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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0deb56 | nt_count_gcd_equals_v1_1520064083_3690 | Let $\phi(n)$ denote Euler's totient function. For each positive integer $n$ from $1$ to $403$, compute
$$
\sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor,
$$
and let $k$ be the number of integers $n$ in this range such that $\gcd\left(n, \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor\right... | 18,556 | graphs = [
Graph(
let={
"_n": Const(403),
"upper": Const(35721),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var... | NT | null | COUNT | sympy | K2 | [
"K2/C4"
] | 87860b | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"C4",
"K2"
] | 2 | 2.928 | 2026-02-08T05:49:10.208084Z | {
"verified": true,
"answer": 18556,
"timestamp": "2026-02-08T05:49:13.135946Z"
} | 227e27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1535
},
"timestamp": "2026-02-12T14:36:06.912Z",
"answer": 18556
},
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
39d41d | comb_factorial_compute_v1_784195855_1865 | Let $u$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 9$. Let $n_2 = u + 1$. Define $t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $a = 2$, $b = 4$, and $n_1 = a + b$. Define $f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 8 + t + f$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(9),
"u": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(nam... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_factorial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.004 | 2026-02-08T05:22:30.463537Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T05:22:30.467179Z"
} | 9af53c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 734
},
"timestamp": "2026-02-24T03:14:08.055Z",
"answer": 40320
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
2434f6 | modular_count_residue_v1_1918700295_8 | Let $m$ be the minimum value of $x + y$ over all positive integers $x$ and $y$ such that $xy = 49$. Let $r = 11$ and let $N$ be the number of positive integers $n$ with $1 \leq n \leq 66049$ such that $n \equiv r \pmod{m}$. Compute the remainder when the Bell number $B_{|N| \bmod{11}}$ is divided by $90589$. | 25,386 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": Const(66049),
"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(49)))), ... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 5 | 0 | [
"B3"
] | 1 | 4.872 | 2026-02-08T02:56:07.643228Z | {
"verified": true,
"answer": 25386,
"timestamp": "2026-02-08T02:56:12.515616Z"
} | 3d18c7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 978
},
"timestamp": "2026-02-08T20:02:37.168Z",
"answer": 25386
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
d79717 | comb_count_partitions_v1_2051736721_5964 | Let $a_1 = 2$ and $b_1 = 2$. Define $n_2 = a_1 + b_1$. Let
$$
h = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $a = 5$ and $b = 3$, and define $n_1 = a + b$. Let
$$
c = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$
Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2... | 63,261 | graphs = [
Graph(
let={
"a1": Const(2),
"b1": Const(2),
"n2": Sum(Ref("a1"), Ref("b1")),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Const(5),
"b": Con... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_count_partitions_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.003 | 2026-02-08T18:52:42.771505Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T18:52:42.774327Z"
} | 7a3e5d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1089
},
"timestamp": "2026-02-18T20:17:14.918Z",
"answer": 63261
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
5255aa | sequence_lucas_compute_v1_784195855_2513 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 111$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 3$, and $t = 6a + 21b$. Compute the $n$th Lucas number. | 64,079 | 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=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:49:20.814723Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T05:49:20.816184Z"
} | 0e9e8c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 2724
},
"timestamp": "2026-02-12T14:47:05.472Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
838938 | modular_mod_compute_v1_677425708_209 | Let $a = -222$ and $m = 35721$. Define $r$ to be the remainder when $a$ is divided by $m$, so $r = a \bmod m$. Let $S$ be the set of all integers $x$ such that $x^2 - 3883x + 289332 = 0$. Let $Q = \left( \sum_{x \in S} x \right) \cdot r \bmod 68455$. Compute $Q$. | 42,702 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-222),
"m": Const(35721),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Mod(value=Mul(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-3883), ... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | e2aa68 | modular_mod_compute_v1 | affine_mod | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T03:08:28.225633Z | {
"verified": true,
"answer": 42702,
"timestamp": "2026-02-08T03:08:28.227916Z"
} | a49012 | 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": 1705
},
"timestamp": "2026-02-08T20:23:58.558Z",
"answer": 42702
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -0.53,
"mid": 1.61,
"hi": 3.47
} | ||
553239 | comb_count_surjections_v1_1419126231_1646 | Let $k = 4$ and $R = k! \cdot S(7, k)$, where $S(7, k)$ is the Stirling number of the second kind. Let $A$ be the set of non-negative integers $a$ with $0 \le a \le 29790$ such that
$$
f(a) = a^5 + a^4 + a^3 + 3a^2 + 4a \bmod 29791
$$
satisfies $f(f(a)) = a$ and $f(a) \ne a$. Let $m = |A|$, and define
$$
s = \sum_{i=\s... | 70,289 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": Const(70125),
"Q": Sum(Summation(var="i", start=Summation(var="k1", start=Const... | COMB | null | COUNT | sympy | STARS_BARS | [
"POLY_ORBIT_HENSEL/BINOMIAL_ALTERNATING"
] | 5ed5b4 | comb_count_surjections_v1 | digits_weighted_mod | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_HENSEL",
"STARS_BARS"
] | 3 | 6.684 | 2026-02-25T11:11:04.839129Z | {
"verified": true,
"answer": 70289,
"timestamp": "2026-02-25T11:11:11.522898Z"
} | 6d1530 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 368,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T13:24:24.116Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
2e1f50 | nt_count_coprime_v1_1520064083_1292 | Compute the number of positive integers $n$ such that $1 \leq n \leq 71824$ and $\gcd(n, 3) = \phi(1)$, where $\phi$ denotes Euler's totient function. | 47,883 | graphs = [
Graph(
let={
"upper": Const(71824),
"k": Const(3),
"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")), EulerPhi(n=Const(1)))))),
},
goal=Ref("r... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_coprime_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 6.416 | 2026-02-08T03:54:41.865242Z | {
"verified": true,
"answer": 47883,
"timestamp": "2026-02-08T03:54:48.280750Z"
} | fcd4e5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 533
},
"timestamp": "2026-02-18T06:53:35.904Z",
"answer": 47883
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
6f0c55 | modular_mod_compute_v1_153355830_2271 | Find the remainder when $25281$ is divided by $76636$. | 25,281 | graphs = [
Graph(
let={
"a": Const(25281),
"m": Const(76636),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_mod_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.008 | 2026-02-08T07:01:29.383113Z | {
"verified": true,
"answer": 25281,
"timestamp": "2026-02-08T07:01:29.391549Z"
} | bc5009 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 62,
"completion_tokens": 353
},
"timestamp": "2026-02-13T07:22:23.624Z",
"answer": 25281
},
{
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
0340d2 | comb_sum_binomial_row_v1_784195855_4550 | Let $n$ be the smallest integer greater than or equal to 2 that divides 4199. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(4199))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T07:09:53.482174Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T07:09:53.482860Z"
} | 5b370f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 593
},
"timestamp": "2026-02-13T08:39:37.999Z",
"answer": 8192
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
2a1fdc | algebra_poly_eval_v1_1742523217_4349 | Let $m = 3$ and let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 1399$. Let $k = 9$. Compute
$$
\left( \sum_{\substack{j=1 \\ n \mid j}}^{1998} 1 \right) \cdot k^m + 6k^2 - 4k - 4.
