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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3e36db | algebra_poly_eval_v1_798873815_229 | Let $b = 27$. Let $S$ be the set of all ordered pairs of positive integers $(p, q)$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Define $k = |S|$.
Compute $4 \cdot b^k - b + 7$. | 2,896 | graphs = [
Graph(
let={
"_n": Const(4),
"b": Const(27),
"result": Sum(Mul(Ref("_n"), Pow(Ref("b"), 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')), r... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T02:31:30.629542Z | {
"verified": true,
"answer": 2896,
"timestamp": "2026-02-08T02:31:30.630736Z"
} | 87194d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 631
},
"timestamp": "2026-02-08T19:12:53.890Z",
"answer": 2896
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"s... | {
"lo": -5.53,
"mid": -3.77,
"hi": -1.89
} | ||
595763 | comb_sum_binomial_mod_v1_1978505735_814 | Let $A$ be the set of all integers $t$ with $22 \le t \le 104$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 7$, $1 \le b \le 21$, and $t = 7a + 2b + 13$. Let $k$ be the number of elements in $A$. Compute the sum $\sum_{j=28}^{k} \binom{97}{j}$, and let $r$ be the remainder when this sum is... | 36,939 | graphs = [
Graph(
let={
"_n": Const(10253),
"sum": Summation(var="k", start=Const(28), end=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(nam... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_mod_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.012 | 2026-02-08T15:37:43.329058Z | {
"verified": true,
"answer": 36939,
"timestamp": "2026-02-08T15:37:43.340583Z"
} | 5bdbb4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 26176
},
"timestamp": "2026-02-24T18:09:02.842Z",
"answer": 36939
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
d502ef | alg_qf_psd_count_v1_1218484723_1071 | Let $P = \max\{ n \mid 2 \le n \le 17,\ n \text{ prime} \}$. Let $B = \min\left\{ 133b_1^3 + 174a_1b_1^2 + 84a_1^2b_1 + 16a_1^3 \mid 1 \le a_1 \le P,\ 1 \le b_1 \le 17 \right\}$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 407$, $1 \le b \le B$, such that $4b^2 + 29a^2 - 20ab = 1006... | 11 | graphs = [
Graph(
let={
"_m": Const(407),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_m")), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(se... | NT | null | COUNT | sympy | POLY4_COUNT | [
"MAX_PRIME_BELOW/POLY3_MIN"
] | a90331 | alg_qf_psd_count_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"POLY3_MIN",
"POLY4_COUNT"
] | 3 | 1.132 | 2026-02-25T02:46:45.979135Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-25T02:46:47.110905Z"
} | cd6a74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 12587
},
"timestamp": "2026-03-10T05:14:28.312Z",
"answer": 11
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status... | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
376257 | alg_poly_orbit_hensel_v1_601307018_10098 | Let $N = (a^2 + a + 371) \bmod 3481$ and $M = (N^2 + N + 371) \bmod 3481$. Find the number of non-negative integers $a$ with $0 \leq a \leq 511706$ such that $M = a$ and $N \neq a$. | 294 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(371)), modulus=Const(3481)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(371)), modulus=Const(3481)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condition=An... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.036 | 2026-03-10T10:35:07.314825Z | {
"verified": true,
"answer": 294,
"timestamp": "2026-03-10T10:35:07.350576Z"
} | 061b3f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 17434
},
"timestamp": "2026-04-19T13:00:43.846Z",
"answer": 294
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
bef471 | nt_num_divisors_compute_v1_1742523217_2925 | Let $n$ be the number of positive integers less than or equal to $131$ whose digit sum is odd. Determine the value of the number of positive divisors of $n$. | 8 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(131)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"result": NumDivisors(n=Ref("n")),
},
... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T05:27:34.920943Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T05:27:34.922640Z"
} | 1cc3bb | 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": 1486
},
"timestamp": "2026-02-12T09:06:34.160Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
41322c | sequence_count_fib_divisible_v1_124444284_3019 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 47961$. Define $u$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $d$ be the smallest integer greater than or equal to $2$ that divides $1773593$. Define $r$ to be the number of positive integers $n \leq u$ such t... | 24,288 | graphs = [
Graph(
let={
"_n": Const(2),
"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(47961)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.022 | 2026-02-08T05:08:42.283192Z | {
"verified": true,
"answer": 24288,
"timestamp": "2026-02-08T05:08:42.305363Z"
} | 3ddf2f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2885
},
"timestamp": "2026-02-11T23:06:00.823Z",
"answer": 24288
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
7faee4_l | antilemma_sum_equals_v1_1520064083_1839 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 99$, $1 \leq j \leq 99$, and $i + j = 100$. Let $Q$ be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|x| + 2$. Find the value of $Q$. | 101 | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.138 | 2026-02-08T04:19:26.905691Z | {
"verified": false,
"answer": 50,
"timestamp": "2026-02-08T04:19:27.043615Z"
} | 83d54f | 7faee4 | 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": 203,
"completion_tokens": 2382
},
"timestamp": "2026-02-24T00:22:29.409Z",
"answer": 50
},
{
"id"... | 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": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | |
e269cd | nt_count_divisible_v1_677425708_1626 | Compute the number of positive integers $n$ such that $1 \leq n \leq 69696$ and $n \equiv \sum_{k=0}^{3} (-1)^k \binom{3}{k} \pmod{26}$. | 2,680 | graphs = [
Graph(
let={
"upper": Const(69696),
"divisor": Const(26),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 6.449 | 2026-02-08T04:19:31.691045Z | {
"verified": true,
"answer": 2680,
"timestamp": "2026-02-08T04:19:38.139848Z"
} | aa66f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 578
},
"timestamp": "2026-02-09T22:32:29.330Z",
"answer": 2680
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
c65e6e | modular_count_residue_v1_1520064083_606 | Let $m = 18$ and $r = 6$. Let $A$ be the set of all positive integers $n$ such that $n \leq 71289$ and $n \equiv r \pmod{m}$. Let $c = 5003$. Let $s = |A|$, the number of elements in $A$. Let $D$ be the set of all integers $d \geq 2$ that divide $10279593263$, and let $d_{\min}$ be the smallest element of $D$. Compute ... | 89,582 | graphs = [
Graph(
let={
"_n": Const(93619),
"upper": Const(71289),
"m": Const(18),
"r": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modul... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | modular_count_residue_v1 | two_moduli | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 7.481 | 2026-02-08T03:29:18.066206Z | {
"verified": true,
"answer": 89582,
"timestamp": "2026-02-08T03:29:25.547067Z"
} | a5c2ac | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 26848
},
"timestamp": "2026-02-23T20:01:34.569Z",
"answer": 89582
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
b0260e | geo_count_lattice_triangle_v1_1520064083_2993 | Let $A = (0,0)$, $B = (120,40)$, and $C = (121,171)$. The area of triangle $ABC$ is half of the absolute value of the expression $120 \cdot 171 + 121 \cdot (-40) + 0 \cdot (-131)$. The number of lattice points on the boundary of triangle $ABC$ is
\[
\gcd(120,40) + \gcd(1,131) + \gcd(121,171).
\]
Using Pick's Theorem, w... | 7,820 | graphs = [
Graph(
let={
"_n": Const(120),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=171)), Mul(Const(value=121), Sub(left=Const(value=0), right=Const(value=40))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=40))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T05:23:28.928626Z | {
"verified": true,
"answer": 7820,
"timestamp": "2026-02-08T05:23:28.934215Z"
} | 35b8e3 | 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": 1430
},
"timestamp": "2026-02-12T08:35:01.948Z",
"answer": 7820
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
30234a | nt_sum_totient_over_divisors_v1_168721529_56 | Let $\lambda(n)$ denote the Liouville function, and let $\varphi(n)$ denote Euler's totient function. Define $p$ to be the number of integers $t$ such that $18 \leq t \leq 174$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 8$, satisfying $t = 10a + 8b$.
