6540
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
2c8b23 | modular_min_linear_v1_1742523217_1097 | Let $a$ be the number of integers $t$ with $33 \leq t \leq 684$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 43$, and $t = 21a + 12b$. Let $b$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 2917264$. Let $m = 20109$. Compute the ... | 17,713 | graphs = [
Graph(
let={
"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=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | modular_min_linear_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.777 | 2026-02-08T03:25:20.218983Z | {
"verified": true,
"answer": 17713,
"timestamp": "2026-02-08T03:25:20.995811Z"
} | 5f522e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 7671
},
"timestamp": "2026-02-10T03:20:40.324Z",
"answer": 17713
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
57dddc | diophantine_fbi2_min_v1_1978505735_2486 | Let $k = 96$. Let $d$ be the smallest integer such that $4 \leq d \leq 106$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Let $r$ be this value of $d$. Compute $$
\sum_{n=1}^{r} d(n),
$$where $d(n)$ denotes the number of positive divisors of $n$. | 8 | graphs = [
Graph(
let={
"k": Const(96),
"a": Const(3),
"b": Const(1),
"upper": Const(106),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Re... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"SUM_ARITHMETIC/MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | a20823 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME",
"SUM_ARITHMETIC"
] | 4 | 0.113 | 2026-02-08T16:54:58.550613Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T16:54:58.663653Z"
} | 28d165 | 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": 856
},
"timestamp": "2026-02-17T15:53:39.092Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SU... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5f5439 | modular_count_residue_v1_1742523217_830 | Let $m$ be the number of integers $t$ such that $9 \le t \le 38$ and there exist positive integers $a$ and $b$ with $1 \le a \le 12$, $1 \le b \le 2$, and $t = 2a + 7b$. Let $U = 84681$. Let $R$ be the number of positive integers $n$ such that $1 \le n \le U$ and $n \equiv 0 \pmod{m}$. Let $c = 37877$. Compute the rema... | 36,258 | graphs = [
Graph(
let={
"upper": Const(84681),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=12)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 7.283 | 2026-02-08T03:17:16.438391Z | {
"verified": true,
"answer": 36258,
"timestamp": "2026-02-08T03:17:23.721186Z"
} | 554611 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1963
},
"timestamp": "2026-02-09T07:39:47.236Z",
"answer": 36258
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5d87d9 | nt_count_gcd_equals_v1_1520064083_1664 | Let $N = 9409$ and $k = 210$. Define $d = 15$. Let $r$ be the number of positive integers $n \le N$ such that $\gcd(n, k) = d$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Compute $r + 2^{r \bmod s} \bmod 64576$. | 277 | graphs = [
Graph(
let={
"upper": Const(9409),
"k": Const(210),
"d": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 385411 | nt_count_gcd_equals_v1 | mod_exp | 5 | 0 | [
"B3"
] | 1 | 1.386 | 2026-02-08T04:12:11.891425Z | {
"verified": true,
"answer": 277,
"timestamp": "2026-02-08T04:12:13.277494Z"
} | 00fb65 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1642
},
"timestamp": "2026-02-10T15:48:31.821Z",
"answer": 277
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
bcf707 | modular_modexp_compute_v1_1520064083_2565 | Let $a = 23$. Let $e$ be the sum of all real solutions $x$ to the equation $x^2 - 3844x + 72675 = 0$. Let $m = 36481$. Compute $a^e \bmod m$. | 34,669 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(23),
"e": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-3844), Var("x")), Const(72675)), Const(0)))),
"m": Const(36481),
"result": ModExp(base=Ref(... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_modexp_compute_v1 | null | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T04:51:59.268908Z | {
"verified": true,
"answer": 34669,
"timestamp": "2026-02-08T04:51:59.270365Z"
} | 53f604 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 6831
},
"timestamp": "2026-02-11T22:23:40.445Z",
"answer": 34669
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
48ee26 | antilemma_k3_v1_48377204_686 | Let $n = 60732$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 60,732 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=60732), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:39:04.225692Z | {
"verified": true,
"answer": 60732,
"timestamp": "2026-02-08T15:39:04.226499Z"
} | c05565 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 437
},
"timestamp": "2026-02-16T10:40:31.161Z",
"answer": 60732
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
49eced | antilemma_cartesian_v1_865884756_6927 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 16$ and $1 \leq b \leq 23$. Compute the remainder when $34329 \cdot x$ is divided by $52115$. | 21,242 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(23)))),
"Q": Mod(value=Mul(Const(34329), Ref("x")), modulus=Const(52115)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T19:27:37.333454Z | {
"verified": true,
"answer": 21242,
"timestamp": "2026-02-08T19:27:37.334170Z"
} | 921d6a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 897
},
"timestamp": "2026-02-18T22:40:31.834Z",
"answer": 21242
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
a96987 | nt_count_intersection_v1_784195855_6683 | Let $N = 100000$. Define $a = 3$. Let $b$ be the number of positive integers $n \leq 240$ such that $12$ divides the $n$-th Fibonacci number. Let $r$ be the number of positive integers $n \leq N$ such that $3$ divides $n$ and $\gcd(n, b) = 1$. Compute the remainder when $58921 \cdot r$ is divided by $68693$. Find the v... | 10,773 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(3),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(240)), Divides(divisor=Const(12), dividend=Fibonacci(arg=Var(name='n')))))),
"result": CountO... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_intersection_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 4.969 | 2026-02-08T08:47:01.715460Z | {
"verified": true,
"answer": 10773,
"timestamp": "2026-02-08T08:47:06.684321Z"
} | 3ec022 | 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": 2586
},
"timestamp": "2026-02-13T21:54:21.267Z",
"answer": 10773
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c327b7 | antilemma_coprime_grid_v1_798873815_12 | Let $\phi$ denote Euler's totient function. Compute the number of ordered pairs $(i, j)$ with $1 \le i \le 38$ and $1 \le j \le 143$ such that $\gcd(i, j) = \phi(\phi(1))$. | 3,363 | 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=EulerPhi(n=Const(1)))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(38)), right=IntegerRange(start=Const(1), end=Const... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 3d404c | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2 | 0.001 | 2026-02-08T02:23:40.231464Z | {
"verified": true,
"answer": 3363,
"timestamp": "2026-02-08T02:23:40.232364Z"
} | 060ff2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 4689
},
"timestamp": "2026-02-08T18:28:59.615Z",
"answer": 3371
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
3e14dc | nt_sum_gcd_range_mod_v1_168721529_1845 | Let $N = 1283$. Let $k$ be the number of positive integers $j$ such that $1 \le j \le 336$ and $j^5 \le 4282490290176$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $M = 11789$. Compute the remainder when $44121$ times the value of $\text{sum}$ modulo $M$ is divided by $62429$. | 41,925 | graphs = [
Graph(
let={
"N": Const(1283),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(336)), Leq(Pow(Var("j"), Const(5)), Const(4282490290176))), domain='positive_integers')),
"M": Const(11789),
"... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"C3"
] | 1 | 0.136 | 2026-02-08T13:57:16.667067Z | {
"verified": true,
"answer": 41925,
"timestamp": "2026-02-08T13:57:16.803042Z"
} | 5e4b39 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 4691
},
"timestamp": "2026-02-11T08:05:53.766Z",
"answer": 41925
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
d6f7e8 | comb_count_partitions_v1_1742523217_2113 | Let $\mathcal{S}$ be the set of all real numbers $x$ such that $x^2 - 9x - 1386 = 0$. Let $\_n$ be the sum of all elements in $\mathcal{S}$. Define $n = \sum_{k=1}^{\_n} k$. Let $\text{result}$ be the number of integer partitions of $n$. Determine the value of $\text{result}$. | 89,134 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-9), Var("x")), Const(-1386)), Const(0)))),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"res... | COMB | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM/SUM_ARITHMETIC"
] | 42ea97 | comb_count_partitions_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T04:28:38.457991Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T04:28:38.460301Z"
} | 3dd8e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 828
},
"timestamp": "2026-02-24T00:44:57.852Z",
"answer": 89134
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ea4ef9 | comb_count_derangements_v1_238844314_982 | Let $n = 7$. Let $r = !n$, the subfactorial of $n$. Let $t$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 108$ and $\gcd(p, q) = 1$. For each digit $d_i$ of $|r|$ (in base 10, starting from the units place as position 0), compute $d_i \cdot (i+1)^t$. Sum these ... | 49,396 | graphs = [
Graph(
let={
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(49284),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result'... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | a9a663 | comb_count_derangements_v1 | digits_weighted_mod | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T13:50:33.043299Z | {
"verified": true,
"answer": 49396,
"timestamp": "2026-02-08T13:50:33.047687Z"
} | 51883e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1774
},
"timestamp": "2026-02-15T21:17:51.034Z",
"answer": 49396
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c2857d | nt_count_divisible_and_v1_1520064083_2641 | Let $g = \gcd(11, 13)$. Define $m = \sum_{d \mid g} \mu(d)$, where $\mu$ is the M\"obius function.