$$ | 7,007 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1399)), IsPrime(Var("n"))))),
"k": Const(9),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("k"), cond... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/C2"
] | 14681d | algebra_poly_eval_v1 | null | 5 | 0 | [
"C2",
"COUNT_PRIMES"
] | 2 | 0.005 | 2026-02-08T07:12:58.188964Z | {
"verified": true,
"answer": 7007,
"timestamp": "2026-02-08T07:12:58.194030Z"
} | c62d22 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1008
},
"timestamp": "2026-02-13T08:35:40.032Z",
"answer": 7007
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c3fb61 | algebra_poly_eval_v1_124444284_9362 | Let $k$ be the number of nonnegative integers $j$ with $0 \leq j \leq 66561$ such that $\binom{66561}{j}$ is odd and $j \geq \sum_{i=0}^{1} (-1)^i \binom{\binom{9}{9}}{i}$. Compute the remainder when $44121 \cdot (3k^3 + 5k^2 - 2k - 3)$ is divided by $57307$. | 18,179 | graphs = [
Graph(
let={
"_n": Const(3),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(1), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Binom(n=Const(9), k=Const(9)), k=Var("k"))))), Leq(Var("j"), Const(66561)),... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N",
"V8"
] | 8ffec6 | algebra_poly_eval_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N",
"V8"
] | 3 | 0.005 | 2026-02-08T12:25:50.768495Z | {
"verified": true,
"answer": 18179,
"timestamp": "2026-02-08T12:25:50.773768Z"
} | cbbc49 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1687
},
"timestamp": "2026-02-24T15:38:28.188Z",
"answer": 18179
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
2d5883 | comb_catalan_compute_v1_677425708_1257 | Let $n_1 = 0$. Define $v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 11v$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n2": Const(0),
"t": Summation(var="k", start=Summation(var="k", start=Const(0), end=Const(3), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(3), k=Var("k")))), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_catalan_compute_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-02-08T04:03:02.250215Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T04:03:02.253039Z"
} | 83ed76 | 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": 1161
},
"timestamp": "2026-02-09T17:36:18.659Z",
"answer": 58786
},
{
"... | 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": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
29c8ea | nt_min_coprime_above_v1_124444284_9648 | Let $a = 51984$ and $b = 52489$. Let $m = 495$. Consider the set of all integers $n$ such that $a < n \leq b$ and $\gcd(n, m) = 1$. Let $r$ be the smallest element of this set. Define
$$
Q = \sum_{i=k}^{d-1} \left( \text{digit}_i(|r|) \cdot (i+1)^2 \right) + 24336,
$$
where $k = \sum_{j=0}^{3} (-1)^j \binom{3}{j}$, $d ... | 24,598 | graphs = [
Graph(
let={
"start": Const(51984),
"upper": Const(52489),
"modulus": Const(495),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(... | COMB | NT | EXTREMUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.061 | 2026-02-08T12:36:48.686049Z | {
"verified": true,
"answer": 24598,
"timestamp": "2026-02-08T12:36:48.747239Z"
} | 08372a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1101
},
"timestamp": "2026-02-15T02:42:13.287Z",
"answer": 24598
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e2be3e | comb_catalan_compute_v1_1918700295_2762 | Let $N$ be the number of ordered pairs $(u,v)$ of integers such that $1\le u\le 64$ and $1\le v\le 72$. Let $n$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying
$$
1\le a\le 5,\quad 1\le b\le 2,\quad 5\le t\le 16,\quad t=2a+3b.
$$
Let $C_n$ be the $n$-th Catalan number.