Let $n_2 = p^2$, and let $h ... | 71,679 | graphs = [
Graph(
let={
"_n": Const(2),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/LIOUVILLE_ONE",
"DIVISOR_PARITY"
] | 5bc01f | nt_sum_totient_over_divisors_v1 | null | 5 | 2 | [
"DIVISOR_PARITY",
"LIN_FORM",
"LIOUVILLE_ONE"
] | 3 | 0.017 | 2026-02-08T12:47:27.857338Z | {
"verified": true,
"answer": 71679,
"timestamp": "2026-02-08T12:47:27.874050Z"
} | ee9efd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 833
},
"timestamp": "2026-02-08T20:59:38.973Z",
"answer": 71679
},
{
"i... | 1 | [
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.77
} | ||
8451fa | nt_sum_gcd_range_mod_v1_1742523217_1760 | Let $N$ be the largest prime number less than or equal to $2347$. Let $k = 84$ and $M = 11779$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 2,687 | graphs = [
Graph(
let={
"_n": Const(2347),
"N": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k": Const(84),
"M": Const(11779),
"sum": Summation(var="n", start=Cons... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.11 | 2026-02-08T04:12:57.118916Z | {
"verified": true,
"answer": 2687,
"timestamp": "2026-02-08T04:12:57.228775Z"
} | 5b7ff4 | 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": 5408
},
"timestamp": "2026-02-10T15:51:40.505Z",
"answer": 2687
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
556677 | nt_count_with_divisor_count_v1_784195855_7919 | Determine the number of positive integers $n$ such that $n \leq 71824$ and the number of positive divisors of $n$ is exactly $15$. | 35 | graphs = [
Graph(
let={
"upper": Const(71824),
"div_count": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("... | NT | null | COUNT | sympy | C4 | [
"C4/ONE_PHI_2"
] | 110689 | nt_count_with_divisor_count_v1 | null | 3 | 0 | [
"C4",
"ONE_PHI_2"
] | 2 | 8.823 | 2026-02-08T09:36:54.091399Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T09:37:02.914697Z"
} | 2cf40c | 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": 2121
},
"timestamp": "2026-02-14T05:19:28.330Z",
"answer": 35
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
},
{
"le... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c26c19 | geo_count_lattice_rect_v1_48377204_591 | Let $a = 225$ and $b = 69$. Define a lattice point as a point in the plane with integer coordinates. Let $R$ be the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $N$ be the number of elements in $R$. Compute the remainder when $8 - N$ is divided by $50830$. | 35,018 | graphs = [
Graph(
let={
"a": Const(225),
"b": Const(69),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(8),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(50830)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.007 | 2026-02-08T15:35:02.134771Z | {
"verified": true,
"answer": 35018,
"timestamp": "2026-02-08T15:35:02.142023Z"
} | 894031 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 489
},
"timestamp": "2026-02-24T18:05:38.994Z",
"answer": 35018
},
{
"... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
01f378 | antilemma_k2_v1_1520064083_7922 | Let
$$x = \sum_{k=1}^{89} \varphi(k)\left\lfloor \frac{89}{k} \right\rfloor,$$
where $\varphi$ denotes Euler's totient function.
Let $N = |x| + 1$. Define $\varphi(N)$ to be Euler's totient function of $N$, and $d(N)$ to be the number of positive divisors of $N$.
Let
$$Q = x + \varphi(N) + d(N).$$
Find the value of ... | 6,011 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(89), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(89), Var("k"))))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))),
},
... | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"K2"
] | fce51d | antilemma_k2_v1 | null | 8 | 0 | [
"IDENTITY_POW_ZERO",
"K2"
] | 2 | 0.001 | 2026-02-08T09:22:48.242875Z | {
"verified": true,
"answer": 6011,
"timestamp": "2026-02-08T09:22:48.243765Z"
} | 2acee7 | 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": 841
},
"timestamp": "2026-02-14T03:54:05.316Z",
"answer": 6011
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"le... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
839f86 | antilemma_k3_v1_784195855_986 | Let $n = 24411$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute $x$. | 24,411 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=24411), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:44:04.457882Z | {
"verified": true,
"answer": 24411,
"timestamp": "2026-02-08T04:44:04.458350Z"
} | 900025 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 756
},
"timestamp": "2026-02-11T21:50:12.605Z",
"answer": 3796
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
513948 | geo_visible_lattice_v1_1820931509_568 | A visible lattice point $(x, y)$ is a point in the coordinate plane with integer coordinates such that $1 \leq x, y \leq 80$ and $\gcd(x, y) = 1$. Let $r$ be the number of such visible lattice points. Compute the remainder when $44121 \cdot r$ is divided by $96484$. | 57,903 | graphs = [
Graph(
let={
"n": Const(80),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(96484)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.958 | 2026-02-08T11:46:33.011412Z | {
"verified": true,
"answer": 57903,
"timestamp": "2026-02-08T11:46:33.969345Z"
} | 1b2712 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 3949
},
"timestamp": "2026-02-24T14:43:07.574Z",
"answer": 57903
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
0ad47f | sequence_fibonacci_compute_v1_1125832087_908 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 10$. For each pair in $S$, compute the product $x \cdot y$. Let $n$ be the maximum value among these products. Define $F_n$ to be the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \ge 3$. ... | 33,435 | graphs = [
Graph(
let={
"_n": Const(66331),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(10)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T03:21:37.868839Z | {
"verified": true,
"answer": 33435,
"timestamp": "2026-02-08T03:21:37.869682Z"
} | 950190 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 1504
},
"timestamp": "2026-02-10T13:19:57.510Z",
"answer": 33435
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
bd83a8 | nt_min_coprime_above_v1_1520064083_1949 | Let $ p $ be a positive integer. Suppose there exists a positive integer $ q $ such that $ pq = 36 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ \_n $ be the number of such integers $ p $. Let $ \text{modulus} $ be the sum of all real solutions $ x $ to the equation $ x^{\_n} - 262x - 12080 = 0 $. Find the smallest integ... | 41,211 | 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=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/VIETA_SUM"
] | 815fe1 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"VIETA_SUM"
] | 2 | 0.07 | 2026-02-08T04:25:04.547155Z | {
"verified": true,
"answer": 41211,
"timestamp": "2026-02-08T04:25:04.617474Z"
} | fbf161 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1672
},
"timestamp": "2026-02-10T16:36:08.022Z",
"answer": 41211
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
16792f | comb_catalan_compute_v1_1918700295_622 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 32$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 6a + 4b$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:21:14.543380Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:21:14.544969Z"
} | 078779 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 605
},
"timestamp": "2026-02-10T13:56:51.514Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"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": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
05a3b1 | comb_bell_compute_v1_1520064083_7406 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 30$ and there exist integers $a$ and $b$, each at least 1 and at most 3, satisfying $t = 6a + 4b$. Let $Q = 33489 - B_n$, where $B_n$ denotes the $n$th Bell number, the number of partitions of a set of $n$ elements. Compute $Q$. | 12,342 | graphs = [
Graph(
let={
"_n": Const(33489),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:00:42.489273Z | {
"verified": true,
"answer": 12342,
"timestamp": "2026-02-08T09:00:42.490411Z"
} | 6b4c27 | 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": 624
},
"timestamp": "2026-02-24T10:20:19.950Z",
"answer": 12342
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
edbff0 | comb_count_derangements_v1_168721529_150 | Let $c = 425$. Let $A$ be the set of all positive integers $k$ such that $1 \leq k \leq v_3(5790!)$ and $17$ divides $k$, where $v_3(5790!)$ is the largest power of 3 dividing $5790!$. Let $t = |A|$ be the number of elements in $A$. Let $n$ be the largest integer such that $2^n$ divides $\binom{425}{t}$. Compute the nu... | 1,854 | graphs = [
Graph(
let={
"_c": Const(425),
"_m": Const(17),
"_n": Const(2),
"n": MaxKDivides(target=Binom(n=Ref("_c"), k=CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), MaxKDivides(target=Factorial(Const(5790)), ... | NT | COMB | COUNT | sympy | V1 | [
"V1/C2/V7"
] | 8e0e60 | comb_count_derangements_v1 | null | 7 | 0 | [
"C2",
"V1",
"V7"
] | 3 | 0.004 | 2026-02-08T12:50:45.820566Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T12:50:45.824788Z"
} | c3c692 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 1789
},
"timestamp": "2026-02-08T21:06:41.771Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
991ca1 | nt_count_primes_v1_677425708_3248 | Let $s$ be the sum of all real solutions $x$ to the equation $x^2 - 2x - 3248 = 0$. Let $N$ be the number of prime numbers $n$ such that $s \leq n \leq 70225$. Compute the remainder when $40153 \cdot N$ is divided by $62301$. | 44,895 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(70225),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-2), Var("x")), Const(-3248)), C... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_primes_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 1.912 | 2026-02-08T05:34:58.980129Z | {
"verified": true,
"answer": 44895,
"timestamp": "2026-02-08T05:35:00.892495Z"
} | f3c6dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 4300
},
"timestamp": "2026-02-12T11:32:46.400Z",
"answer": 44895
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
95b095 | alg_poly3_count_v1_1218484723_3896 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 30$ such that $25b_1^2 - 18a_1b_1 + 10a_1^2 \le p_{\max}$, where $p_{\max}$ is the largest prime less than or equal to $1993$. Let $A = |S|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le A$... | 74 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), conditi... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/QF_PSD_COUNT_LEQ"
] | 27f428 | alg_poly3_count_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.206 | 2026-02-25T05:30:56.156558Z | {
"verified": true,
"answer": 74,
"timestamp": "2026-02-25T05:30:56.362461Z"
} | 6f88f6 | 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": 5149
},
"timestamp": "2026-03-29T12:46:58.605Z",
"answer": 74
},
{
"id"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