Determine the number of positive integers $n$ such that $m \leq n \leq 112830$, $n$ is divisible by 10, and $n$ is divisible by 15. | 3,761 | graphs = [
Graph(
let={
"upper": Const(112830),
"d1": Const(10),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=11), b=Const(value=13)), var='d', expr=MoebiusMu(n=Var(name=... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_and_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 12.826 | 2026-02-08T04:53:44.174709Z | {
"verified": true,
"answer": 3761,
"timestamp": "2026-02-08T04:53:57.000341Z"
} | 9456f2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 400
},
"timestamp": "2026-02-18T14:35:19.370Z",
"answer": 3761
}
] | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
45e94b | nt_count_gcd_equals_v1_260342960_91 | Let $n_1 = 2$, and define $m = \lambda(n_1) + 1$, where $\lambda(n)$ is the Liouville function. Let $n = 1 + m$ and $w = \Omega(n)$, the number of prime factors of $n$ counted with multiplicity. Let $\text{upper}$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 24511$ and $\binom{24511}{j} \equiv 1 \... | 2,704 | graphs = [
Graph(
let={
"_n": Const(2),
"n1": Const(2),
"m": Sum(LiouvilleLambda(n=Ref(name='n1')), Const(1)),
"n": Sum(Const(1), Ref("m")),
"w": BigOmega(n=Ref(name='n')),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=... | NT | null | COUNT | sympy | LIOUVILLE_MINUS_ONE | [
"LIOUVILLE_MINUS_ONE",
"BIG_OMEGA_ZERO",
"V8"
] | 373f95 | nt_count_gcd_equals_v1 | null | 6 | 2 | [
"BIG_OMEGA_ZERO",
"LIOUVILLE_MINUS_ONE",
"V8"
] | 3 | 0.643 | 2026-02-08T11:13:45.159109Z | {
"verified": true,
"answer": 2704,
"timestamp": "2026-02-08T11:13:45.801761Z"
} | 81400f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 2943
},
"timestamp": "2026-02-08T20:28:21.204Z",
"answer": 2704
},
{
"i... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"statu... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
4ecb38 | algebra_quadratic_discriminant_v1_124444284_8529 | Let $a = -9$, $b = 10$, and $c = 5$. Compute $b^2 - 4ac$. | 280 | graphs = [
Graph(
let={
"a": Const(-9),
"b": Const(10),
"c": Const(5),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 7b2633 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.021 | 2026-02-08T09:45:22.355545Z | {
"verified": true,
"answer": 280,
"timestamp": "2026-02-08T09:45:22.376625Z"
} | 14a708 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 177
},
"timestamp": "2026-02-15T20:48:39.744Z",
"answer": 280
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
759d07 | nt_count_coprime_v1_898971024_2932 | Let $k = 2$ and let $\text{result}$ be the number of positive integers $n$ with $1 \leq n \leq 58081$ such that $\gcd(n, k) = 1$. Let $A$ be the set of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $a = |A|$. Define $Q = \text{result} + (a^{\... | 29,043 | graphs = [
Graph(
let={
"upper": Const(58081),
"k": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
"Q": Sum(Ref("result"), Mod(va... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 64a51e | nt_count_coprime_v1 | mod_exp | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 6.12 | 2026-02-08T17:04:32.042774Z | {
"verified": true,
"answer": 29043,
"timestamp": "2026-02-08T17:04:38.162896Z"
} | 159875 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1019
},
"timestamp": "2026-02-17T18:41:54.283Z",
"answer": 29043
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
45af9a | algebra_quadratic_discriminant_v1_1742523217_1064 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 4$. Let $m$ be the maximum value of $xy$ over all such pairs. Compute $4^2 - 2 \cdot m \cdot 2$. | 0 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(4),
"c": Const(2),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.014 | 2026-02-08T03:24:03.670229Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T03:24:03.684659Z"
} | cc463f | 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": 423
},
"timestamp": "2026-02-10T02:47:22.715Z",
"answer": 0
},
{
"id": ... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e43a97_l | nt_min_coprime_above_v1_1116507919_68 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 93025$.
Let $U$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1371241$.
Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such ... | 2,029 | NT | null | EXTREMUM | sympy | B3 | [
"B3/COMB1"
] | e26f7e | nt_min_coprime_above_v1 | null | 7 | 0 | [
"B3",
"COMB1"
] | 2 | 0.066 | 2026-02-08T02:24:13.363621Z | {
"verified": false,
"answer": 2028,
"timestamp": "2026-02-08T02:24:13.430105Z"
} | ea4990 | e43a97 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 6643
},
"timestamp": "2026-02-08T18:59:46.819Z",
"answer": 2028
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"... | {
"lo": -1.86,
"mid": 0.05,
"hi": 1.73
} | |
da5aae | comb_count_partitions_v1_124444284_10099 | Let $n$ be the largest integer $k$ such that $2^k \leq 7397537483903$. Compute the number of unordered ways to write $n$ as a sum of positive integers, disregarding order. | 53,174 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(7397537483903)))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_count_partitions_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T12:49:16.968114Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T12:49:16.968984Z"
} | 50a6d1 | 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": 833
},
"timestamp": "2026-02-24T16:23:26.313Z",
"answer": 53174
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DI... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
dd9f7a | comb_bell_compute_v1_124444284_2305 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 308700$, $\gcd(p, q) = 1$, and $p < q$. Compute the Bell number $B_n$. | 4,140 | 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=308700)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T04:35:37.027577Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T04:35:37.028665Z"
} | 260172 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1084
},
"timestamp": "2026-02-10T17:15:11.283Z",
"answer": 4140
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
adf1bf | sequence_lucas_compute_v1_1526740231_53 | Let $n$ be the number of ordered pairs of positive integers $(i, j)$ such that $i + j = 23$ and $1 \leq i, j \leq 23$. Compute the $n$-th Lucas number. | 39,603 | graphs = [
Graph(
let={
"_n": Const(23),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Con... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T11:20:03.625476Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T11:20:03.636420Z"
} | d304f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 778
},
"timestamp": "2026-02-14T11:56:08.459Z",
"answer": 39603
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ca57ce | sequence_count_fib_divisible_v1_2051736721_4453 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 77$ and $n$ is divisible by $11$. Let $U$ be the sum of all elements in $S$. Compute the number of positive integers $n_1$ with $1 \leq n_1 \leq U$ such that the $n_1$-th Fibonacci number is divisible by $12$. Then compute the remainder when $4412... | 8,895 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(77)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
"d": Const(12),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.021 | 2026-02-08T17:59:40.755542Z | {
"verified": true,
"answer": 8895,
"timestamp": "2026-02-08T17:59:40.776226Z"
} | bcb5f4 | 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": 1348
},
"timestamp": "2026-02-18T11:31:42.995Z",
"answer": 8895
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d1163 | antilemma_sum_factor_cartesian_v1_677425708_2939 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 6$ and $1 \leq j \leq 5$. Define $x$ to be the sum of $i \cdot j$ over all pairs $(i,j)$ in $S$. Let $Q = \sum_{n = \varphi(2)}^{|x|} \tau(n)$, where $\varphi$ is Euler's totient function and $\tau(n)$ is the number of positive divisors of ... | 1,867 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(5)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"SUM_FACTOR_CARTESIAN",
"ONE_PHI_2"
] | 09bd3b | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.022 | 2026-02-08T05:22:53.066679Z | {
"verified": true,
"answer": 1867,
"timestamp": "2026-02-08T05:22:53.088903Z"
} | 3c9671 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 555
},
"timestamp": "2026-02-18T16:03:22.432Z",
"answer": 3072
}
] | 0 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
33f3af | comb_catalan_compute_v1_153355830_2662 | Let $ n = 11 $. Define $ r = C_n $, the $ n $-th Catalan number. Let $ s = |r| + \binom{16}{16} $ and $ t = |r| + 1 $. Compute the value of $ (r + \phi(s) + \tau(t)) \bmod{68254} $, where $ \phi $ denotes Euler's totient function and $ \tau $ denotes the number of positive divisors function. | 49,320 | graphs = [
Graph(
let={
"n": Const(11),
"result": Catalan(Ref("n")),
"Q": Mod(value=Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Binom(n=Const(16), k=Const(16)))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), Const(1)))), modulus=Const(68254)),