Let $M$ be th... | 36,988 | graphs = [
Graph(
let={
"_m": Const(51480),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(64)), right=IntegerRange(start=Const(1), end=Const(72)))),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), ... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1",
"LIN_FORM"
] | 824a4c | comb_catalan_compute_v1 | negation_mod | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.004 | 2026-02-08T08:11:55.394606Z | {
"verified": true,
"answer": 36988,
"timestamp": "2026-02-08T08:11:55.398740Z"
} | b5d879 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 324,
"completion_tokens": 1414
},
"timestamp": "2026-02-24T09:01:34.229Z",
"answer": 36988
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
f2c5d2 | algebra_poly_eval_v1_1520064083_2459 | Let $a$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 6$. Compute $2a^2 + 2a + 8$. | 188 | graphs = [
Graph(
let={
"_n": Const(8),
"a": 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(6)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T04:45:54.668324Z | {
"verified": true,
"answer": 188,
"timestamp": "2026-02-08T04:45:54.669541Z"
} | 4d340b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 395
},
"timestamp": "2026-02-11T21:57:15.293Z",
"answer": 188
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_F... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
568f9c | nt_num_divisors_compute_v1_784195855_5322 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4000000$. Define $n$ to be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $d(n)$ denote the number of positive divisors of $n$. Find the remainder when $16941 \cdot d(n)$ is divided by 64570. | 19,164 | graphs = [
Graph(
let={
"_n": Const(16941),
"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(4000000)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T07:49:38.670203Z | {
"verified": true,
"answer": 19164,
"timestamp": "2026-02-08T07:49:38.675210Z"
} | 274d1f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1717
},
"timestamp": "2026-02-13T12:32:43.570Z",
"answer": 19164
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
314940 | comb_factorial_compute_v1_1874849503_976 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 66056$ and $\binom{66056}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(66056)), Eq(Mod(value=Binom(n=Const(66056), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T13:29:41.095882Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T13:29:41.097401Z"
} | 88288d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 911
},
"timestamp": "2026-02-09T23:16:21.990Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
fdcdbe | alg_poly4_count_v1_601307018_2643 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 359$ and $1 \le b \le \left|\{ (a_1, b_1) : a_1, b_1 \in \mathbb{Z}^+,\ 1 \le a_1, b_1 \le 20,\ 41a_1^2 + 20b_1^2 - 12a_1b_1 \le 14521 \}\right|$ such that $81a^4 = 132211504881$. | 359 | graphs = [
Graph(
let={
"_n": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(359)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_count_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 2.886 | 2026-03-10T03:18:23.627297Z | {
"verified": true,
"answer": 359,
"timestamp": "2026-03-10T03:18:26.512997Z"
} | fe1387 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 17451
},
"timestamp": "2026-03-29T06:00:08.947Z",
"answer": 359
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
262b3b | sequence_count_fib_divisible_v1_1080341949_210 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 197136$. Define $\text{sum}(x, y) = x + y$. Let $\text{upper}$ be the minimum value of $\text{sum}(x, y)$ over all $(x, y) \in S$. Let $d = 18$. Determine the value of $Q$, the number of positive integers $n$ such that $1 \leq n \leq ... | 74 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(197136)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(1... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.041 | 2026-02-08T13:18:11.609206Z | {
"verified": true,
"answer": 74,
"timestamp": "2026-02-08T13:18:11.650463Z"
} | b1b9f9 | 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": 2209
},
"timestamp": "2026-02-15T12:16:49.553Z",
"answer": 74
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a9e69d | antilemma_coprime_grid_v1_124444284_806 | Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 54$, $1 \leq j \leq 133$, and $\gcd(i, j) = 1$. | 4,422 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(54)), right=IntegerRange(start=Const(1), end=Const(133))))),
},
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0 | 2026-02-08T03:31:51.373447Z | {
"verified": true,
"answer": 4422,
"timestamp": "2026-02-08T03:31:51.373828Z"
} | 658f3e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 5268
},
"timestamp": "2026-02-09T06:17:20.724Z",
"answer": 4422
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
98bdab | nt_num_divisors_compute_v1_1125832087_66 | Let $m = 576$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $n$ be the largest prime number satisfying $2 \leq n \leq s$. Let $\tau(n)$ denote the number of positive divisors of $n$. Compute $42436 - \tau(n)$. | 42,434 | graphs = [
Graph(
let={
"_m": Const(576),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T02:51:10.478992Z | {
"verified": true,
"answer": 42434,
"timestamp": "2026-02-08T02:51:10.480956Z"
} | 7bd383 | 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": 699
},
"timestamp": "2026-02-10T11:41:30.759Z",
"answer": 42434
},
{
"i... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"l... | {
"lo": -9.16,
"mid": -6.07,
"hi": -3.82
} | ||
9430ed | sequence_lucas_compute_v1_677425708_1923 | Let $c=2$ and $m=65507$.
Let $M$ be the smallest possible value of $x+y$ over all ordered pairs $(x,y)$ of positive integers satisfying $xy=1125721$.