56f769 | modular_mod_compute_v1_2051736721_5731 | Let $m$ be the number of integers $t$ such that $10 \leq t \leq 3746$ and there exist integers $a$ and $b$ with $1 \leq a \leq 17$, $1 \leq b \leq 911$, and $t = 6a + 4b$. Let $r$ be the remainder when $-37$ is divided by $m$, and let $Q$ be the remainder when $47307 \cdot r$ is divided by $64795$. Find the value of $Q... | 5,690 | graphs = [
Graph(
let={
"_n": Const(64795),
"a": Const(-37),
"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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T18:46:34.983574Z | {
"verified": true,
"answer": 5690,
"timestamp": "2026-02-08T18:46:34.987992Z"
} | 3d8334 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 5636
},
"timestamp": "2026-02-18T19:23:06.153Z",
"answer": 5690
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
baac52 | antilemma_k2_v1_458359167_2894 | Let $m = 97031$ and let $n = \sum_{d \mid 418} \phi(d)$, where $\phi$ denotes Euler's totient function. Let
$$
x = \sum_{k=1}^{418} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$
Compute $x + 2^{x \bmod 16} \bmod m$. | 87,579 | graphs = [
Graph(
let={
"_m": Const(97031),
"_n": SumOverDivisors(n=Const(value=418), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Const(418), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Sum(R... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T06:49:33.038081Z | {
"verified": true,
"answer": 87579,
"timestamp": "2026-02-08T06:49:33.039633Z"
} | a88be4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1054
},
"timestamp": "2026-02-13T05:21:23.412Z",
"answer": 87579
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lem... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
7e065a | antilemma_k2_v1_1520064083_7080 | Let $m = 2$. Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 439x + 2170 = 0$. Compute $$\sum_{k=1}^{439} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.$$ | 96,580 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-439), Var("x")), Const(2170)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Const(439), expr=Mul(EulerPhi(n=Var("k")),... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T08:45:25.697340Z | {
"verified": true,
"answer": 96580,
"timestamp": "2026-02-08T08:45:25.698778Z"
} | 349fc5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 916
},
"timestamp": "2026-02-13T21:30:27.821Z",
"answer": 96580
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1c4d3d | antilemma_cartesian_v1_1520064083_8569 | Compute the number of ordered pairs $(a, b)$ such that $a$ is an integer satisfying $1 \leq a \leq 24$ and $b$ is an integer satisfying $1 \leq b \leq 41$. | 984 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(24)), right=IntegerRange(start=Const(1), end=Const(41)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T10:15:27.826753Z | {
"verified": true,
"answer": 984,
"timestamp": "2026-02-08T10:15:27.827465Z"
} | 90f7b0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 137
},
"timestamp": "2026-02-24T11:54:38.973Z",
"answer": 984
},
{
"id"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
c2ec38 | alg_qf_psd_count_leq_v1_601307018_5511 | Let $T = \left|\{ t : t = 2a + 3b \text{ for some integers } a, b \text{ with } 1 \leq a \leq 24,\, 1 \leq b \leq 139,\, \text{and } 5 \leq t \leq 465 \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 459$ and $1 \leq b \leq T$ such that
$$
26a^2 + 20ab + 26b^2 \leq 2884136.... | 70,336 | 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(459)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exi... | ALG | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"LIN_FORM"
] | 7b2633 | alg_qf_psd_count_leq_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 1.6 | 2026-03-10T06:06:48.694264Z | {
"verified": true,
"answer": 70336,
"timestamp": "2026-03-10T06:06:50.294530Z"
} | 92c890 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 15494
},
"timestamp": "2026-04-19T02:16:51.195Z",
"answer": 70336
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
63437c | alg_qf_psd_min_v1_1218484723_3057 | Let $B$ be the number of integers $t$ such that $7 \le t \le 312$ and $t = 2a + 5b$ for some integers $a, b$ with $1 \le a \le 31$, $1 \le b \le 50$. Find the minimum value of $85068 \cdot b^2$ over all positive integers $a, b$ with $1 \le a \le 302$ and $1 \le b \le B$. | 85,068 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(302)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Var("t"), ... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_qf_psd_min_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.13 | 2026-02-25T04:49:15.950714Z | {
"verified": true,
"answer": 85068,
"timestamp": "2026-02-25T04:49:16.081054Z"
} | 1a1f4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 5250
},
"timestamp": "2026-03-29T08:05:49.950Z",
"answer": 85068
},
{
"... | 2 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
7aee7a | lin_form_endings_v1_1125832087_727 | Let $a = 16$ and $b = 12$. Let $g = \gcd(a, b)$, and let $r = \left\lfloor \frac{16}{g} \right\rfloor$. Let $s = 5748 \cdot r$, and let $M = 69735$. Compute the remainder when $s$ is divided by $M$. | 22,992 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(12),
"_inner_result": Floor(Div(Const(16), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(5748),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:13:53.498348Z | {
"verified": true,
"answer": 22992,
"timestamp": "2026-02-08T03:13:53.499257Z"
} | a66497 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 396
},
"timestamp": "2026-02-10T13:33:11.815Z",
"answer": 22992
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
16cfdb | modular_mod_compute_v1_1520064083_5686 | Let $a = 30976$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2829124$. Let $m$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Define $\text{result} = a \bmod m$. Find the value of $\text{result}$. | 700 | graphs = [
Graph(
let={
"a": Const(30976),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2829124)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T07:32:56.221057Z | {
"verified": true,
"answer": 700,
"timestamp": "2026-02-08T07:32:56.222699Z"
} | 39a574 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1392
},
"timestamp": "2026-02-13T10:52:27.805Z",
"answer": 700
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b1b643 | nt_sum_over_divisible_v1_1470522791_733 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1849$. Let $d$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 89401$ and $n$ is divisible by $d$. Let $B$ be the sum of all elements in $T$. Compute the re... | 77,029 | graphs = [
Graph(
let={
"_n": Const(73589),
"upper": Const(89401),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 4.367 | 2026-02-08T13:12:46.936525Z | {
"verified": true,
"answer": 77029,
"timestamp": "2026-02-08T13:12:51.303202Z"
} | 03dd22 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1955
},
"timestamp": "2026-02-15T10:32:06.123Z",
"answer": 77029
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
98ebb7 | antilemma_sum_equals_v1_397696148_1594 | Let $n = 102$. Consider the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 100$, $1 \leq j \leq 100$, and $i + j = n$. Compute the number of such ordered pairs. | 99 | graphs = [
Graph(
let={
"_n": Const(102),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(100)), right=IntegerRange(start=Const(1), end=C... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.054 | 2026-02-08T12:39:31.438230Z | {
"verified": true,
"answer": 99,
"timestamp": "2026-02-08T12:39:31.492147Z"
} | 33ef05 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 561
},
"timestamp": "2026-02-24T16:11:55.286Z",
"answer": 99
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
32ebb5 | comb_sum_binomial_row_v1_865884756_1116 | Let $j$ be a positive integer such that $1 \leq j \leq 4$ and $j^4 \leq 256$. Let $c$ be the number of such integers $j$. Define $n = \sum_{k=1}^{c} k$. Let $r = 2^n$. Let $p$ be the largest prime number less than or equal to $6$. Compute the remainder when $p - r$ is divided by $50977$. | 49,958 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(4)), Leq(Pow(Var("j"), Ref("_m")), Const(256))), domain='positive_int... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"C3/SUM_ARITHMETIC"
] | c747e7 | comb_sum_binomial_row_v1 | negation_mod | 3 | 0 | [
"C3",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.006 | 2026-02-08T15:47:47.582194Z | {
"verified": true,
"answer": 49958,
"timestamp": "2026-02-08T15:47:47.587864Z"
} | 60b2e6 | 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": 506
},
"timestamp": "2026-02-16T13:36:13.614Z",
"answer": 49958
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9889ff | algebra_poly_eval_v1_865884756_5641 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $4n^3 + 9n^2 + 4n - 7$. | 2,649 | graphs = [
Graph(
let={
"_n": Const(16),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T18:44:41.730242Z | {
"verified": true,
"answer": 2649,
"timestamp": "2026-02-08T18:44:41.733506Z"
} | 39d817 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 464
},
"timestamp": "2026-02-16T15:02:28.076Z",
"answer": 2644
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
91608a | algebra_poly_eval_v1_1218484723_4308 | Let $n$ be the number of ordered pairs $(a,b)$ of positive integers with $1 \le a \le b \le 35$ such that
$$2b^{2} + 2a^{2} - 4ab = 72.$$
Compute
$$\frac{24n^{3} - 70n^{2} + 31n + 21}{167}.$$ | 3,158 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(72),
"_n": Const(2),
"n": CountOverSet(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(elem... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/POLY3_MIN/QF_PSD_ORBIT"
] | 1d3282 | algebra_poly_eval_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"POLY3_MIN",
"QF_PSD_ORBIT"
] | 3 | 0.011 | 2026-02-25T05:56:17.453651Z | {
"verified": true,
"answer": 3158,
"timestamp": "2026-02-25T05:56:17.465068Z"
} | e0751a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1125
},
"timestamp": "2026-03-29T14:55:11.468Z",
"answer": 3158
},
{
"i... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
202a9f | antilemma_v1_legendre_601307018_250 | Let $d$ be the largest positive divisor of $82437188$ such that $d^2 \le 82437188$. Let $x$ be the largest integer $k$ such that $2^k$ divides $d!$. Find $x$. | 9,061 | graphs = [
Graph(
let={
"_n": Const(2),
"x": MaxKDivides(target=Factorial(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(82437188)), Leq(Mul(Var("d"), Var("d")), Const(82437188)))))), base=Ref("_n")),
... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/V1",
"V1"
] | 497ead | antilemma_v1_legendre | null | 3 | 0 | [
"B3_CLOSEST",
"V1"
] | 2 | 0.002 | 2026-03-10T00:48:43.445744Z | {
"verified": true,
"answer": 9061,
"timestamp": "2026-03-10T00:48:43.447607Z"
} | f91758 | CC BY 4.0 | null | null | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
3b41ef | modular_mod_compute_v1_1742523217_3432 | Let $n$ be the number of integers $t$ such that $30 \leq t \leq 7449$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 1069$, $1 \leq b \leq 298$, and
$$
t = 5a + 7b + 18.