... | COMB | NT | COMPUTE | sympy | ONE_BINOM_N | [
"ONE_BINOM_N"
] | 9c72e5 | comb_catalan_compute_v1 | null | 4 | 0 | [
"ONE_BINOM_N"
] | 1 | 0.001 | 2026-02-08T07:15:37.073634Z | {
"verified": true,
"answer": 49320,
"timestamp": "2026-02-08T07:15:37.075041Z"
} | e9f3c2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 8030
},
"timestamp": "2026-02-24T07:51:14.027Z",
"answer": 49320
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
0a9812 | lte_diff_endings_v1_1520064083_4869 | Let $a = 101$, $b = 1$, $p = 5$, $n = 125$, and $m = 250$. Let $v_{p}(x)$ denote the largest integer $k$ such that $p^k$ divides $x$. Define $v_{p1} = v_p(a^n - b^n)$ and $v_{p2} = v_p(a^m - b^m)$. Let $s = 10637$ and $M = 72431$. Compute the remainder when $s \cdot (v_{p1} + v_{p2})$ is divided by $M$. | 33,939 | graphs = [
Graph(
let={
"a_val": Const(101),
"b_val": Const(1),
"p_val": Const(5),
"n_val": Const(125),
"m_val": Const(250),
"a_pow_n": Pow(Ref("a_val"), Ref("n_val")),
"b_pow_n": Pow(Ref("b_val"), Ref("n_val")),
... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T06:27:57.122811Z | {
"verified": true,
"answer": 33939,
"timestamp": "2026-02-08T06:27:57.123687Z"
} | e022ff | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 821
},
"timestamp": "2026-02-19T08:35:21.749Z",
"answer": 33939
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
512510 | nt_euler_phi_compute_v1_1915831931_522 | Let $n = 30628$ and $k = 21$. Compute $\phi(n)$, Euler's totient function of $n$. Let $S$ be the set of all positive integers $n_2$ such that $1 \le n_2 \le 12247$ and $\gcd(n_2, 21) = 1$. Let $s$ be the number of elements in $S$. Let $T$ be the set of all positive integers $n_1$ such that $1 \le n_1 \le s$ and
\[
n_1 ... | 47,268 | graphs = [
Graph(
let={
"_n": Const(21),
"n": Const(30628),
"result": EulerPhi(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq... | NT | null | COMPUTE | sympy | C4 | [
"C4/L3C"
] | 0b9e4c | nt_euler_phi_compute_v1 | quadratic_mod | 6 | 0 | [
"C4",
"L3C"
] | 2 | 0.004 | 2026-02-08T15:30:28.460660Z | {
"verified": true,
"answer": 47268,
"timestamp": "2026-02-08T15:30:28.464431Z"
} | 120a7e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 3219
},
"timestamp": "2026-02-16T07:15:13.487Z",
"answer": 47268
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21dc6a | antilemma_k2_v1_1918700295_3958 | Let $n = 310$. Compute the value of
$$
\sum_{k=1}^{310} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid n} \phi(d) \right\rfloor.
$$ | 48,205 | graphs = [
Graph(
let={
"_n": Const(310),
"x": Summation(var="k", start=Const(1), end=Const(310), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T09:03:48.476497Z | {
"verified": true,
"answer": 48205,
"timestamp": "2026-02-08T09:03:48.478740Z"
} | 83be07 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 1014
},
"timestamp": "2026-02-13T23:59:20.718Z",
"answer": 48205
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d3e11b | diophantine_product_count_v1_1520064083_9131 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 129600$. Define $k$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $T$ be the set of all positive integers $x$ such that $1 \leq x \leq 278$, $x$ divides $k$, and $\frac{k}{x} \leq 278$. Compute the value of
$$
\s... | 91 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(129600)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(2... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.033 | 2026-02-08T10:33:48.961425Z | {
"verified": true,
"answer": 91,
"timestamp": "2026-02-08T10:33:48.994106Z"
} | bb4d9d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 2450
},
"timestamp": "2026-02-14T07:46:38.237Z",
"answer": 91
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0c6ec2 | comb_count_permutations_fixed_v1_865884756_1334 | Let $n = 10$ and let $k$ be the smallest divisor of $1001$ that is greater than or equal to $2$. Compute the remainder when
$$
44121 \cdot \binom{n}{k} \cdot !(n - k)
$$
is divided by $66625$, where $!m$ denotes the number of derangements of $m$ elements. Determine the value of this remainder. | 62,290 | graphs = [
Graph(
let={
"_n": Const(1001),
"n": Const(10),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T15:57:26.056185Z | {
"verified": true,
"answer": 62290,
"timestamp": "2026-02-08T15:57:26.058549Z"
} | 780996 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1274
},
"timestamp": "2026-02-16T17:55:17.114Z",
"answer": 62290
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
afc9b0 | comb_count_surjections_v1_238844314_269 | Let $k$ be the number of ordered pairs $(i, j)$ where $i$ and $j$ are integers and $1 \leq i \leq 2$, $1 \leq j \leq 2$. Let $n = 6$. Define $S(n, k)$ to be the number of ways to partition a set of $n$ elements into $k$ nonempty subsets, and let $k!$ denote the factorial of $k$. Compute the remainder when $13967 \cdot ... | 82,768 | graphs = [
Graph(
let={
"_n": Const(88958),
"n": Const(6),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(2)))),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'),... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T13:12:29.518195Z | {
"verified": true,
"answer": 82768,
"timestamp": "2026-02-08T13:12:29.520161Z"
} | 42c29a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 2064
},
"timestamp": "2026-02-24T17:33:21.887Z",
"answer": 82768
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
4db21e | nt_sum_over_divisible_v1_48377204_1475 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 40320$ and $$n \equiv \sum_{k=0}^{9} (-1)^k \binom{9}{k} \pmod{89}.$$ Let $r$ be the sum of all elements of $S$. Compute the remainder when $41594 \cdot r$ is divided by $67639$. | 39,961 | graphs = [
Graph(
let={
"upper": Const(40320),
"divisor": Const(89),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Const(0), ... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 1.303 | 2026-02-08T16:07:20.251617Z | {
"verified": true,
"answer": 39961,
"timestamp": "2026-02-08T16:07:21.554564Z"
} | 21c242 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2541
},
"timestamp": "2026-02-24T19:53:23.475Z",
"answer": 39961
},
{
... | 1 | [
{
"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": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
18328f_n | alg_poly4_count_v1_1218484723_6324 | Two players each choose an integer between 1 and 326 inclusive. Let $a$ and $b$ be their choices. They compute the symmetric expression $337a^4 + 1348a^3b + 2022a^2b^2 + 1348ab^3 + 337b^4$. If the result equals 26,191,814,787,072, they win. In how many ways can they choose $(a, b)$ to win? | 125 | ALG | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE",
"B1"
] | 612274 | alg_poly4_count_v1 | null | 6 | null | [
"B1",
"POLY_ORBIT_LEGENDRE"
] | 2 | 4.476 | 2026-02-25T07:53:08.427403Z | null | d78489 | 18328f | narrative | 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": 5848
},
"timestamp": "2026-03-31T01:09:04.692Z",
"answer": 125
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
2bb6ad | nt_min_coprime_above_v1_1978505735_3882 | Let $m = 65536$ and $n = 16$. Let $a$ be the number of positive integers $k$ such that $1 \leq k \leq m$ and $n$ divides $k$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 5076009$, and let $b$ be the minimum value of $x + y$ over all such pairs. Let $c$ be the smallest integer $... | 4,097 | graphs = [
Graph(
let={
"_m": Const(65536),
"_n": Const(16),
"start": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_m")), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"up... | NT | null | EXTREMUM | sympy | C2 | [
"C2",
"B3"
] | 83578c | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 0.06 | 2026-02-08T17:54:51.809018Z | {
"verified": true,
"answer": 4097,
"timestamp": "2026-02-08T17:54:51.868541Z"
} | 1d1e97 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 4218
},
"timestamp": "2026-02-18T09:55:06.664Z",
"answer": 4097
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
79cd85 | antilemma_sum_equals_v1_898971024_1520 | Let $m = 76198$. Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $i + j = 57$, $1 \le i \le 57$, and $1 \le j \le 57$. Let $k$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(i_1, j_1)$ of positive integers such that $i_1 + j_1 = k$, $1 \le i_1 \le 54$, and $1... | 25,710 | graphs = [
Graph(
let={
"_m": Const(76198),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(57)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(57)), right=IntegerRange(start=Const(1), end... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.025 | 2026-02-08T16:11:12.473767Z | {
"verified": true,
"answer": 25710,
"timestamp": "2026-02-08T16:11:12.499156Z"
} | dee60c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 1047
},
"timestamp": "2026-02-24T20:04:34.053Z",
"answer": 25710
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
7705dd | nt_sum_divisors_compute_v1_798873815_226 | Let $p_1 = 5$. Compute $w = (4! + 1) \bmod p_1$. Let $p = 41$, $q = 61$, and let $r$ be the smallest divisor of $16155911$ that is at least $2$.