Consider all nonnegative integers $j$ with $0\le j\le 2122$ such that the binomial coefficient $\binom{M}{j}$ is odd. Let $N$ be the number of such integers $j$, and de... | 17,368 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(65507),
"_n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2122)), Eq(Mod(value=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/V8/COMB1"
] | 55bcb2 | sequence_lucas_compute_v1 | quadratic_mod | 8 | 0 | [
"B3",
"COMB1",
"V8"
] | 3 | 0.005 | 2026-02-08T04:39:12.424228Z | {
"verified": true,
"answer": 17368,
"timestamp": "2026-02-08T04:39:12.428893Z"
} | 32211b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 19574
},
"timestamp": "2026-02-24T01:28:27.695Z",
"answer": 17368
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": 2.14,
"mid": 3.65,
"hi": 5.01
} | ||
6916b8 | algebra_poly_eval_v1_1520064083_675 | Let $z$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 144$. Compute the value of $10z^2 - z - 2$. | 5,734 | graphs = [
Graph(
let={
"_n": Const(2),
"z": 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(144)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:31:42.099178Z | {
"verified": true,
"answer": 5734,
"timestamp": "2026-02-08T03:31:42.100512Z"
} | 3901f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 455
},
"timestamp": "2026-02-10T14:56:50.954Z",
"answer": 5734
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
25cbdf | nt_sum_totient_over_divisors_v1_124444284_1099 | Let $n = 41399$. Define $\sigma = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 62500$. Compute the remainder when $c - \sigma$ is divided by 86088. | 45,189 | graphs = [
Graph(
let={
"_n": Const(62500),
"n": Const(41399),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_sum_totient_over_divisors_v1 | negation_mod | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:41:05.707126Z | {
"verified": true,
"answer": 45189,
"timestamp": "2026-02-08T03:41:05.709436Z"
} | fc4bc1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 762
},
"timestamp": "2026-02-09T09:43:18.996Z",
"answer": 45189
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6992fc | comb_binomial_compute_v1_717093673_657 | Let $n_2 = 0$. Define $w = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}$. Let $a = 4$ and $b = 2$, and define $n_1 = a + b$. Define $h = \sum_{k_2=0}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}$. Let $n = 12w$. Let $k$ be $h$ plus the number of integers $t$ such that $15 \leq t \leq 36$ and there exist integers $a$ and $b$ wit... | 924 | graphs = [
Graph(
let={
"n2": Const(0),
"w": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"a": Const(4),
"b": Const(2),
"n1": Sum(Ref("a"), Ref("b")),
"h": Sum... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T15:35:36.098658Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T15:35:36.102856Z"
} | 341a46 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 316,
"completion_tokens": 863
},
"timestamp": "2026-02-24T18:14:52.904Z",
"answer": 924
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
783a10 | geo_count_lattice_triangle_v1_1918700295_4320 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(169,66)$, and $(43,128)$, multiplied by $2$. Let $B$ be the number of lattice points on the boundary of this triangle, computed as the sum of the greatest common divisors of the absolute differences of coordinates along each edge:
\begin{align*}
B = &\gcd(... | 14,940 | graphs = [
Graph(
let={
"_m": Const(169),
"_n": Const(66),
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=128)), Mul(Const(value=43), Sub(left=Const(value=0), right=Const(value=66))))),
"boundary": Sum(GCD(a=Abs(arg=Ref(name='_m')), b=Abs(arg=Ref(nam... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"C4"
] | 90e51f | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.007 | 2026-02-08T09:17:41.766115Z | {
"verified": true,
"answer": 14940,
"timestamp": "2026-02-08T09:17:41.773115Z"
} | bbe70f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1294
},
"timestamp": "2026-02-14T02:25:43.786Z",
"answer": 14940
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
76eae5 | algebra_vieta_sum_v1_124444284_5196 | Let $S$ be the set of all real numbers $x$ such that
$$
2x^3 - 6x^2 - 122x + 126 = 0.
$$
Compute the sum of all elements of $S$. | 3 | graphs = [
Graph(
let={
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(2), Pow(Var("x"), Const(3))), Mul(Const(-6), Pow(Var("x"), Const(2))), Mul(Const(-122), Var("x")), Const(126)), Const(0)))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_vieta_sum_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.022 | 2026-02-08T06:26:49.524682Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T06:26:49.546666Z"
} | a9407a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 945
},
"timestamp": "2026-02-15T17:32:57.805Z",
"answer": 4
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
79950f | algebra_poly_eval_v1_1520064083_8791 | Let $z = 5$ and $n = 19$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 216$ and $\gcd(p, q) = 1$. Define
$$
\text{result} = \frac{20z^4 + nz^3 - 13z^k + 28z - 32}{21}.
$$
Compute the remainder when $44121 \cdot \text{result}$ is divided by $71249$. | 16,890 | graphs = [
Graph(
let={
"_n": Const(19),
"z": Const(5),
"result": Div(Sum(Mul(Const(20), Pow(Ref("z"), Const(4))), Mul(Ref("_n"), Pow(Ref("z"), Const(3))), Mul(Const(-13), Pow(Ref("z"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T10:23:33.299515Z | {
"verified": true,
"answer": 16890,
"timestamp": "2026-02-08T10:23:33.302364Z"
} | 060616 | 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": 1735
},
"timestamp": "2026-02-14T07:14:46.595Z",
"answer": 16890
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
484416 | modular_mod_compute_v1_717093673_4049 | Let $A$ be the set of all integers $t$ such that $18 \leq t \leq 216$ and there exist integers $a$, $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 47$, and $t = 14a + 4b$. Let $N = |A|$. Let $M$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = N$, and define $m$ to be the maximum value of $xy... | 1,951 | graphs = [
Graph(
let={
"a": Const(12996),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"), con... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | modular_mod_compute_v1 | null | 5 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T18:01:53.622983Z | {
"verified": true,
"answer": 1951,
"timestamp": "2026-02-08T18:01:53.629747Z"
} | 025816 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1841
},
"timestamp": "2026-02-18T12:19:07.381Z",
"answer": 1951
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5be24b | comb_count_partitions_v1_1353956133_331 | Let $n$ be the smallest integer greater than or equal to 2 that divides 82861. Compute the number of integer partitions of $n$. Then, find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by the sum of this partition number and 2. Compute $k$. | 2,280 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(82861))))),
"result": Partition(arg=Ref(name='n')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_partitions_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:25:02.293304Z | {
"verified": true,
"answer": 2280,
"timestamp": "2026-02-08T11:25:02.294455Z"
} | dee8dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 3075
},
"timestamp": "2026-02-14T13:41:15.415Z",
"answer": 2280