$$
Let $m$ be the largest positive integer at most $n$ that divides $54811756$. Compute the remainder when $576$ is divided by $m$. | 576 | 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=1069)), Geq(left=Var(name='b'), right=Const(val... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR"
] | 8c55ae | modular_mod_compute_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 0.003 | 2026-02-08T05:52:01.239219Z | {
"verified": true,
"answer": 576,
"timestamp": "2026-02-08T05:52:01.241758Z"
} | 118ae7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 6727
},
"timestamp": "2026-02-12T16:27:30.227Z",
"answer": 60
},
{... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6258e1 | nt_sum_divisors_mod_v1_784195855_852 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 14288400$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10399$. | 8,002 | 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(14288400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(103... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T04:39:23.320778Z | {
"verified": true,
"answer": 8002,
"timestamp": "2026-02-08T04:39:23.323863Z"
} | c6d245 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1964
},
"timestamp": "2026-02-11T21:44:43.220Z",
"answer": 8002
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
0c5756 | nt_min_phi_inverse_v1_1439011603_1362 | Let $k$ be the number of integers $t$ such that $5 \leq t \leq 24$ and $t = 3a + 2b$ for some integers $a$ and $b$ with $1 \leq a \leq 2$ and $1 \leq b \leq 9$. Let $n$ be the smallest positive integer at most 60 such that $\phi(n) = k$, where $\phi$ denotes Euler's totient function. Compute $n$. | 19 | graphs = [
Graph(
let={
"upper": Const(60),
"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=2)), Geq(left=Va... | NT | null | EXTREMUM | sympy | C5 | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.12 | 2026-02-08T16:02:49.770979Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T16:02:49.890675Z"
} | 5b25fa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1235
},
"timestamp": "2026-02-16T06:52:27.629Z",
"answer": 21
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
f79a73 | antilemma_k3_v1_677425708_1937 | Let $ x $ be the sum of $ \phi(d) $ over all positive divisors $ d $ of $ 19140 $, where $ \phi $ denotes Euler's totient function. Compute the remainder when $ 44121 \cdot x $ is divided by $ 89162 $. | 22,638 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=19140), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(89162)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:39:55.153054Z | {
"verified": true,
"answer": 22638,
"timestamp": "2026-02-08T04:39:55.153428Z"
} | b6d526 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1232
},
"timestamp": "2026-02-10T03:22:03.589Z",
"answer": 22638
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
87a6ce | nt_count_coprime_v1_458359167_2671 | Let $k = 28$ and let $U = 10816$. Define $r$ to be the number of positive integers $n$ such that $1 \leq n \leq U$ and $\gcd(n, k) = 1$. Let $m = 8$ and $n = 32$. Compute the value of
$$
r^{s} + n \cdot r + c,
$$
where $s$ is the number of positive integers $j$ such that $1 \leq j \leq 2$ and $j^3 \leq m$, and $c$ is ... | 35,005 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(32),
"upper": Const(10816),
"k": Const(28),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k"))... | NT | null | COUNT | sympy | B3 | [
"B3",
"C3"
] | 296a9d | nt_count_coprime_v1 | quadratic_mod | 6 | 0 | [
"B3",
"C3"
] | 2 | 9.583 | 2026-02-08T06:42:42.256151Z | {
"verified": true,
"answer": 35005,
"timestamp": "2026-02-08T06:42:51.839565Z"
} | 6e4624 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1712
},
"timestamp": "2026-02-13T03:56:31.266Z",
"answer": 35005
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a94d2c | geo_count_lattice_rect_v1_784195855_4628 | Compute the number of lattice points in the rectangle $[0, 66] \times [0, 130]$. | 8,777 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(130),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T07:13:16.265938Z | {
"verified": true,
"answer": 8777,
"timestamp": "2026-02-08T07:13:16.267015Z"
} | 4b432f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 281
},
"timestamp": "2026-02-24T07:44:13.833Z",
"answer": 8777
},
{
"id... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
ae19f5 | modular_min_linear_v1_784195855_7500 | Let $a = 853$. Let $b$ be the number of integers $t$ such that $5 \leq t \leq 8856$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 3261$, $1 \leq b' \leq 778$, and $t = 2a' + 3b'$. Let $m = 13140$. Define $\text{result}$ to be the smallest positive integer $x$ such that $1 \leq x \leq m$ and $853x... | 31,966 | graphs = [
Graph(
let={
"a": Const(853),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3261)), Geq(left=Va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 1.053 | 2026-02-08T09:21:12.862286Z | {
"verified": true,
"answer": 31966,
"timestamp": "2026-02-08T09:21:13.915708Z"
} | 8aa181 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 6661
},
"timestamp": "2026-02-14T03:29:29.819Z",
"answer": 31966
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fee5c2 | diophantine_fbi2_count_v1_349078426_2006 | Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 2903$. Let $T$ be the set of ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 729$. Let $s$ be the minimum value of $x + y$ over all elements of $T$. Find the number of positive integers $d$ such that $5 \leq d \leq s$, $d$ divides $k... | 16,234 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(94838),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2903)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"COUNT_PRIMES",
"B3"
] | 8c28d5 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"COUNT_PRIMES"
] | 3 | 0.017 | 2026-02-08T14:03:51.109977Z | {
"verified": true,
"answer": 16234,
"timestamp": "2026-02-08T14:03:51.126973Z"
} | ffe2da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2265
},
"timestamp": "2026-02-15T23:16:23.788Z",
"answer": 16234
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemm... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ce7feb | comb_count_permutations_fixed_v1_1978505735_3989 | Let $m = 2$ and $n' = \sum_{k_1=1}^{m} k_1$. Define $n = \sum_{k_2=1}^{3} \phi(k_2) \left\lfloor \frac{n'}{k_2} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k = 0$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!r$ denotes the number of derangements of $r$ elements. | 265 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Summation(var="k1", start=Const(1), end=Ref("_m"), expr=Var("k1")),
"n": Summation(var="k2", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k2")), Floor(Div(Ref("_n"), Var("k2"))))),
"k": Const(0),
... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 06cc86 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.004 | 2026-02-08T17:58:22.015289Z | {
"verified": true,
"answer": 265,
"timestamp": "2026-02-08T17:58:22.018866Z"
} | 5a1be9 | 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": 923
},
"timestamp": "2026-02-18T10:39:07.595Z",
"answer": 265
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b5d6b3 | nt_min_coprime_above_v1_784195855_8797 | Let $p_0$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
\[pq=6,\quad \gcd(p,q)=1,\quad p<q.
\]
Let $S$ be the number of integers $j$ with $0\le j\le 90044$ such that
\[\binom{90044}{j}\equiv 1\pmod{p_0}.