Define $n_1 = p^{2 + w} \cdot q \cdot r$. Let $s = \mu(n_1)^k$, where $k$ is the number of prime numbers $n$ such that $2 \leq n \leq 3$.
Let $n = 41209$. Compute $\sigma(n)... | 22,102 | graphs = [
Graph(
let={
"p1": Const(5),
"w": Mod(value=Sum(Factorial(Sub(Ref("p1"), Const(1))), Const(1)), modulus=Ref("p1")),
"p": Const(41),
"q": Const(61),
"r": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Div... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_SQUAREFREE",
"COUNT_PRIMES/MOBIUS_SQUAREFREE",
"WILSON"
] | 5b5586 | nt_sum_divisors_compute_v1 | null | 5 | 2 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR",
"MOBIUS_SQUAREFREE",
"WILSON"
] | 4 | 0.004 | 2026-02-08T02:31:30.469939Z | {
"verified": true,
"answer": 22102,
"timestamp": "2026-02-08T02:31:30.473950Z"
} | 46301f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 3658
},
"timestamp": "2026-02-08T19:12:50.879Z",
"answer": 22102
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"sta... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
f82e39 | modular_count_residue_v1_655260480_1581 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = \sum_{k=1}^{3} \phi(k) \cdot \left\lfloor \frac{3}{k} \right\rfloor$. Let $m$ be the maximum value of $x \cdot y$ over all pairs $(x, y) \in T$. Determine the number of positive integers $n$ such that $n \leq 53361$ and $n \equiv 1... | 21,121 | graphs = [
Graph(
let={
"_n": Const(91138),
"upper": Const(53361),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Summation(v... | NT | null | COUNT | sympy | K2 | [
"K2/B1"
] | 995da8 | modular_count_residue_v1 | null | 5 | 0 | [
"B1",
"K2"
] | 2 | 3.909 | 2026-02-08T16:13:34.022823Z | {
"verified": true,
"answer": 21121,
"timestamp": "2026-02-08T16:13:37.931522Z"
} | 62c05f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 2091
},
"timestamp": "2026-02-16T22:53:00.912Z",
"answer": 21121
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
afdd51 | comb_sum_binomial_row_v1_601307018_6636 | Let $M = a^3 + 3a \bmod 2197$ and $R = M^3 + 3M \bmod 2197$. Let $S$ be the number of non-negative integers $a$ with $0 \le a \le 2196$ such that $R = a$ and $M \ne a$. Let $n$ be the smallest positive divisor of $537251$. Compute $S^n$. | 2,048 | graphs = [
Graph(
let={
"_m": Const(2197),
"_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(2196)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), con... | COMB | NT | SUM | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/MIN_PRIME_FACTOR"
] | c8b7af | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"POLY_ORBIT_HENSEL"
] | 2 | 0.002 | 2026-03-10T07:17:37.849577Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-03-10T07:17:37.852066Z"
} | 9ed40b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 5004
},
"timestamp": "2026-04-19T04:54:48.344Z",
"answer": 2048
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
064c68 | algebra_poly_eval_v1_1419126231_28 | Let $R = \frac{72 \cdot 6^{5} -97 \cdot 6^{4} -167 \cdot 6^{3} + 69 \cdot 6^{2} -29\cdot6 + 20}{\left|\{ (a, b) : 1 \le a \le 35,\ 1 \le b \le N,\ b^2 + 4a^2 - 4ab = 9 \}\right|}$, where $N = \left|\{ v : 32 \le v \le 2048,\ \exists\, a,b \in \mathbb{Z}^+\, (1 \le a,b \le 8)\ \text{such that}\ 26a^2 + 26b^2 -20ab = v \... | 11,777 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(2),
"k": Const(6),
"result": Div(Sum(Mul(Const(72), Pow(Ref("k"), Ref("_m"))), Mul(Const(-97), Pow(Ref("k"), Const(4))), Mul(Const(-167), Pow(Ref("k"), Const(3))), Mul(Const(69), Pow(Ref("k"), Const(2))), Mul... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/QF_PSD_COUNT"
] | a6a878 | algebra_poly_eval_v1 | null | 5 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.007 | 2026-02-25T09:33:35.626177Z | {
"verified": true,
"answer": 11777,
"timestamp": "2026-02-25T09:33:35.633018Z"
} | 6bfd99 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T06:37:09.372Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
bb2353 | antilemma_k3_v1_1439011603_120 | Let $N = 29511$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $N$. | 29,511 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=29511), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T15:13:37.745558Z | {
"verified": true,
"answer": 29511,
"timestamp": "2026-02-08T15:13:37.747844Z"
} | 657f4a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 1072
},
"timestamp": "2026-02-16T03:43:07.555Z",
"answer": 29511
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4e85ef | nt_sum_gcd_range_mod_v1_1742523217_765 | Let $N = 2411$ and $k = 84$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Let $M = 11719$ and let $\text{result}$ be the remainder when $\text{sum}$ is divided by $M$. Let $d_{\text{min}}$ be the smallest integer greater than or equal to 2 that divides $75809$. Compute the remainder when $\text{result}^2 + d_{\text... | 82,747 | graphs = [
Graph(
let={
"_n": Const(95615),
"N": Const(2411),
"k": Const(84),
"M": Const(11719),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("M")... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 76121b | nt_sum_gcd_range_mod_v1 | quadratic_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.284 | 2026-02-08T03:12:48.408513Z | {
"verified": true,
"answer": 82747,
"timestamp": "2026-02-08T03:12:48.692381Z"
} | f653b7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 4506
},
"timestamp": "2026-02-09T06:46:47.922Z",
"answer": 82747
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2a8053 | nt_count_digit_sum_v1_238844314_240 | Let $S$ be the set of all pairs of positive integers $(p, q)$ such that $p \cdot q = 1021020$, $\gcd(p, q) = 1$, and $p < q$. Let $M$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = |S|$. Determine the number of positive integers $n \leq 11923$ such that the sum of th... | 778 | graphs = [
Graph(
let={
"upper": Const(11923),
"target_sum": 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=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | nt_count_digit_sum_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.482 | 2026-02-08T13:12:16.467369Z | {
"verified": true,
"answer": 778,
"timestamp": "2026-02-08T13:12:16.949538Z"
} | 1866a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 3475
},
"timestamp": "2026-02-15T11:13:23.752Z",
"answer": 778
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
618342 | comb_catalan_compute_v1_865884756_2510 | Let $n = 10$. Compute the $n$-th Catalan number, denoted $C_n$. Let $a = |C_n| + 0!$ and $b = |C_n| + \binom{14}{14}$. Compute $C_n + \phi(a) + \tau(b)$, where $\phi$ denotes Euler's totient function and $\tau(k)$ denotes the number of positive divisors of $k$. Find the value of this sum. | 26,964 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Factorial(Const(0)))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), Binom(n=Const(14), k=Const(14))))),
},
goal=Ref("... | COMB | NT | COMPUTE | sympy | ONE_FACTORIAL_0 | [
"ONE_FACTORIAL_0",
"ONE_BINOM_N"
] | 7463f0 | comb_catalan_compute_v1 | null | 3 | 0 | [
"ONE_BINOM_N",
"ONE_FACTORIAL_0"
] | 2 | 0.002 | 2026-02-08T16:48:01.182613Z | {
"verified": true,
"answer": 26964,
"timestamp": "2026-02-08T16:48:01.184527Z"
} | 6b8cc1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1424
},
"timestamp": "2026-02-17T11:50:58.106Z",
"answer": 26964
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
0d8ccf | nt_count_gcd_equals_v1_1520064083_7469 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 12446784$. Define $T$ to be the set of all values $x + y$ where $(x,y) \in S$. Let $m$ be the minimum value in $T$.
Let $k$ be the number of integers $t$ with $7 \leq t \leq 472$ for which there exist positive integers $a$ and $b$ suc... | 917 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(12446784)))), expr=Sum(Var("x"), Var("y")))),
"k": Count... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 1.007 | 2026-02-08T09:03:39.772923Z | {
"verified": true,
"answer": 917,
"timestamp": "2026-02-08T09:03:40.779556Z"
} | 9cfd79 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 4761
},
"timestamp": "2026-02-13T23:40:53.722Z",
"answer": 917
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lem... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
f82a4f | comb_count_permutations_fixed_v1_784195855_5172 | Let $n = 6$ and $k = 2$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remainder when $29 - r$ is divided by $85103$.