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_C... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9a54e1 | sequence_fibonacci_compute_v1_1978505735_1021 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 320$, $8$ divides $k$, and $\gcd(k, 21) = 1$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \geq 3$. | 28,657 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(320)), Divides(divisor=Ref("_n"), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Const(21)), Const(1))))),
"result": Fibonacc... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T15:44:42.186490Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T15:44:42.188019Z"
} | 3c3fb4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 937
},
"timestamp": "2026-02-16T13:03:17.043Z",
"answer": 28657
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
13a7c7 | lin_form_endings_v1_1080341949_41 | Let $a = 42$, $b = 12$, $A = 5$, and $B = 27$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $s = a'A + b'B - a'b'$. Compute the remainder when $16611 \cdot s$ is divided by $54670$. | 43,085 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(12),
"A_val": Const(5),
"B_val": Const(27),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:09:40.643886Z | {
"verified": true,
"answer": 43085,
"timestamp": "2026-02-08T13:09:40.645330Z"
} | fc7b7f | 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": 1191
},
"timestamp": "2026-02-15T10:41:08.433Z",
"answer": 43085
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9e9f3f | sequence_fibonacci_compute_v1_1978505735_1681 | Let $t$ be an integer. Let $n$ be the number of values of $t$ in the range $7 \leq t \leq 33$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 3$, and $t = 3a + 4b$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute ... | 3,673 | 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=7)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:21:17.159856Z | {
"verified": true,
"answer": 3673,
"timestamp": "2026-02-08T16:21:17.162774Z"
} | b08fca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1742
},
"timestamp": "2026-02-17T01:00:34.314Z",
"answer": 3673
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bef3ff | nt_count_divisors_in_range_v1_1918700295_505 | Let $n = 498960$. Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 64$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq 2318$. | 121 | graphs = [
Graph(
let={
"n": Const(498960),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(64)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.32 | 2026-02-08T03:17:30.822416Z | {
"verified": true,
"answer": 121,
"timestamp": "2026-02-08T03:17:31.142700Z"
} | c39d12 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 6526
},
"timestamp": "2026-02-10T13:10:58.954Z",
"answer": 121
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
745233 | modular_modexp_compute_v1_124444284_999 | Let $j_0$ be the smallest nonnegative integer such that $j_0 \geq \sum_{d \mid \gcd(75,60)} \mu(d)$, where $\mu$ denotes the Möbius function. Consider the set of all nonnegative integers $j$ such that $j_0 \leq j \leq 45$ and $\binom{45}{j}$ is odd. Let $e$ be the sum of all elements in this set. Compute the remainder ... | 7,263 | graphs = [
Graph(
let={
"_n": Const(91855),
"a": Const(17),
"e": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=GCD(a=Const(value=75), b=Const(value=60)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("j"), Const(45)), Eq(Mod... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"V8"
] | 0d4771 | modular_modexp_compute_v1 | null | 6 | 0 | [
"MOBIUS_COPRIME",
"V8"
] | 2 | 0.002 | 2026-02-08T03:38:38.083043Z | {
"verified": true,
"answer": 7263,
"timestamp": "2026-02-08T03:38:38.084722Z"
} | eb3748 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 3873
},
"timestamp": "2026-02-10T01:06:55.162Z",
"answer": 64039
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
884226 | comb_count_derangements_v1_48377204_254 | Let $n$ be the number of positive integers $p$ such that $p < q$, $pq = 5250$, and $\gcd(p, q) = 1$ for some integer $q$.
Let $D$ be the number of derangements of $n$ elements. Find $24649 - D$. | 9,816 | 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=5250)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T15:19:15.128225Z | {
"verified": true,
"answer": 9816,
"timestamp": "2026-02-08T15:19:15.131812Z"
} | 6db8ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1705
},
"timestamp": "2026-02-16T03:05:47.211Z",
"answer": 9816
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
93792b | diophantine_fbi2_count_v1_677425708_3419 | Define
$$
k = \sum_{k=1}^{15} \varphi(k) \left\lfloor \frac{15}{k} \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. Let $S$ be the set of all integers $d$ such that $4 \leq d \leq 114$, $d$ divides $k$, and $6 \leq \frac{k}{d} \leq 116$. Let $r$ be the number of elements in $S$. Compute the remainder... | 23,730 | graphs = [
Graph(
let={
"k": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(15), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(114)), Divides(divisor=Var... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES",
"K2"
] | 54ac42 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"COUNT_PRIMES",
"K2"
] | 2 | 0.027 | 2026-02-08T05:41:54.697705Z | {
"verified": true,
"answer": 23730,
"timestamp": "2026-02-08T05:41:54.724248Z"
} | f51555 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1229
},
"timestamp": "2026-02-12T13:55:57.984Z",
"answer": 23730
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
63a748 | nt_count_digit_sum_v1_153355830_2262 | Let $\alpha$ be the number of ordered pairs $(p,q)$ of positive integers such that $pq = 36$, $\gcd(p,q) = 1$, and $p < q$.
Let $U$ be the set of all positive integers $x$ such that
$$
x^\alpha - 9999x + 69944 = 0.
$$
Let $u$ be the sum of all elements of $U$.
Determine the number of positive integers $n$ such that $... | 633 | graphs = [
Graph(
let={
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), 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=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/VIETA_SUM"
] | 815fe1 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"VIETA_SUM"
] | 2 | 1.913 | 2026-02-08T07:01:26.442515Z | {
"verified": true,
"answer": 633,
"timestamp": "2026-02-08T07:01:28.355566Z"
} | 3d4d21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2297
},
"timestamp": "2026-02-13T07:24:05.516Z",
"answer": 633
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
09c2d5 | nt_count_divisible_v1_1526740231_108 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 26$. Let $P$ be the maximum value of $xy$ as $(x, y)$ ranges over $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $d$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. L... | 1,191 | graphs = [
Graph(
let={
"upper": Const(30976),
"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")), MaxOverSet(set=MapOverSet(set=Solutio... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisible_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 1.085 | 2026-02-08T11:21:06.417035Z | {
"verified": true,
"answer": 1191,
"timestamp": "2026-02-08T11:21:07.501913Z"
} | ef52a4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 391
},
"timestamp": "2026-02-15T21:47:32.283Z",
"answer": 182
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
287a76 | algebra_quadratic_discriminant_v1_784195855_3368 | Let $n=2$, and let $a=2$, $b=16$, and $c=-40$. Consider the quadratic expression
\[
ax^2+bx+c.