\]
Let $U$ be the number of primes $n$ with $2\le n\le 43711$. Let ... | 4,097 | graphs = [
Graph(
let={
"_n": Const(43711),
"start": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(90044)), Eq(Mod(value=Binom(n=Const(90044), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPos... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8",
"COUNT_PRIMES"
] | fb4ea0 | nt_min_coprime_above_v1 | null | 8 | 0 | [
"COPRIME_PAIRS",
"COUNT_PRIMES",
"V8"
] | 3 | 0.082 | 2026-02-08T16:21:58.183061Z | {
"verified": true,
"answer": 4097,
"timestamp": "2026-02-08T16:21:58.264974Z"
} | 8764ab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 3159
},
"timestamp": "2026-02-17T01:11:23.637Z",
"answer": 4097
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
618381 | comb_sum_binomial_row_v1_1915831931_938 | Let $u = 8$ and $n_1 = u + 1$. Compute the sum $s = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $u_1 = 0$ and $n_2 = u_1 + 1$. Compute the sum $v = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n = 10 + v$. Define $r = (2 + s)^n$. Multiply $r$ by $44121$, and let $Q$ be the remainder when the product is divided by $87... | 33,614 | graphs = [
Graph(
let={
"u1": Const(0),
"n2": Sum(Ref("u1"), Const(1)),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(8),
"n1": Sum(Ref("u"), Const(1)),
... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T15:45:57.495773Z | {
"verified": true,
"answer": 33614,
"timestamp": "2026-02-08T15:45:57.497606Z"
} | 08fea5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 886
},
"timestamp": "2026-02-24T18:27:25.897Z",
"answer": 33614
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
0cb091 | comb_count_surjections_v1_1248542787_683 | Let $n = 4$ and $k = 3$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $A = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, and define $a = |\text{result}|$. Compute $$\sum_{n = A}^{a} \phi(n),$$ where $\phi(n)$ is Euler's totient function. Find the value of this su... | 396 | graphs = [
Graph(
let={
"n": Const(4),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Summation(var="n", start=Factorial(Summation(var="k", start=Const(0), end=Const(7), expr=Mul(Pow(Const(-1), Var("k")), B... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 8794cb | comb_count_surjections_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 2 | 0.002 | 2026-02-08T03:19:42.936965Z | {
"verified": true,
"answer": 396,
"timestamp": "2026-02-08T03:19:42.939327Z"
} | 3a7fee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 2900
},
"timestamp": "2026-02-09T06:59:22.398Z",
"answer": 396
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
67b705 | comb_catalan_compute_v1_784195855_7898 | Let $n = 10$. Define $\text{result}$ to be the $n$-th Catalan number. Compute the remainder when $\sum_{k=1}^{\text{result}} \tau(k)$ is divided by $79487$, where $\tau(k)$ denotes the number of positive divisors of $k$. (Note: the summation starts at $k = 1$, as $0! = 1$ and the absolute value of $\text{result}$ is $\... | 7,021 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Mod(value=Summation(var="n", start=Factorial(Const(0)), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n"))), modulus=Const(79487)),
},
goal=Ref("Q"),
)
] | COMB | NT | COMPUTE | sympy | ONE_FACTORIAL_0 | [
"ONE_FACTORIAL_0"
] | 7064c7 | comb_catalan_compute_v1 | null | 4 | 0 | [
"ONE_FACTORIAL_0"
] | 1 | 0.001 | 2026-02-08T09:36:31.846386Z | {
"verified": true,
"answer": 7021,
"timestamp": "2026-02-08T09:36:31.847609Z"
} | dcae59 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 15672
},
"timestamp": "2026-02-24T11:36:37.992Z",
"answer": 7021
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
58318b | algebra_quadratic_discriminant_v1_1218484723_5715 | Let $R$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 40$ such that
$$-68a_1b_1^{3} + 17a_1^{4} + 17b_1^{4} - 68a_1^{3}b_1 + 102a_1^{2}b_1^{2} = 4352.$$
Define
$$D = -2^{2} - \left|\left\{(a_2, b_2) : 1 \le a_2, b_2 \le 10,\ a_2 \le b_2,\ C \cdot b_2^{2} - 4a_2b_2 + 2a_2^{2} ... | 0 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(40)), Geq(Var("b1"), Const(1)), Leq(Var("b1"), Const(40)), Eq(Sum(Mul(Const... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_ORBIT",
"POLY3_MIN/QF_PSD_ORBIT"
] | 42c797 | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"POLY3_MIN",
"POLY4_COUNT",
"QF_PSD_ORBIT"
] | 3 | 0.31 | 2026-02-25T07:15:51.547399Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-25T07:15:51.857857Z"
} | 1d2fa4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 421,
"completion_tokens": 3357
},
"timestamp": "2026-03-29T22:26:01.749Z",
"answer": 0
},
{
"id":... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
0f059f | geo_count_lattice_rect_v1_1915831931_3216 | Let $a = 81$ and $b = 77$. Define $S$ as the set of all lattice points $(x, y)$ such that $0 \leq x \leq 81$ and $0 \leq y \leq 77$. Compute the number of elements in $S$. | 6,396 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(77),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T17:25:44.089610Z | {
"verified": true,
"answer": 6396,
"timestamp": "2026-02-08T17:25:44.090573Z"
} | b401a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 492
},
"timestamp": "2026-02-24T22:39:52.189Z",
"answer": 6396
},
{
... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
9a27ce | comb_binomial_compute_v1_153355830_2877 | Let $m = 105$. Define $S$ to be the set of positive integers $n$ such that $1 \leq n \leq m$ and $13$ divides the $n$-th Fibonacci number. Let $k = 6$. Compute $\binom{|S|}{k}$. | 5,005 | graphs = [
Graph(
let={
"_n": Const(105),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(13), dividend=Fibonacci(arg=Var(name='n')))))),
"k": Const(6),
"result": Binom(n=R... | ALG | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_binomial_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T07:27:29.697213Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-02-08T07:27:29.698781Z"
} | 173b37 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1749
},
"timestamp": "2026-02-13T10:26:29.795Z",
"answer": 5005
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5b66f1 | nt_count_intersection_v1_865884756_3330 | Let $a$ be the smallest divisor of 847 that is at least 2, and let $b = 10$. Compute the number of positive integers $n$ less than or equal to 100000 such that $a$ divides $n$ and $\gcd(n, 10) = 1$. | 5,714 | graphs = [
Graph(
let={
"N": Const(100000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(847))))),
"b": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.69 | 2026-02-08T17:18:25.351257Z | {
"verified": true,
"answer": 5714,
"timestamp": "2026-02-08T17:18:29.041167Z"
} | e22b12 | 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": 1400
},
"timestamp": "2026-02-17T23:33:47.466Z",
"answer": 5714
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f6741e | comb_count_permutations_fixed_v1_865884756_2807 | Let $n = 10$. Let $k$ be the smallest divisor of 245 that is at least 2. Compute the value of $\binom{n}{k} \cdot !(n-k)$, where $!m$ denotes the number of derangements of $m$ elements. | 11,088 | graphs = [
Graph(
let={
"n": Const(10),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(245))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref... | NT | COMB | COUNT | sympy | V8 | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"V8"
] | 2 | 0.013 | 2026-02-08T16:57:06.936589Z | {
"verified": true,
"answer": 11088,
"timestamp": "2026-02-08T16:57:06.949343Z"
} | f062c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 787
},
"timestamp": "2026-02-17T16:14:13.395Z",
"answer": 11088
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8566e3 | antilemma_k2_v1_1125832087_898 | Let $n = \sum_{d \mid 372} \phi(d)$, where $\phi$ denotes Euler's totient function. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{372}{k} \right\rfloor.
$$
Compute the remainder when $54643 \cdot x$ is divided by $96350$. | 34,954 | graphs = [
Graph(
let={
"_m": Const(96350),
"_n": SumOverDivisors(n=Const(value=372), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(372), Var("k"))))),
"_c": Cons... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 4 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T03:21:24.685390Z | {
"verified": true,
"answer": 34954,
"timestamp": "2026-02-08T03:21:24.686266Z"
} | 47101d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 3412
},
"timestamp": "2026-02-10T14:02:54.138Z",
"answer": 34954
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
8269a6 | geo_count_lattice_rect_v1_151522320_46 | Let $ a = 27 $ and $ b = 50 $. Define $ R $ to be the rectangle $ [0, a] \times [0, b] $ in the coordinate plane. Let $ N $ be the number of lattice points (points with integer coordinates) that lie inside or on the boundary of $ R $. Compute the remainder when $ 55789 \cdot N $ is divided by $ 58350 $. | 18,942 | graphs = [
Graph(
let={
"a": Const(27),
"b": Const(50),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(55789), Ref("result")), modulus=Const(58350)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T02:56:17.348377Z | {
"verified": true,
"answer": 18942,
"timestamp": "2026-02-08T02:56:17.351160Z"
} | 70e472 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1512
},
"timestamp": "2026-02-10T11:57:19.697Z",
"answer": 18942
},
{
"... | 1 | [] | {
"lo": -0.15,
"mid": 1.46,
"hi": 2.88
} | ||||
b9e768 | nt_lcm_compute_v1_349078426_1733 | Let $a$ be the largest positive divisor of $2274055$ that is at most $1505$. Let $b = 2801$. Define $\text{result} = \text{lcm}(a, b)$. Let $c = 15242$. Compute the remainder when $c \cdot \text{result}$ is divided by $94025$. | 85,285 | graphs = [
Graph(
let={
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(1505)), Divides(divisor=Var("d"), dividend=Const(2274055))))),
"b": Const(2801),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": Cons... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_lcm_compute_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T13:53:53.111595Z | {
"verified": true,
"answer": 85285,
"timestamp": "2026-02-08T13:53:53.113019Z"
} | a21bfd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 5209
},
"timestamp": "2026-02-15T22:01:32.433Z",
"answer": 85285
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
4ca704 | comb_count_permutations_fixed_v1_898971024_1724 | Let $T$ be the set of all integers $t$ such that $24 \leq t \leq 45$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 9a + 6b + 9$. Let $n = 9$ and let $k$ be the largest prime number that is at most the number of elements in $T$.