Find the value of $Q$. | 84,997 | graphs = [
Graph(
let={
"n": Const(6),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Mod(value=Sub(Const(29), Ref("result")), modulus=Const(85103)),
},
goal=Ref... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"BINOMIAL_ALTERNATING"
] | 094a2e | comb_count_permutations_fixed_v1 | negation_mod | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.038 | 2026-02-08T07:42:38.412255Z | {
"verified": true,
"answer": 84997,
"timestamp": "2026-02-08T07:42:38.450257Z"
} | cea821 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 389
},
"timestamp": "2026-02-24T08:28:20.511Z",
"answer": 84997
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
e36bba | alg_qf_psd_sum_v1_1218484723_7695 | Let
$$E = \left|\left\{ (a2, b2) : a2 \ge 1,\ a2 \le 15,\ b2 \ge 1,\ b2 \le 15,\ 91a2^{3} + 48a2 b2^{2} - 8b2^{3} - 96a2^{2} b2 = 40824 \right\}\right|.$$
Consider all ordered triples $(a1, b1, c1)$ of positive integers satisfying
$$a1^{2} + b1^{2} + c1^{E} = a1 b1 + b1 c1 + c1 a1, \quad 9a1 + 8b1 + 4c1 = 42, \quad a1 ... | 37,584 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(84),
"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"), SumOverSet(set=MapOverSet(set=Solutio... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/SUM_SQUARES_IDENTITY"
] | c95cc6 | alg_qf_psd_sum_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"SUM_SQUARES_IDENTITY"
] | 2 | 0.09 | 2026-02-25T09:10:38.662724Z | {
"verified": true,
"answer": 37584,
"timestamp": "2026-02-25T09:10:38.752359Z"
} | c81a4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 507,
"completion_tokens": 21565
},
"timestamp": "2026-03-30T05:57:41.669Z",
"answer": 37584
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok_later"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
9b2b8c | alg_sym_quad_system_v1_1419126231_112 | Let $S$ be the set of positive integer solutions $(a, b, c)$ to the system:
\n$$
a^2 + b^2 + c^2 = ab + bc + ca \quad \text{and} \quad a + 8b + 6c = 2115.
$$
Let $M = \left( \sum_{(a,b,c) \in S} a^3 + b^3 + c^3 \right) \bmod m$, where $m = \min\{ x + y \mid x > 0, y > 0,\ xy = 2085136 \}$. Compute $|M|$. | 2,695 | graphs = [
Graph(
let={
"_n": Const(2115),
"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")), ... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sym_quad_system_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-25T09:38:25.645073Z | {
"verified": true,
"answer": 2695,
"timestamp": "2026-02-25T09:38:25.658917Z"
} | c56b7a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 2155
},
"timestamp": "2026-03-30T07:05:57.725Z",
"answer": 2695
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
727c82 | lin_form_endings_v1_784195855_8119 | Let $a = 16$ and $b = 12$. Let $A = 49$ and $B = 10$. Define $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $$
T = a'A + b'B - a'b'.
$$ Let $$
S = aA + bB - a - b + 1.
$$ Define $k = 17127$ and $M = 72124$. Compute the remainder when $k(S - T)$ is... | 31,733 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(12),
"A_val": Const(49),
"B_val": Const(10),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T10:49:35.364238Z | {
"verified": true,
"answer": 31733,
"timestamp": "2026-02-08T10:49:35.366610Z"
} | 7e9a0d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 908
},
"timestamp": "2026-02-16T16:08:37.143Z",
"answer": 31733
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
72ef36 | algebra_vieta_sum_v1_1520064083_249 | Let $x$ be a real number satisfying the equation
\[
x^3 + \left( \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor \right) x^2 + 44x - 60 = 0.
\]
Let $r$ be the sum of all real solutions to this equation. Compute $|r|$. | 15 | graphs = [
Graph(
let={
"_n": Const(44),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(3)), Mul(Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))), Pow(Var("x"), Const(2))), Mul(R... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_vieta_sum_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.008 | 2026-02-08T03:08:59.048493Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T03:08:59.056045Z"
} | 5bfbec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1014
},
"timestamp": "2026-02-10T13:34:57.670Z",
"answer": 15
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e9b3e5 | comb_binomial_compute_v1_1978505735_4489 | Let $T$ be the set of all integers $t$ with $15 \le t \le 54$ for which there exist integers $a$ and $b$ such that $1 \le a \le 3$, $1 \le b \le 4$, and $t = 6a + 9b$. Let $n$ be the number of elements in $T$. Compute the remainder when $44121 \cdot \binom{n}{6}$ is divided by 95026. | 1,650 | graphs = [
Graph(
let={
"_n": Const(95026),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:16:04.461415Z | {
"verified": true,
"answer": 1650,
"timestamp": "2026-02-08T18:16:04.463285Z"
} | a62b54 | 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": 1776
},
"timestamp": "2026-02-18T15:40:10.415Z",
"answer": 1650
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
86ccf2 | comb_factorial_compute_v1_784195855_9482 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy$ equals the number of positive integers $p$ for which there exists a positive integer $q$ satisfying $pq = 25467750$, $\gcd(p,q) = 1$, and $p < q$. Let $n$ be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Compute $58081 - n!... | 17,761 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | comb_factorial_compute_v1 | null | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.001 | 2026-02-08T16:50:55.077934Z | {
"verified": true,
"answer": 17761,
"timestamp": "2026-02-08T16:50:55.079414Z"
} | 21b631 | 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": 1775
},
"timestamp": "2026-02-17T13:46:11.479Z",
"answer": 17761
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fbc999 | modular_count_residue_v1_124444284_6856 | Let $m$ be the number of integers $t$ such that $14 \leq t \leq 80$ and $t = 4a + 10b$ for some integers $a, b$ with $1 \leq a \leq 10$ and $1 \leq b \leq 4$. Let $r$ be the number of positive integers $n \leq 145$ such that $\gcd(n, 12) = 1$, and then define $r$ again as the number of positive integers $n \leq r$ such... | 2,594 | graphs = [
Graph(
let={
"_n": Const(15),
"upper": Const(77841),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ri... | NT | null | COUNT | sympy | C4 | [
"C4/C4",
"LIN_FORM"
] | 472959 | modular_count_residue_v1 | null | 6 | 0 | [
"C4",
"LIN_FORM"
] | 2 | 7.698 | 2026-02-08T08:40:28.834138Z | {
"verified": true,
"answer": 2594,
"timestamp": "2026-02-08T08:40:36.531856Z"
} | 10e020 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2369
},
"timestamp": "2026-02-13T20:39:47.690Z",
"answer": 2594
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"le... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3a4126 | comb_sum_binomial_row_v1_1440796553_299 | Let $n$ be the number of positive integers $m$ such that $1 \leq m \leq 79$ and $m \equiv \left\lfloor \frac{m}{2} \right\rfloor \pmod{5}$. Compute $2^n$. | 32,768 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(79)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
"re... | NT | null | SUM | sympy | L3C | [
"L3C"
] | 73f8b0 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T11:43:25.106625Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T11:43:25.107592Z"
} | b0fd58 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 1728
},
"timestamp": "2026-02-14T17:43:05.250Z",
"answer": 32768
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1cb6af | nt_count_divisible_and_v1_1116507919_253 | Let $d_1=6$. Let $d_2$ be the number of integers $j$ with $0\le j\le 36865$ such that the binomial coefficient $\binom{36865}{j}$ is odd.
Let $S$ be the sum
$$S=\sum_{d\mid 95} \mu(d),$$
where $\mu$ denotes the Möbius function.