\]
Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
\[
pq=72, \quad \gcd(p,q)=1, \quad \text{and} \quad p<q.
\]
Let $D$ be the value of $b^{N}-4ac$. Define
\[
\text{result... | 3,299 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Const(16),
"c": Const(-40),
"D": Sub(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=... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1",
"COPRIME_PAIRS"
] | 4a9d53 | algebra_quadratic_discriminant_v1 | quadratic_mod | 7 | 0 | [
"B1",
"B3",
"COPRIME_PAIRS"
] | 3 | 0.014 | 2026-02-08T06:22:36.617237Z | {
"verified": true,
"answer": 3299,
"timestamp": "2026-02-08T06:22:36.630835Z"
} | a5f7c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 337,
"completion_tokens": 1554
},
"timestamp": "2026-02-12T23:26:12.144Z",
"answer": 3299
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma":... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
2c7038 | sequence_fibonacci_compute_v1_579913215_68 | Let $n = \sum_{k=1}^{6} k$. Compute the $n$-th Fibonacci number, denoted $F_n$, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Find the remainder when $44121 \cdot F_n$ is divided by $93350$. | 48,916 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(93350)),
},
goal=Ref("Q"),
... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T12:50:39.404011Z | {
"verified": true,
"answer": 48916,
"timestamp": "2026-02-08T12:50:39.405373Z"
} | db3ef4 | 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": 2097
},
"timestamp": "2026-02-15T06:13:13.178Z",
"answer": 48916
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d84c0c | nt_sum_divisors_mod_v1_1742523217_5730 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $11897$. | 4,368 | 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(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11897... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T11:12:37.453195Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T11:12:37.457143Z"
} | 4daecf | 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": 1555
},
"timestamp": "2026-02-14T10:43:34.672Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
365c78 | comb_factorial_compute_v1_971394319_1241 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 7x - 60 = 0$. Let $Q = 49209 \cdot n!$. Compute the remainder when $Q$ is divided by $84605$. | 36,105 | graphs = [
Graph(
let={
"_n": Const(84605),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-7), Var("x")), Const(-60)), Const(0)))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(49209), Ref("result... | ALG | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | comb_factorial_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T13:32:29.255268Z | {
"verified": true,
"answer": 36105,
"timestamp": "2026-02-08T13:32:29.256680Z"
} | 2c4f9d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T18:41:12.493Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
88d838 | diophantine_product_count_v1_2051736721_3905 | Let $k = 420$ and $\text{upper} = 329$. Define $\text{result}$ to be the number of positive integers $x$ such that $1 \le x \le \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \le \text{upper}$. Let $Q = \text{result} + \phi(|\text{result}| + 1) + \tau(|\text{result}| + 1)$, where $\phi$ denotes Euler's totient functi... | 46 | graphs = [
Graph(
let={
"k": Const(420),
"upper": Const(329),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.058 | 2026-02-08T17:37:08.186482Z | {
"verified": true,
"answer": 46,
"timestamp": "2026-02-08T17:37:08.244231Z"
} | e0fcbe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1339
},
"timestamp": "2026-02-18T05:00:15.578Z",
"answer": 46
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e2f2dd | nt_gcd_compute_v1_1080341949_375 | Let $a = 292065$ and $b = 642543$. Let $g = \gcd(a, b)$. Let $s$ be the sum of $d_i \cdot (i+1)^2$ over all digits $d_i$ of $|g|$, where the digits are indexed from right to left starting at position $0$. Let $t$ be the sum of $\varphi(d)$ over all positive divisors $d$ of $5041$. Compute $s + t$. | 5,337 | graphs = [
Graph(
let={
"_n": Const(5041),
"a": Const(292065),
"b": Const(642543),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(D... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 57059b | nt_gcd_compute_v1 | digits_weighted_mod | 4 | 0 | [
"K3"
] | 1 | 0.004 | 2026-02-08T13:27:17.697743Z | {
"verified": true,
"answer": 5337,
"timestamp": "2026-02-08T13:27:17.701804Z"
} | 0ddbfb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1053
},
"timestamp": "2026-02-15T16:09:13.099Z",
"answer": 5337
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3f31d9 | nt_count_coprime_and_v1_1978505735_2646 | Let $n$ be a positive integer such that $1 \leq n \leq 78810$, $\gcd(n, 4) = 1$, and $\gcd(n, 9) = 1$. Let $A$ be the number of such integers $n$. Let $B$ be the sum of all real solutions $x$ to the equation $x^2 - 729x + 62900 = 0$. Compute the remainder when $A^2 + 43A + B$ is divided by $78526$. | 57,387 | graphs = [
Graph(
let={
"upper": Const(78810),
"k1": Const(4),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("n... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 833c91 | nt_count_coprime_and_v1 | quadratic_mod | 5 | 0 | [
"VIETA_SUM"
] | 1 | 8.465 | 2026-02-08T17:02:23.266950Z | {
"verified": true,
"answer": 57387,
"timestamp": "2026-02-08T17:02:31.731848Z"
} | 6bb3c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1693
},
"timestamp": "2026-02-17T18:36:40.530Z",
"answer": 57387
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d68c13 | antilemma_sum_equals_v1_151522320_1815 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 102$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 8$, and $t = 10a + 4b$. Determine the value of the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 40$ and $1 \leq j \leq 40$ such that $i + j = n$. | 40 | 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=7)), 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 | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.047 | 2026-02-08T04:23:38.899797Z | {
"verified": true,
"answer": 40,