Compute the value of
\[
\binom{n}{k} \cdot ! (n ... | 1,134 | 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=2)), Geq(left=Var(name='b'), right=Const(value=... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T16:16:19.044927Z | {
"verified": true,
"answer": 1134,
"timestamp": "2026-02-08T16:16:19.048903Z"
} | ff730b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 905
},
"timestamp": "2026-02-16T23:45:06.474Z",
"answer": 1134
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
56b78e | antilemma_sum_equals_v1_1520064083_3213 | Let $N$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 2$, $1 \leq j \leq 23$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 46$, $1 \leq j \leq 46$, and $i + j = N$. Compute $$\sum_{n=1}^{|x|} \varphi(n),$$ where $\varphi(n)$ denotes Euler's totient function. | 628 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(23)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.008 | 2026-02-08T05:31:26.980752Z | {
"verified": true,
"answer": 628,
"timestamp": "2026-02-08T05:31:26.988985Z"
} | 9a8775 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1995
},
"timestamp": "2026-02-24T03:53:20.588Z",
"answer": 628
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
5a413e | modular_count_residue_v1_1915831931_3954 | Let $n$ be a positive integer such that $1 \leq n \leq 33856$ and $n \equiv 1 \pmod{18}$. Compute the number of such integers $n$. | 1,881 | graphs = [
Graph(
let={
"upper": Const(33856),
"m": Const(18),
"r": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_COPRIME",
"B1/MOBIUS_COPRIME"
] | 0c7197 | modular_count_residue_v1 | null | 2 | 0 | [
"B1",
"LIN_FORM",
"MOBIUS_COPRIME"
] | 3 | 3.369 | 2026-02-08T18:01:42.951702Z | {
"verified": true,
"answer": 1881,
"timestamp": "2026-02-08T18:01:46.320983Z"
} | 0767d7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 550
},
"timestamp": "2026-02-18T11:58:47.911Z",
"answer": 1881
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc8f97 | modular_mod_compute_v1_1978505735_4034 | Let $m$ be the number of nonnegative integers $j$ such that $0 \le j \le 58749$ and $\binom{58749}{j}$ is odd. Find the remainder when $-43$ is divided by $m$. | 2,005 | graphs = [
Graph(
let={
"_n": Const(58749),
"a": Const(-43),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(58749)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegativ... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_mod_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T17:59:07.031848Z | {
"verified": true,
"answer": 2005,
"timestamp": "2026-02-08T17:59:07.033410Z"
} | b5587e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1804
},
"timestamp": "2026-02-18T10:44:56.515Z",
"answer": 2005
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
d2c0f9 | nt_count_phi_equals_v1_458359167_2466 | Let $k = 1210$ and $u = 2500$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = k$, where $\phi(n)$ denotes Euler's totient function. | 1 | graphs = [
Graph(
let={
"upper": Const(2500),
"k": Const(1210),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
},
goal=Ref("result"),
)
] | NT | null | COUNT | sympy | LIOUVILLE_MINUS_ONE | [
"COUNT_PRIMES"
] | 07c874 | nt_count_phi_equals_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"LIOUVILLE_MINUS_ONE"
] | 2 | 2.828 | 2026-02-08T05:26:22.208406Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T05:26:25.036348Z"
} | 9d965b | 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": 6735
},
"timestamp": "2026-02-12T22:45:18.787Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8955bd | algebra_quadratic_discriminant_v1_397696148_1785 | Let $a = -1$, $c = -49$, and let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 49$. Compute $b^2 - 4ac$. | 0 | graphs = [
Graph(
let={
"_n": Const(49),
"a": Const(-1),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Su... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.041 | 2026-02-08T12:46:11.446138Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T12:46:11.487483Z"
} | cd3ec5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 455
},
"timestamp": "2026-02-16T04:04:27.604Z",
"answer": 0
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
a95710 | antilemma_k3_v1_151522320_688 | Let $n = 92057$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Find the value of this sum. | 92,057 | graphs = [
Graph(
let={
"_n": Const(92057),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:27:32.903160Z | {
"verified": true,
"answer": 92057,
"timestamp": "2026-02-08T03:27:32.903727Z"
} | af60b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 2234
},
"timestamp": "2026-02-10T14:32:50.438Z",
"answer": 92057
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
1f8af9 | nt_count_with_divisor_count_v1_1439011603_1909 | Let $N = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq 41209$ and the number of positive divisors of $n$ is equal to $N$. | 27 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(41209),
"div_count": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(G... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"K2"
] | 1 | 9.277 | 2026-02-08T16:21:10.950565Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T16:21:20.227423Z"
} | 10cd4f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 2425
},
"timestamp": "2026-02-17T01:43:51.635Z",
"answer": 27
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b32605 | sequence_fibonacci_compute_v1_1918700295_3018 | Let $m = 2$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 288$ and the sum of the decimal digits of $n$ is divisible by $m$. Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = N$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $F_n$ denote t... | 20,116 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(76301),
"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=S... | NT | null | COMPUTE | sympy | L3B | [
"L3B/B3"
] | f2ec8b | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3",
"L3B"
] | 2 | 0.003 | 2026-02-08T08:21:14.804101Z | {
"verified": true,
"answer": 20116,
"timestamp": "2026-02-08T08:21:14.807465Z"
} | 8fadbd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 3195
},
"timestamp": "2026-02-13T17:48:41.171Z",
"answer": 20116
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
114792 | diophantine_fbi2_min_v1_1520064083_6269 | Let $n = 2$ and $k = 125$. Define $\text{upper}$ to be $7$ more than the number of nonnegative integers $j$ such that $0 \leq j \leq 18257$ and
$$
\binom{18257}{j} \equiv 1 \pmod{2}.
$$
Let $\text{result}$ be the smallest integer $d$ satisfying $5 \leq d \leq \text{upper}$, such that $d$ divides $k$ and $\frac{k}{d} \g... | 32,137 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(125),
"upper": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(18257)), Eq(Mod(value=Binom(n=Const(18257), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='no... | NT | null | EXTREMUM | sympy | V8 | [
"V8"
] | 86348e | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.01 | 2026-02-08T07:59:01.011501Z | {
"verified": true,
"answer": 32137,
"timestamp": "2026-02-08T07:59:01.021646Z"
} | 39b10c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1648
},
"timestamp": "2026-02-13T13:56:17.370Z",
"answer": 32137
},
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
593ea7 | sequence_fibonacci_compute_v1_124444284_5254 | Let $n$ be the largest prime number less than or equal to 28. Let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \ge 3$. Compute the remainder when $33185 \cdot F_n$ is divided by 95208. | 45,041 | graphs = [
Graph(
let={
"_n": Const(33185),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(28)), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("result"... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:31:06.255644Z | {
"verified": true,
"answer": 45041,
"timestamp": "2026-02-08T06:31:06.256919Z"
} | 640ae3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1382
},
"timestamp": "2026-02-13T01:13:41.923Z",
"answer": 45041
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d241c6 | geo_count_lattice_rect_v1_1440796553_806 | Let $a = 25$ and $b = 54$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $Q$ be the remainder when $64675$ times this number is divided by $77537$. Find the value of $Q$. | 61,146 | graphs = [
Graph(
let={
"a": Const(25),
"b": Const(54),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(64675), Ref("result")), modulus=Const(77537)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T11:59:18.382817Z | {
"verified": true,
"answer": 61146,
"timestamp": "2026-02-08T11:59:18.383978Z"
} | 013382 | 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": 1278
},
"timestamp": "2026-02-24T15:07:37.321Z",
"answer": 61146
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
38ba0f | geo_visible_lattice_v1_124444284_5588 | Let $n = 90$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $44121 \cdot L$ is divided by $80320$. | 4,359 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(80320)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.678 | 2026-02-08T06:43:44.890116Z | {
"verified": true,
"answer": 4359,
"timestamp": "2026-02-08T06:43:45.568229Z"
} | 99cff6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T06:55:36.562Z",
"answer": 12281
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
aa5e04 | antilemma_sum_equals_v1_1520064083_694 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 73$ and $1 \leq i, j \leq 71$. Let $Q$ be the sum of the squares of the digit positions (counting from the right, starting at position 1) weighted by the corresponding digits of $|x|$, plus $2704$. Specifically,
$$
Q = \sum_{i=0}^{\... | 2,732 | graphs = [
Graph(
let={
"_n": Const(73),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(71)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.005 | 2026-02-08T03:32:59.468671Z | {
"verified": true,
"answer": 2732,
"timestamp": "2026-02-08T03:32:59.473300Z"
} | 2e64ca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1043
},
"timestamp": "2026-02-10T14:57:49.394Z",
"answer": 2732
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
97c469 | comb_count_derangements_v1_458359167_3878 | Let $n$ be the largest prime number such that $2 \leq n \leq 10$. Define $r = !n$, the subfactorial of $n$. Compute the remainder when $86009 \cdot r$ is divided by $75591$. | 39,267 | graphs = [
Graph(
let={
"_n": Const(75591),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(10)), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(86009),
"Q": Mo... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T11:24:09.723529Z | {
"verified": true,
"answer": 39267,
"timestamp": "2026-02-08T11:24:09.724676Z"
} | 6ffad0 | 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": 2202
},
"timestamp": "2026-02-14T13:50:33.136Z",
"answer": 39267
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
555da8 | geo_visible_lattice_v1_458359167_1757 | A lattice point $(x, y)$ is said to be visible from the origin if $\gcd(x, y) = 1$. Find the number of visible lattice points $(x, y)$ with $1 \le x, y \le 90$. | 4,959 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.3 | 2026-02-08T04:50:17.942248Z | {
"verified": true,
"answer": 4959,
"timestamp": "2026-02-08T04:50:18.242066Z"
} | 54534b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T02:03:51.189Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
ce4290 | comb_sum_binomial_row_v1_655260480_607 | Let $n = 14$. Define $P$ to be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $P$. Compute $k^n$. | 16,384 | graphs = [
Graph(
let={
"n": Const(14),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:29:01.153940Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T15:29:01.155631Z"
} | 90c1e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1497
},
"timestamp": "2026-02-16T07:09:31.362Z",
"answer": 16384
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d99936 | modular_min_modexp_v1_238844314_16 | Let $a=11$ and $b$ be the value of
$$
\sum_{k=1}^{24} \varphi(k)\left\lfloor\frac{24}{k}\right\rfloor,
$$
where $\varphi$ is Euler's totient function. Let $m$ be the number of integers $n$ with $1\le n\le 1079$ such that
$$
n \equiv \left\lfloor\frac{n}{2}\right\rfloor \pmod{3}.