Let $T$ be the number of integers $n$ with $1\le n\le 70656$ such that $n\equiv 0\pmod{d_1... | 2,944 | graphs = [
Graph(
let={
"upper": Const(70656),
"d1": Const(6),
"d2": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(36865)), Eq(Mod(value=Binom(n=Const(36865), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonn... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"V8"
] | 0d4771 | nt_count_divisible_and_v1 | null | 8 | 0 | [
"MOBIUS_COPRIME",
"V8"
] | 2 | 2.198 | 2026-02-08T02:29:54.047812Z | {
"verified": true,
"answer": 2944,
"timestamp": "2026-02-08T02:29:56.245611Z"
} | 12b21f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 1011
},
"timestamp": "2026-02-08T19:16:45.399Z",
"answer": 2944
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -4.6,
"mid": 0.15,
"hi": 4.61
} | ||
9a6eab | modular_inverse_v1_717093673_289 | Let $a$ be the number of integers $t$ with $5 \leq t \leq 14$ that can be written in the form $3a + 2b$ for positive integers $a$ and $b$ satisfying $1 \leq a \leq 2$ and $1 \leq b \leq 4$. Let $m$ be the number of positive integers $j$ such that $1 \leq j \leq 157$ and $j^2 \leq 24649$. Let $x$ be the smallest positiv... | 249 | graphs = [
Graph(
let={
"_n": Const(2),
"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=2)), Geq(left=Var(na... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"C3"
] | ea43fe | modular_inverse_v1 | null | 6 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.023 | 2026-02-08T15:17:36.113709Z | {
"verified": true,
"answer": 249,
"timestamp": "2026-02-08T15:17:36.136407Z"
} | 7c99ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2136
},
"timestamp": "2026-02-16T03:40:34.814Z",
"answer": 249
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
87052b | nt_min_coprime_above_v1_124444284_6053 | Let $m = 2019$ and $M = 2108$. Let $d_0$ be the smallest divisor of $48436559$ that is at least $2$. Find the smallest integer $n > m$ with $n \leq M$ such that $\gcd(n, d_0) = 1$. | 2,020 | graphs = [
Graph(
let={
"_n": Const(2),
"start": Const(2019),
"upper": Const(2108),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(48436559))))),
"result": MinOv... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.022 | 2026-02-08T08:06:06.381233Z | {
"verified": true,
"answer": 2020,
"timestamp": "2026-02-08T08:06:06.403236Z"
} | 4fa119 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1296
},
"timestamp": "2026-02-13T14:45:26.568Z",
"answer": 2020
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1db309 | sequence_count_fib_divisible_v1_1125832087_1031 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 49$. Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 266$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 28$, $1 \leq b \leq 35$, satisfying $t = 7a + 2b$. Let $d$ be the number of ord... | 43,090 | graphs = [
Graph(
let={
"_m": Const(53455),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(49)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_SUM_EQUALS",
"LIN_FORM"
] | 7d5c7c | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.024 | 2026-02-08T03:28:00.455474Z | {
"verified": true,
"answer": 43090,
"timestamp": "2026-02-08T03:28:00.479612Z"
} | 3daa01 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 6162
},
"timestamp": "2026-02-10T14:30:20.022Z",
"answer": 43090
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
bcb4fa | geo_visible_lattice_v1_784195855_4681 | Let $n = 89$. Define a lattice point $(x, y)$ to be visible from the origin if $\gcd(x, y) = 1$. Let $r$ be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute $|r|$. | 4,911 | graphs = [
Graph(
let={
"n": Const(89),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.173 | 2026-02-08T07:16:09.659913Z | {
"verified": true,
"answer": 4911,
"timestamp": "2026-02-08T07:16:09.832661Z"
} | 810195 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 6600
},
"timestamp": "2026-02-24T07:51:26.322Z",
"answer": 4911
},
{
"i... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
89b231 | alg_linear_system_2x2_v1_601307018_5272 | Let $\mathrm{det} = (-15)(-19) - (-9) \cdot \left|\left\{ (a, b) : 1 \leq a, b \leq 25,\ 64a^3 + \left|\left\{ v : 4 \leq v \leq 2917,\ \exists\, 1 \leq a', b' \leq 14\ \text{s.t.}\ 16a'^2 - 16a'b' + 5b'^2 = v \right\}\right| \cdot a^2 b + 108ab^2 + 27b^3 = 438976 \right\}\right|$, $R = (-460104)(-19) - (-265463)(6)$, ... | 30,017 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(25),
"num_x": Sub(Mul(Const(-460104), Const(-19)), Mul(Const(-265463), Const(6))),
"num_y": Sub(Mul(Const(-15), Const(-265463)), Mul(Const(-9), Const(-460104))),
"det": Sub(Mul(Const(-15), Const(-... | ALG | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"QF_PSD_DISTINCT/POLY3_COUNT"
] | 5dc0d1 | alg_linear_system_2x2_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"POLY_ORBIT_LEGENDRE",
"QF_PSD_DISTINCT"
] | 3 | 0.118 | 2026-03-10T05:56:40.859944Z | {
"verified": true,
"answer": 30017,
"timestamp": "2026-03-10T05:56:40.977967Z"
} | 89be18 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 24561
},
"timestamp": "2026-04-19T01:43:47.918Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
aefe1b | comb_count_surjections_v1_601307018_758 | Let $f(x) = x^5 - 2x^2 - 4x + 3$. Define $R = f(a) \bmod 3721$, $S = f(R) \bmod 3721$, and $T = f(S) \bmod 3721$. Let $k$ be the number of non-negative integers $a$ with $0 \le a \le \left|\{ (x_1, x_2) \in \mathbb{Z}^+ \times \mathbb{Z}^+ : x_1 \text{ odd}, x_2 \text{ odd}, x_1 + x_2 = 7440 \}\right|$ such that $T = a... | 1,806 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(3),
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/POLY_ORBIT_HENSEL"
] | 311256 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"POLY_ORBIT_HENSEL"
] | 2 | 0.006 | 2026-03-10T01:23:22.335596Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-03-10T01:23:22.341965Z"
} | 451dfb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 20215
},
"timestamp": "2026-03-29T00:04:36.713Z",
"answer": 1806
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lem... | {
"lo": 1.27,
"mid": 3.84,
"hi": 5.91
} | ||
ae6374 | comb_count_partitions_v1_865884756_679 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 441$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $12993 \cdot p(n)$ is divided by $65726$. | 43,796 | graphs = [
Graph(
let={
"_n": Const(441),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_partitions_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T15:33:14.072755Z | {
"verified": true,
"answer": 43796,
"timestamp": "2026-02-08T15:33:14.074857Z"
} | 290e5c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1681
},
"timestamp": "2026-02-24T18:00:44.923Z",
"answer": 43796
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
f0b22d | comb_count_surjections_v1_48377204_1596 | Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 42$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 9a + 6b$. Let $n$ be the number of elements in $T$. Let $K$ be the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2\}$, and let $k$ be the number of elements ... | 40,824 | 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 | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | efa619 | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T16:13:05.067007Z | {
"verified": true,
"answer": 40824,
"timestamp": "2026-02-08T16:13:05.070486Z"
} | 296d5e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 1229
},
"timestamp": "2026-02-24T20:13:17.301Z",
"answer": 40824
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
60a886 | comb_bell_compute_v1_1742523217_4965 | Let $u = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $c = \sum_{k=0}^{3} (-1)^k \binom{3}{k}$. Let $n = 9u + c$. Compute the $n$-th Bell number. | 21,147 | graphs = [
Graph(
let={
"n2": Const(0),
"u": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(3),
"c": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T10:41:31.190125Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T10:41:31.190847Z"
} | bc008a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 393
},
"timestamp": "2026-02-24T12:13:12.486Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
bd55bc | nt_sum_totient_over_divisors_v1_1470522791_22 | Let $n = 44780$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Call this sum $s$.