"timestamp": "2026-02-08T04:23:38.946505Z"
} | 25ca29 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T00:39:20.748Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
193f50 | comb_factorial_compute_v1_601307018_9876 | Let $S = \min\left\{ -84a_1^2b_1 + 54a_1b_1^2 + 72a_1^3 - 7b_1^3 : a_1, b_1 \in \mathbb{Z}^+,\, 1 \le a_1 \le 5,\, 1 \le b_1 \le 5 \right\}$. Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le S$ and $1 \le b \le 35$ such that $25b^2 + 9a^2 + 30ab = 12769$. Let $R = n!$. Find the rem... | 31,784 | graphs = [
Graph(
let={
"_m": Const(74014),
"_n": Const(9),
"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(elements=[Var("a1"), Var("b1"... | COMB | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN/QF_PSD_COUNT"
] | f192ae | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY3_MIN",
"QF_PSD_COUNT"
] | 2 | 0.004 | 2026-03-10T10:16:16.462088Z | {
"verified": true,
"answer": 31784,
"timestamp": "2026-03-10T10:16:16.466266Z"
} | be7064 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 3760
},
"timestamp": "2026-04-19T12:20:30.274Z",
"answer": 31784
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "V7",
"st... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
576493 | algebra_quadratic_discriminant_v1_971394319_341 | Let $a = 3$, $b = -4$, and $n = 2$. Let $s$ be the sum of all real solutions $x$ to the equation $x^2 - 4x - 320 = 0$. Define $\text{result} = b^n - a \cdot s \cdot 12$, and let $Q$ be the remainder when $43883 \cdot \text{result}$ is divided by $73032$. Compute $Q$. | 6,440 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(3),
"b": Const(-4),
"c": Const(12),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-4), Var("x")), Const(-... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T13:00:30.947412Z | {
"verified": true,
"answer": 6440,
"timestamp": "2026-02-08T13:00:30.948855Z"
} | d2a7fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 965
},
"timestamp": "2026-02-15T08:48:57.138Z",
"answer": 6440
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
888ef7 | comb_bell_compute_v1_677425708_651 | Let $n = 9$. Define $a = B_n$, where $B_n$ is the Bell number, the number of partitions of an $n$-element set.
Let $b = \varphi(1)$ and $c = \varphi(2)$, where $\varphi$ is Euler's totient function.
Let $p = |a| + b$ and $q = |a| + c$.
Define $Q = a + \varphi(p) + \tau(q)$, where $\tau(m)$ denotes the number of posi... | 31,079 | graphs = [
Graph(
let={
"n": Const(9),
"result": Bell(Ref("n")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(1)))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(2))))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | ONE_PHI_2 | [
"ONE_PHI_2",
"ONE_PHI_1"
] | a76f7e | comb_bell_compute_v1 | null | 5 | 0 | [
"ONE_PHI_1",
"ONE_PHI_2"
] | 2 | 0.003 | 2026-02-08T03:38:22.832412Z | {
"verified": true,
"answer": 31079,
"timestamp": "2026-02-08T03:38:22.834975Z"
} | 9a03d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 1195
},
"timestamp": "2026-02-08T20:52:34.455Z",
"answer": 31079
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
cf917a | nt_count_coprime_v1_238844314_535 | Let $k$ be the largest prime number between $2$ and $11$, inclusive. Let $U = 75076$. Compute the number of positive integers $n \leq U$ such that $\gcd(n, k) = 1$. | 68,251 | graphs = [
Graph(
let={
"upper": Const(75076),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 6.116 | 2026-02-08T13:23:32.128318Z | {
"verified": true,
"answer": 68251,
"timestamp": "2026-02-08T13:23:38.244765Z"
} | b80290 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 474
},
"timestamp": "2026-02-15T15:11:07.143Z",
"answer": 68251
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a27f2e | nt_count_divisible_v1_48377204_2671 | Let $n$ be a positive integer such that $1 \leq n \leq 32041$. Define $d = \sum_{k=1}^{6} k$. Compute the number of such integers $n$ for which $n$ is divisible by $d$. Find the value of this count. | 1,525 | graphs = [
Graph(
let={
"upper": Const(32041),
"divisor": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modu... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.024 | 2026-02-08T16:54:48.958905Z | {
"verified": true,
"answer": 1525,
"timestamp": "2026-02-08T16:54:49.982726Z"
} | e75021 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 550
},
"timestamp": "2026-02-17T14:34:26.648Z",
"answer": 1525
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8bddda | lin_form_endings_v1_784195855_5584 | Let $a = 16$ and $b = 20$. Let $g = \gcd(a,b)$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 34$ and $B = 53$. Compute the value of $$a'A + b'B - a'b',$$ multiply it by $6685$, and find the remainder when the result is divided by $95692$. | 58,993 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(20),
"A_val": Const(34),
"B_val": Const(53),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T07:59:09.362641Z | {
"verified": true,
"answer": 58993,
"timestamp": "2026-02-08T07:59:09.363163Z"
} | 23a88e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 759
},
"timestamp": "2026-02-13T13:44:19.823Z",
"answer": 58993
},
{... | 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": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7cfd79 | nt_sum_divisors_mod_v1_458359167_1661 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10613$. | 8,731 | 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(1061... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T04:48:03.736332Z | {
"verified": true,
"answer": 8731,
"timestamp": "2026-02-08T04:48:03.741083Z"
} | 24726a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1560
},
"timestamp": "2026-02-11T21:58:10.283Z",
"answer": 8731
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
7598f9 | nt_count_divisors_in_range_v1_124444284_1463 | Let $n = 20160$. Define $b$ to be the number of positive integers $n \leq 69120$ for which the $n$th Fibonacci number is divisible by $14$. Compute the number of positive divisors $d$ of $n$ such that $39 \leq d \leq b$. | 55 | graphs = [
Graph(
let={
"n": Const(20160),