$$
Let $u$ be the smallest integer $d\g... | 48,530 | graphs = [
Graph(
let={
"_n": Const(81115),
"a": Const(11),
"b": Summation(var="k", start=Const(1), end=Const(24), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(24), Var("k"))))),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Co... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"L3C",
"K2"
] | 8d8d1c | modular_min_modexp_v1 | null | 8 | 0 | [
"K2",
"L3C",
"MIN_PRIME_FACTOR"
] | 3 | 0.022 | 2026-02-08T13:05:05.335220Z | {
"verified": true,
"answer": 48530,
"timestamp": "2026-02-08T13:05:05.356861Z"
} | a66794 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 4066
},
"timestamp": "2026-02-15T09:32:19.014Z",
"answer": 48530
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
780c85 | algebra_quadratic_discriminant_v1_1978505735_7132 | Let $a = 2$, $b = -20$, and let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 256$. Compute $b^2 - 4ac$. Find the value of this expression. | 144 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Const(-20),
"c": 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("... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T20:04:12.353091Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T20:04:12.356294Z"
} | 8073ab | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 305
},
"timestamp": "2026-02-16T18:47:43.765Z",
"answer": 144
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b71c8f | geo_count_lattice_triangle_v1_548369836_34 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(169,4)$, and $(66,100)$. The area of this triangle is given by $\frac{1}{2} \left| 169 \cdot 100 - 66 \cdot 4 \right|$. Let $B$ be the number of lattice points on the boundary of the triangle, which is given by
\[
\gcd(169, 4) + \gcd(|66 - 169|, |100 - 4|) +... | 8,317 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=100)), Mul(Const(value=66), Sub(left=Const(value=0), right=Const(value=4))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=4))), GCD(a=Abs(arg=Sub(left=Const(value=66), right=C... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.002 | 2026-02-08T02:43:13.974956Z | {
"verified": true,
"answer": 8317,
"timestamp": "2026-02-08T02:43:13.976979Z"
} | d0f52e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1478
},
"timestamp": "2026-02-08T19:43:45.420Z",
"answer": 8317
},
{
"i... | 1 | [] | {
"lo": -4.81,
"mid": -2.89,
"hi": -0.92
} | ||||
4e2d09 | comb_binomial_compute_v1_1918700295_981 | Let $J$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 9360$ and $\binom{9360}{j}$ is odd. Let $m$ be the number of elements in $J$. Let $N$ be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $n \equiv 0 \pmod{16}$. Let $n_{\text{sum}}$ be the sum of all elements in $N$. Comput... | 82,936 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(9360)), Eq(Mod(value=Binom(n=Const(93... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8/SUM_DIVISIBLE"
] | 47a987 | comb_binomial_compute_v1 | null | 7 | 0 | [
"SUM_DIVISIBLE",
"V8"
] | 2 | 0.003 | 2026-02-08T05:25:41.861663Z | {
"verified": true,
"answer": 82936,
"timestamp": "2026-02-08T05:25:41.864484Z"
} | 748551 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 3138
},
"timestamp": "2026-02-24T03:51:09.411Z",
"answer": 82936
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
{
... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
8772de | comb_count_surjections_v1_784195855_5607 | Let $n$ be the number of positive integers $t$ such that there exist integers $a$ and $b$ with $1 \le a \le 2$, $1 \le b \le 3$, $31 \le t \le 52$, and $t = 9a + 6b + 16$.
Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10$. Let $k$ be the number of ordered pairs $(i... | 73,336 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(10))))),
"n"... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"LIN_FORM"
] | 9d0a12 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.012 | 2026-02-08T07:59:34.742917Z | {
"verified": true,
"answer": 73336,
"timestamp": "2026-02-08T07:59:34.755382Z"
} | 841143 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 327,
"completion_tokens": 4794
},
"timestamp": "2026-02-24T08:44:00.991Z",
"answer": 73336
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
4793d0 | comb_factorial_compute_v1_717093673_2118 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 448$ and $\binom{448}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(448),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(448)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"resul... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 4 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T16:33:45.964484Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T16:33:45.967546Z"
} | bb1d5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1192
},
"timestamp": "2026-02-24T21:45:26.632Z",
"answer": 40320
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.09,
"mid": -2.96,
"hi": -0.71
} | ||
03b095 | nt_sum_divisors_mod_v1_124444284_7360 | Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 6350400$. For each such pair, compute $x + y$, and let $n$ be the smallest value of $x + y$ over all such pairs.
Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $11... | 7,847 | 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(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1149... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T09:05:01.640625Z | {
"verified": true,
"answer": 7847,
"timestamp": "2026-02-08T09:05:01.641952Z"
} | c6c98c | 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": 1543
},
"timestamp": "2026-02-14T00:30:19.780Z",
"answer": 7847
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
666b50 | comb_bell_compute_v1_1520064083_2815 | Let $p$ be a positive integer. Suppose there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of such integers $p$. Let $n_0$ be the smallest divisor of $347633$ that is at least $m$. Now let $p$ be a positive integer such that there exists a positive intege... | 15 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/COPRIME_PAIRS"
] | 522d3d | comb_bell_compute_v1 | bell_mod | 7 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.04 | 2026-02-08T05:14:21.139148Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T05:14:21.179276Z"
} | 1ce8fa | 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": 2272
},
"timestamp": "2026-02-12T05:43:11.736Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4c73e6 | modular_modexp_compute_v1_168721529_205 | Let $e$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 66$. Let $a = 7$ and $m = 84681$. Define $\text{result} = a^e \bmod m$. Let $c = 59049$. Compute the remainder when $c - \text{result}$ is divided by $60587$. Find the value of this remainder. | 56,050 | graphs = [
Graph(
let={
"_n": Const(66),
"a": Const(7),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T12:54:12.956536Z | {
"verified": true,
"answer": 56050,
"timestamp": "2026-02-08T12:54:12.959428Z"
} | 6b9250 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 4612
},
"timestamp": "2026-02-11T07:29:47.107Z",
"answer": 56050
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
6585e7 | sequence_lucas_compute_v1_1742523217_5273 | Let $S$ be the set of all integers $t$ such that $9 \leq t \leq 141$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 24$, satisfying $t = 5a + 4b$. Let $c$ be the number of elements in $S$. Let $T$ be the set of all pairs of positive integers $(x, y)$ such that $xy = c$. Let $m$ be the... | 39,603 | graphs = [
Graph(
let={
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1/B3",
"B3/B1/B3"
] | 2bb1fe | sequence_lucas_compute_v1 | null | 7 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T10:53:59.112371Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T10:53:59.116145Z"
} | 403e94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 5020
},
"timestamp": "2026-02-14T09:13:32.166Z",
"answer": 39603
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
37a41d | nt_euler_phi_compute_v1_168721529_732 | Let $p_1 = 11$, $q = 13$, and $r = 73$. Define $n_1 = p_1 \cdot q \cdot r$. Let $f = \mu(n_1)^2$, where $\mu$ denotes the M\"obius function. Define $p = 53 \cdot f$, and let $u = \Omega(p)$, where $\Omega(n)$ denotes the number of prime factors of $n$ counted with multiplicity. Finally, let $n = 70756 \cdot u$. Compute... | 28,728 | graphs = [
Graph(
let={
"p1": Const(11),
"q": Const(13),
"r": Const(73),
"n1": Mul(Ref("p1"), Ref("q"), Ref("r")),
"f": Pow(MoebiusMu(n=Ref(name='n1')), Const(2)),
"p": Mul(Const(53), Ref("f")),
"u": BigOmega(n=Ref(name='p')... | NT | null | COMPUTE | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE",
"BIG_OMEGA_ONE"
] | 0d6627 | nt_euler_phi_compute_v1 | null | 4 | 2 | [
"BIG_OMEGA_ONE",
"MOBIUS_SQUAREFREE"
] | 2 | 0.005 | 2026-02-08T13:15:12.905360Z | {
"verified": true,
"answer": 28728,
"timestamp": "2026-02-08T13:15:12.910569Z"
} | 281296 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1255
},
"timestamp": "2026-02-09T08:27:44.645Z",
"answer": 28728
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"stat... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
924dba | modular_sum_quadratic_residues_v1_1520064083_7857 | Let $m = 2$. Let $n$ be the number of integers $t$ such that $10 \leq t \leq 626$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 20$, $1 \leq b \leq 162$, and $t = 7a + 3b$. Let $p$ be the largest prime number satisfying $m \leq p \leq n$. Compute $\frac{p(p-1)}{4}$. | 90,150 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=20)), Geq(left=Var(... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T09:20:49.619598Z | {
"verified": true,
"answer": 90150,
"timestamp": "2026-02-08T09:20:49.621734Z"
} | 0b48e5 | 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": 6072
},
"timestamp": "2026-02-14T03:15:18.001Z",
"answer": 90150
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
558917 | antilemma_sum_equals_v1_151522320_766 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 80$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 12$, and $t = 4a + 5b$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 58$, $j \leq 59$, and $i + j = n$. Compute
$$
\sum_{k=1}^{x} \phi(... | 1,028 | 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=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T03:30:01.748089Z | {
"verified": true,
"answer": 1028,
"timestamp": "2026-02-08T03:30:01.755972Z"
} | f70d4f | 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": 3655
},
"timestamp": "2026-02-10T15:01:24.452Z",
"answer": 1028
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
215f26 | geo_count_lattice_triangle_v1_153355830_4 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 913168100344500$, $\gcd(p, q) = 1$, and $p < q$. Let $a = 100 |A| - 25 \cdot 19$.