Now compute the sum
$$
\sum_{k=1}^{44} \phi(k) \left\lfloor \frac{44}{k} \right\rfloor
$$
and subtract $s$ from it. Find the remainder when this difference is divided b... | 34,232 | graphs = [
Graph(
let={
"_n": Const(44),
"n": Const(44780),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 9468ae | nt_sum_totient_over_divisors_v1 | negation_mod | 6 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T12:47:47.685472Z | {
"verified": true,
"answer": 34232,
"timestamp": "2026-02-08T12:47:47.688292Z"
} | bf0a96 | 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": 583
},
"timestamp": "2026-02-15T05:06:53.348Z",
"answer": 34232
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
38d1f8 | comb_count_surjections_v1_124444284_9933 | Let $n_2 = 0!$. Define
$$
e = \sum_{k=\sum_{j=0}^{2} (-1)^j \binom{2}{j}}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $m = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$, and let $k = 4 + e + m$. Compute $k! \cdot S(4, k)$, where $S(n,k)$ denotes the Stirling number of the second kind. | 24 | graphs = [
Graph(
let={
"n2": Factorial(Const(0)),
"e": Summation(var="k", start=Summation(var="k", start=Const(0), end=Const(2), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(2), k=Var("k")))), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 8794cb | comb_count_surjections_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 3 | 0.028 | 2026-02-08T12:43:46.264413Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T12:43:46.292802Z"
} | 9bbf96 | 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": 849
},
"timestamp": "2026-02-24T16:16:22.925Z",
"answer": 24
},
{
"id":... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
c32f7c | alg_poly3_min_v1_1218484723_2751 | Let $A = \min\left\{ 16a_1b_1 + 32b_1^2 + 4a_1^2 : 1 \le a_1, b_1 \le 17 \right\}$. Find the remainder when $$\min\left\{ -65a^3 - 42a^2b - 24ab^2 + 7b^3 : 1 \le a \le A,\, 1 \le b \le 52 \right\}$$ is divided by $99594$. | 93,152 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]),... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_poly3_min_v1 | null | 5 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.016 | 2026-02-25T04:27:35.732462Z | {
"verified": true,
"answer": 93152,
"timestamp": "2026-02-25T04:27:35.748563Z"
} | cd6915 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 2744
},
"timestamp": "2026-03-29T06:22:12.291Z",
"answer": 93152
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
fa5598 | nt_count_coprime_and_v1_1520064083_176 | Let $p$ be the smallest divisor of $41327$ that is at least $2$. Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $k_2$ be the largest prime number between $m$ and $p$, inclusive. Compute the number of positive i... | 28,205 | graphs = [
Graph(
let={
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(41327))))),
"upper": Const(36195),
"k1": Const(7),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COPRIME_PAIRS/MAX_PRIME_BELOW"
] | a2a2d0 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 16.227 | 2026-02-08T03:07:00.328223Z | {
"verified": true,
"answer": 28205,
"timestamp": "2026-02-08T03:07:16.555570Z"
} | 59e6b3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 1718
},
"timestamp": "2026-02-10T12:49:35.078Z",
"answer": 28205
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
1b361d | comb_factorial_compute_v1_153355830_29 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 8$. Let $P$ be the maximum value of $xy$ over all such pairs. Now, let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = P$. Let $n$ be the minimum value of $x + y$ over all pairs in $T$. Compute $n!$.... | 50,598 | graphs = [
Graph(
let={
"_n": Const(55197),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_factorial_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T02:51:18.273107Z | {
"verified": true,
"answer": 50598,
"timestamp": "2026-02-08T02:51:18.274842Z"
} | cd1243 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2055
},
"timestamp": "2026-02-10T11:43:56.905Z",
"answer": 50598
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 0.04,
"mid": 1.71,
"hi": 3.18
} | ||
fbf1f9 | nt_count_digit_sum_v1_1520064083_1241 | Let $t$ be an integer. A pair of positive integers $(a, b)$ is called \emph{valid} if $1 \leq a \leq 13$, $1 \leq b \leq 2$, and $t = 6a + 21b$. Define $S$ to be the set of all integers $t$ such that $27 \leq t \leq 120$ and there exists a valid pair $(a, b)$ for $t$. Let $m$ be the number of elements in $S$.
Now, let... | 21,799 | graphs = [
Graph(
let={
"_n": Const(67513),
"upper": Const(381924),
"target_sum": 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(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 25.341 | 2026-02-08T03:52:22.414150Z | {
"verified": true,
"answer": 21799,
"timestamp": "2026-02-08T03:52:47.754879Z"
} | ad254a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 6449
},
"timestamp": "2026-02-10T14:41:31.136Z",
"answer": 21799
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
db8065 | alg_poly3_count_v1_601307018_4130 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 478$ such that $$\left| \left\{ (a_1, b_1) : a_1, b_1 \in \mathbb{Z}^+,\ 1 \le a_1, b_1 \le 35,\ 2b_1^2 - 2a_1b_1 + 13a_1^2 \le 1418 \right\} \right| \cdot b^3 + 702a^2b - 234a^3 - 702ab^2 = -29250.$$ | 473 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(478)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(478)), Eq(Sum(Mul(CountOverSet(set=SolutionsSet(var... | ALG | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_count_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"QF_PSD_COUNT_LEQ"
] | 2 | 12.652 | 2026-03-10T04:43:30.224686Z | {
"verified": true,
"answer": 473,
"timestamp": "2026-03-10T04:43:42.876462Z"
} | b8cd31 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 6612
},
"timestamp": "2026-03-29T11:09:51.819Z",
"answer": 473
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
d056ca | nt_count_gcd_equals_v1_655260480_4532 | Let $k$ be the number of integers $t$ in the range $21 \leq t \leq 285$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 17$, and $t = 6a + 15b$. Let $d = 5$. Compute the number of positive integers $n$ such that $1 \leq n \leq 45369$ and $\gcd(n, k) = d$. Let $r$ be this count. Compute... | 74,952 | graphs = [
Graph(
let={
"upper": Const(45369),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 3.674 | 2026-02-08T17:58:45.917944Z | {
"verified": true,
"answer": 74952,
"timestamp": "2026-02-08T17:58:49.591601Z"
} | 52a1f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 3885
},
"timestamp": "2026-02-18T11:42:46.885Z",
"answer": 74952
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1b7c98 | comb_count_partitions_v1_1520064083_158 | Let $T$ be the set of all positive integers $t$ such that $25 \leq t \leq 125$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 12$, and $t = 14a + 4b + 7$. Let $n$ be the number of elements in $T$. Compute the number of integer partitions of $n$. | 89,134 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:06:45.453563Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T03:06:45.456291Z"
} | e873e8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1991
},
"timestamp": "2026-02-10T12:58:46.666Z",
"answer": 89134
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
dca83d | nt_count_divisible_and_v1_1431428450_169 | Let $d_1 = 6$. Let $d_2$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 15750$, $\gcd(p, q) = 1$, and $p < q$. Compute the number of positive integers $n$ such that $n \leq 55584$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 2,316 | graphs = [
Graph(
let={
"upper": Const(55584),
"d1": Const(6),
"d2": 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=15750)), Eq(l... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_and_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.602 | 2026-02-08T13:17:10.493691Z | {
"verified": true,
"answer": 2316,
"timestamp": "2026-02-08T13:17:13.096181Z"
} | 8c486c | 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": 2579
},
"timestamp": "2026-02-15T12:02:14.479Z",
"answer": 2316
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
76a41c | diophantine_fbi2_min_v1_1742523217_3905 | Let $k = 10$. Determine the smallest integer $d$ such that $5 \leq d \leq 20$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Find the value of this $d$. | 5 | graphs = [
Graph(
let={
"k": Const(10),
"a": Const(4),
"b": Const(1),
"upper": Const(20),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | C4 | [
"COPRIME_PAIRS/K2"
] | 846647 | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"C4",
"COPRIME_PAIRS",
"K2"
] | 3 | 0.088 | 2026-02-08T06:07:50.368535Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T06:07:50.456890Z"
} | 0b1e90 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 357
},
"timestamp": "2026-02-15T17:04:17.993Z",
"answer": 2
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
6e03e1 | comb_count_partitions_v1_1520064083_6654 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 180$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 5$, and $$t = 15a + 12b.$$
Let $p(n)$ denote the number of integer partitions of $n$.
Let $Q$ be the remainder when $43464 \cdot p(n)$ is divided by 55643.