Let $d_{\min}$ be the smallest divisor of 367517 that is at least 2. Let $b_1 = \gcd(100, 19)$, $b_2 = \gcd(|100 - 25|, |128 - ... | 6,162 | graphs = [
Graph(
let={
"_c": Const(21),
"_m": Const(25),
"_n": Const(128),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), CountOverSet(set=SolutionsSet(var=Var(name='p'), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(le... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS"
] | af27e9 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 3 | 0.015 | 2026-02-08T02:50:55.606247Z | {
"verified": true,
"answer": 6162,
"timestamp": "2026-02-08T02:50:55.621442Z"
} | 87a883 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:22:08.600Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",... | {
"lo": 1.97,
"mid": 3.57,
"hi": 5.16
} | ||
2d536a | antilemma_cartesian_v1_2080023795_56 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 29$ and $1 \leq b \leq 48$. Compute $29929 - x$. | 28,537 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=Const(48)))),
"Q": Sub(Const(29929), Ref("x")),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T11:30:51.921006Z | {
"verified": true,
"answer": 28537,
"timestamp": "2026-02-08T11:30:51.921783Z"
} | f01f02 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2858
},
"timestamp": "2026-02-08T20:39:00.365Z",
"answer": 29750
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -5.98,
"mid": -3.99,
"hi": -2
} | ||
aec783 | sequence_count_fib_divisible_v1_1526740231_412 | Let $d_1$ be the smallest integer greater than or equal to 2 that divides 1356277. Let $u$ be the smallest integer greater than or equal to 2 that divides 870473. Compute the number of positive integers $n \leq u$ such that $d_1$ divides the $n$th Fibonacci number. | 132 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(870473))))),
"d": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), D... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.05 | 2026-02-08T11:30:50.229278Z | {
"verified": true,
"answer": 132,
"timestamp": "2026-02-08T11:30:50.279154Z"
} | 8e5c6a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 5754
},
"timestamp": "2026-02-14T15:15:01.935Z",
"answer": 132
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bc39a9 | nt_min_with_divisor_count_v1_784195855_40 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 11$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $d$ be the number of elements in $S$. Determine the value of the smallest positive integer $m$ such that $1 \leq m \leq 27225$ and the number of positive divisors of $m$ is equal to $d... | 4 | graphs = [
Graph(
let={
"upper": Const(27225),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"L3C"
] | 73f8b0 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"L3C"
] | 2 | 9.923 | 2026-02-08T02:55:12.537073Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T02:55:22.460537Z"
} | 5f1dd8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 781
},
"timestamp": "2026-02-10T11:54:06.401Z",
"answer": 4
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.88,
"mid": -1.29,
"hi": 0.91
} | ||
6f54aa | comb_sum_binomial_row_v1_784195855_5062 | Let $m = 20$. Define $c$ to be the number of positive integers $n$ with $1 \leq n \leq 6630$ such that $m$ divides the $n$-th Fibonacci number. Let $d$ be the smallest integer $d \geq 2$ that divides $c$. Compute $2^d$. Find the value of $2^d$. | 8,192 | graphs = [
Graph(
let={
"_m": Const(20),
"_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("n... | NT | null | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MIN_PRIME_FACTOR"
] | 0c6279 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T07:38:57.568149Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T07:38:57.571116Z"
} | 662208 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1029
},
"timestamp": "2026-02-13T11:20:47.860Z",
"answer": 8192
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b211ab | modular_inverse_v1_655260480_691 | Let $a$ be the largest positive divisor of $92961$ that is at most $297$. Let $m = 563$. Find the smallest positive integer $x$ such that $1 \leq x \leq 562$ and $ax \equiv 1 \pmod{m}$. Compute the remainder when $44121$ times this $x$ is divided by $80219$. | 72,317 | graphs = [
Graph(
let={
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(297)), Divides(divisor=Var("d"), dividend=Const(92961))))),
"m": Const(563),
"upper": Const(562),
"result": MinOverSet(set=Solutio... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_inverse_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.04 | 2026-02-08T15:32:00.476353Z | {
"verified": true,
"answer": 72317,
"timestamp": "2026-02-08T15:32:00.516288Z"
} | a2435e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1882
},
"timestamp": "2026-02-16T08:32:03.902Z",
"answer": 72317
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f66706 | sequence_fibonacci_compute_v1_153355830_2026 | Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 40$ and there exist integers $a, b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 10a + 4b$. Let $s$ be the number of elements in $T$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = s$. Define $n$ to be the m... | 7,435 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(92231),
"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(s... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T06:52:26.725256Z | {
"verified": true,
"answer": 7435,
"timestamp": "2026-02-08T06:52:26.727443Z"
} | 1d268f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1704
},
"timestamp": "2026-02-13T05:19:49.675Z",
"answer": 7435
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
37cb40 | antilemma_sum_equals_v1_397696148_1207 | Let $S$ be the set of all ordered pairs of positive integers $(i, j)$ such that $i + j = 92$, $1 \leq i \leq 90$, and $1 \leq j \leq 91$. Let $x$ be the number of elements in $S$. Compute the remainder when $67000 \cdot x$ is divided by $69047$. | 22,911 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(92)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(90)), right=IntegerRange(start=Const(1), end=Const(91))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.003 | 2026-02-08T12:25:02.005690Z | {
"verified": true,
"answer": 22911,
"timestamp": "2026-02-08T12:25:02.008933Z"
} | 3b55e8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 879
},
"timestamp": "2026-02-24T15:41:36.607Z",
"answer": 22911
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
25220b | comb_binomial_compute_v1_898971024_2968 | Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $T$. Let $k$ be the largest prime number $n_2$ such that $n_2 \geq m$ and $n_2 \leq 10$. Compute $\binom{12}{k}$, then find the remainde... | 63,337 | graphs = [
Graph(
let={
"_m": Const(95563),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(10)), IsPrime(Var("n1"))))),
"n": Const(12),
"k": MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 5bbe0a | comb_binomial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.009 | 2026-02-08T17:05:47.453914Z | {
"verified": true,
"answer": 63337,
"timestamp": "2026-02-08T17:05:47.463129Z"
} | b82abe | 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": 1307
},
"timestamp": "2026-02-17T18:44:10.329Z",
"answer": 63337
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8edfe0 | modular_modexp_compute_v1_2051736721_2586 | Let $ a = 31 $ and $ m = 15120 $. Define $ e = \sum_{k=1}^{103} \phi(k) \left\lfloor \frac{103}{k} \right\rfloor $, where $ \phi $ denotes Euler's totient function. Let $ r $ be the remainder when $ a^e $ is divided by $ m $. Let $ c = 18373 $ and let $ Q $ be the remainder when $ c \cdot r $ is divided by $ 73109 $. F... | 30,981 | graphs = [
Graph(
let={
"_n": Const(73109),
"a": Const(31),
"e": Summation(var="k", start=Const(1), end=Const(103), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(103), Var("k"))))),
"m": Const(15120),
"result": ModExp(base=Ref("a"), exp=Ref("e"), ... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | modular_modexp_compute_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T16:47:56.419556Z | {
"verified": true,
"answer": 30981,
"timestamp": "2026-02-08T16:47:56.421730Z"
} | 03b296 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2419
},
"timestamp": "2026-02-17T12:01:10.853Z",
"answer": 30981
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eb1561 | comb_factorial_compute_v1_1439011603_907 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 15$ and the sum of the decimal digits of $n_1$ is even. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(15)), Eq(Mod(value=DigitSum(Var("n1")), modulus=Ref("_n")), Const(0))))),
"result": Factorial(Ref("n")),
},
... | ALG | COMB | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | comb_factorial_compute_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T15:48:16.139130Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T15:48:16.140750Z"
} | c552a4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 344
},
"timestamp": "2026-02-24T18:43:37.737Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} |
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