Find th... | 30,737 | graphs = [
Graph(
let={
"_n": Const(55643),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T08:15:30.357527Z | {
"verified": true,
"answer": 30737,
"timestamp": "2026-02-08T08:15:30.359962Z"
} | 09e2de | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 4535
},
"timestamp": "2026-02-24T09:14:05.651Z",
"answer": 30737
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
84343d | comb_count_surjections_v1_677425708_616 | Let $n = 7$. Let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 8$, where $1 \leq i \leq 7$ and $1 \leq j \leq 8$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $63760 \cdot \text{result}$ is ... | 10,293 | graphs = [
Graph(
let={
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(8... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T03:37:39.058601Z | {
"verified": true,
"answer": 10293,
"timestamp": "2026-02-08T03:37:39.070181Z"
} | b77eb8 | 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": 2015
},
"timestamp": "2026-02-08T20:50:43.870Z",
"answer": 10293
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
a007a1 | comb_catalan_compute_v1_1218484723_4722 | Let $C_n$ denote the $n$-th Catalan number. Let $n$ be the number of integers $t$ in the range $31 \leq t \leq 67$ that can be expressed as $t = 9a + 6b + 16$ for integers $a, b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$. Compute $C_n$. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T06:23:40.232118Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-25T06:23:40.233789Z"
} | bfe3bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1462
},
"timestamp": "2026-03-29T17:12:07.645Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
3db1fe | nt_sum_divisors_mod_v1_1520064083_2795 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 32400$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11287$. | 1,170 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11287)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T05:12:55.329318Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T05:12:55.331927Z"
} | d6e545 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 716
},
"timestamp": "2026-02-11T23:07:47.203Z",
"answer": 1170
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
542b91 | comb_factorial_compute_v1_153355830_1824 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 265$ such that $\binom{265}{j}$ is odd. Let $r = 16384 - n!$. Compute the remainder when $r$ is divided by 66370. Find the value of this remainder. | 42,434 | graphs = [
Graph(
let={
"_n": Const(16384),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(265)), Eq(Mod(value=Binom(n=Const(265), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"re... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 4 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T06:38:39.834550Z | {
"verified": true,
"answer": 42434,
"timestamp": "2026-02-08T06:38:39.837030Z"
} | 8ab98d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 559
},
"timestamp": "2026-02-24T06:40:27.337Z",
"answer": 42434
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
e04b65 | nt_max_prime_below_v1_971394319_859 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 2$ and the sum of the digits of $n$ is odd. Let $B$ be the set of all prime numbers $n$ such that $n \geq |A|$ and $n \leq 71824$. Let $p_{\text{max}}$ be the largest element of $B$. Compute the remainder when $44121 \cdot p_{\text{max}}$ is divid... | 43,988 | graphs = [
Graph(
let={
"upper": Const(71824),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | nt_max_prime_below_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 1.841 | 2026-02-08T13:20:08.873968Z | {
"verified": true,
"answer": 43988,
"timestamp": "2026-02-08T13:20:10.715259Z"
} | 95ebf6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 2954
},
"timestamp": "2026-02-15T14:13:52.069Z",
"answer": 43988
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f17e27 | comb_sum_binomial_row_v1_601307018_4205 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that $$\left|\{ v : 41 \le v \le 11849,\ \exists\text{ integers } a, b \text{ with } 1 \le a \le 17,\ 1 \le b \le 17 \text{ such that } 41 \cdot b^{2} = v \}\right| \cdot a^{4} + 102 \cdot a^{2} \cdot b^{2} + \left|\{ (a_... | 1,024 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(17),
"_n": Const(4),
"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"), Const(... | COMB | null | SUM | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY4_COUNT",
"POLY4_COUNT/POLY4_COUNT"
] | 548a79 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.027 | 2026-03-10T04:50:19.730525Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-03-10T04:50:19.757501Z"
} | 9207a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 405,
"completion_tokens": 2179
},
"timestamp": "2026-03-29T11:24:26.983Z",
"answer": 1024
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma... | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
ece7db | nt_count_divisible_and_v1_50713871_92 | Let $A$ be the set of all integers $n$ such that $1 \leq n \leq 106590$, $n$ is divisible by 6, and $n$ is divisible by 10. Compute the number of elements in $A$. | 3,553 | graphs = [
Graph(
let={
"upper": Const(106590),
"d1": Const(6),
"d2": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=9), b=Const(value=14)), var='d', expr=MoebiusMu(n=Var(name='d... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_divisible_and_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 3.326 | 2026-02-08T02:45:11.008404Z | {
"verified": true,
"answer": 3553,
"timestamp": "2026-02-08T02:45:14.333998Z"
} | 34196d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 386
},
"timestamp": "2026-02-08T19:48:30.756Z",
"answer": 3553
},
{
"id... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"... | {
"lo": -10,
"mid": -6.86,
"hi": -3.72
} | ||
2a3ddf | nt_count_intersection_v1_1520064083_2760 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 196$.
Let $b$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = k$.
Let $N = 50000$. Determine the number of positive integers $n \leq N$ such that $11$ divides $n$ and... | 48,103 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(196)))), expr=Sum(Var("x"), Var("y")))),
"N": Const(50000),... | NT | null | COUNT | sympy | B3 | [
"B3/COMB1"
] | e26f7e | nt_count_intersection_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 2.065 | 2026-02-08T04:59:46.426578Z | {
"verified": true,
"answer": 48103,
"timestamp": "2026-02-08T04:59:48.491225Z"
} | 42d31e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1719
},
"timestamp": "2026-02-11T22:39:26.305Z",
"answer": 48103
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
41e142 | nt_sum_gcd_range_mod_v1_458359167_524 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 115600$. Let $T$ be the set of all values $x+y$ where $(x,y) \in S$. Let $m$ be the minimum value in $T$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $3$ divides the $n$th Fibonacci number. Let $N$ b... | 1,500 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(... | NT | null | COMPUTE | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE/B1"
] | 397de5 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"B1",
"B3",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.416 | 2026-02-08T03:23:39.317983Z | {
"verified": true,
"answer": 1500,
"timestamp": "2026-02-08T03:23:39.733624Z"
} | 1c0380 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 5083
},
"timestamp": "2026-02-10T14:08:46.721Z",
"answer": 1500
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
637022 | nt_sum_gcd_range_mod_v1_784195855_8717 | Let $N$ be the largest positive divisor of $35212331$ that is at most $5929$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 20736$. Let $s = \sum_{n=1}^{N} \gcd(n, k)$. Find the remainder when $s$ is divided by $11839$. | 931 | graphs = [
Graph(
let={
"_n": Const(5929),
"N": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(35212331))))),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(ele... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"B3"
] | a4accf | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.541 | 2026-02-08T16:17:20.225868Z | {
"verified": true,
"answer": 931,
"timestamp": "2026-02-08T16:17:20.767132Z"
} | d4c7dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 2750
},
"timestamp": "2026-02-17T01:05:14.438Z",
"answer": 931
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
597355 | algebra_poly_eval_v1_1918700295_271 | Let $n$ be the number of integers $t$ with $9 \leq t \leq 30$ for which there exist positive integers $a$ and $b$ such that $a \leq 8$, $b \leq 2$, and $t = 2a + 7b$. Let $m$ be the number of unordered pairs of coprime positive integers $(p, q)$ such that $p < q$ and $pq = 72$. Define
$$
\text{result} = 8n^3 + 8n^m - ... | 49,293 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T03:08:11.097173Z | {
"verified": true,
"answer": 49293,
"timestamp": "2026-02-08T03:08:11.100087Z"
} | 2232a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 5224
},
"timestamp": "2026-02-10T13:11:20.143Z",
"answer": 49293
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
cac7d8 | nt_num_divisors_compute_v1_124444284_7979 | Let $m = 44121$. Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 45481$ and $\gcd(n, 14) = 1$. Let $k$ be the number of elements in $S$. Let $d$ be the smallest integer greater than or equal to 2 that divides $k$. Let $r$ be the number of positive divisors of $d$. Compute $m \cdot r$. | 88,242 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/C4/MIN_PRIME_FACTOR"
] | 171be9 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"C4",
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 3 | 0.006 | 2026-02-08T09:29:34.830367Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T09:29:34.836572Z"
} | ce7e6b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 2611
},
"timestamp": "2026-02-14T04:38:11.310Z",
"answer": 88242
},
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_la... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e17144 | nt_sum_divisors_mod_v1_655260480_2264 | Let $m = 8$. Let $p$ be the largest prime number such that $2 \leq p \leq m$. Consider the set of all ordered pairs $(x, y)$ of positive integers satisfying $xy = 518400$. For each such pair, compute $x + y$, and let $S$ be the set of all such sums. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \l... | 546 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_m")), IsPrime(Var("n1"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(1)), Leq... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_FIB_DIVISIBLE",
"B3/COUNT_FIB_DIVISIBLE"
] | 147494 | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 3 | 0.006 | 2026-02-08T16:39:19.071364Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T16:39:19.077580Z"
} | 51b50e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1870
},
"timestamp": "2026-02-17T08:26:24.545Z",
"answer": 546
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d96c0a | alg_qf_psd_count_leq_v1_1218484723_3875 | Let $Q$ be the number of ordered pairs $(a,b)$ of positive integers with $1 \le a \le 86$ and $1 \le b \le 86$ such that
$$-36ab + K b^{2} + 12a^{2} \le 87576,$$
where $K$ is the number of ordered pairs $(a_1,b_1)$ of positive integers with $1 \le a_1 \le 40$ and $1 \le b_1 \le 40$ satisfying
$$68a_1^{3}b_1 + L b_1^{4}... | 6,513 | graphs = [
Graph(
let={
"_m": Const(68),
"_n": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(86)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(86)), Leq(Sum(Mul(Const... | ALG | null | COUNT | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/POLY4_COUNT"
] | 84aa99 | alg_qf_psd_count_leq_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT"
] | 2 | 0.044 | 2026-02-25T05:30:30.943040Z | {
"verified": true,
"answer": 6513,
"timestamp": "2026-02-25T05:30:30.987516Z"
} | 899892 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 370,
"completion_tokens": 10739
},
"timestamp": "2026-03-29T12:42:26.963Z",
"answer": 6413
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} |
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