"a": Const(39),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(69120)), Divides(divisor=Const(14), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Coun... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.11 | 2026-02-08T03:54:21.891693Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T03:54:22.002048Z"
} | 2cc664 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 3845
},
"timestamp": "2026-02-10T14:48:09.553Z",
"answer": 55
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
84f178 | antilemma_k3_v1_124444284_8249 | Let $n = 88674$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $c = 89291$. Compute the remainder when $c \cdot x$ is divided by $72546$. | 47,148 | graphs = [
Graph(
let={
"_n": Const(88674),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(89291),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(72546)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T09:37:09.751061Z | {
"verified": true,
"answer": 47148,
"timestamp": "2026-02-08T09:37:09.751603Z"
} | c81863 | 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": 1290
},
"timestamp": "2026-02-14T05:13:03.503Z",
"answer": 47148
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
65c7ff | comb_catalan_compute_v1_1742523217_5476 | Let $m = 22$. Let $A$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $k$ be the number of elements in $A$. Let $B$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 10$, $1 \le j \le 11$, and $i + j = k$. Let $n$ be the number of e... | 16,796 | graphs = [
Graph(
let={
"_m": Const(22),
"_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")), R... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS"
] | 4d9cac | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T11:01:24.256286Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T11:01:24.267064Z"
} | 264a79 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 798
},
"timestamp": "2026-02-24T12:44:39.398Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
c7c131 | comb_count_surjections_v1_2051736721_352 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Let $k = 2$ and define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Compute the sum of the number of positive divisors of ... | 41 | 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(8))))),
"k": ... | COMB | NT | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T15:22:24.177946Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T15:22:24.181668Z"
} | 14be8d | 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": 1436
},
"timestamp": "2026-02-24T20:39:30.620Z",
"answer": 41
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.26
} | ||
033df3 | nt_lcm_compute_v1_1456120455_77 | Let $a$ be the number of integers $t$ such that $5 \leq t \leq 2982$ and there exist positive integers $x$ and $y$ with $1 \leq x \leq 408$, $1 \leq y \leq 722$, and $t = 2x + 3y$. Let $b = 1584$. Compute the value of $\mathrm{lcm}(a, b)$. | 98,208 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=408)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"LIN_FORM"
] | 7b2633 | nt_lcm_compute_v1 | null | 5 | 0 | [
"LIN_FORM",
"VIETA_SUM"
] | 2 | 0.01 | 2026-02-08T02:53:03.526891Z | {
"verified": true,
"answer": 98208,
"timestamp": "2026-02-08T02:53:03.537062Z"
} | 9631b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 7140
},
"timestamp": "2026-02-23T17:47:59.544Z",
"answer": 98208
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}... | {
"lo": 2.18,
"mid": 4.01,
"hi": 5.72
} | ||
f951e8 | nt_count_divisible_v1_784195855_9582 | Compute the number of positive integers $n \leq 31543$ such that $$n \equiv \sum_{k=0}^{1} (-1)^k \binom{1}{k} \pmod{29},$$ where the modulus is determined by the value of $\sum_{k=0}^{3} (-1)^k \binom{3}{k}$. | 1,087 | graphs = [
Graph(
let={
"upper": Const(31543),
"divisor": Const(29),
"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=Summatio... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 1.104 | 2026-02-08T16:53:59.164458Z | {
"verified": true,
"answer": 1087,
"timestamp": "2026-02-08T16:54:00.268265Z"
} | 7528d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 2172
},
"timestamp": "2026-02-24T22:00:51.197Z",
"answer": 1087
},
{... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
e643b7 | comb_count_surjections_v1_677425708_1286 | Let $ T $ be the set of all integers $ t $ with $ 5 \leq t \leq 15 $ for which there exist positive integers $ a $ and $ b $, each at most 3, such that $ t = 2a + 3b $. Let $ n $ be the number of elements in $ T $. Now consider the set of all ordered pairs $ (i, j) $ with $ 1 \leq i \leq 8 $ and $ 1 \leq j \leq 9 $ suc... | 5,796 | 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=3)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T04:03:41.071078Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T04:03:41.083257Z"
} | 255d39 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 1517
},
"timestamp": "2026-02-09T17:57:50.697Z",
"answer": 5796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": ... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
51bdf2 | alg_linear_system_2x2_v1_1218484723_3582 | Let $\det = 8 \cdot 9 - (-11) \cdot (-7)$. Let $R = 409504 \cdot \left|\{ (a, b) : a \geq 1,\ a \leq \left|\{ v : v \geq 68,\ v \leq 1700,\ \text{there exist integers } a, b \text{ with } 1 \leq a \leq 5,\ 1 \leq b \leq 5 \text{ such that } 13b^{2} + 41a^{2} + 14ab = v \}\right|,\ b \geq 1,\ b \leq 25,\ -8ab + b^{2} + ... | 47,542 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(9),
"num_x": Sub(Mul(Const(409504), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(G... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/QF_PSD_COUNT"
] | a6a878 | alg_linear_system_2x2_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.007 | 2026-02-25T05:12:14.797879Z | {
"verified": true,
"answer": 47542,
"timestamp": "2026-02-25T05:12:14.804780Z"
} | 5bcbc0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 362,
"completion_tokens": 7994
},
"timestamp": "2026-03-29T11:05:52.883Z",
"answer": 47542
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
0cf05c | nt_max_prime_below_v1_717093673_2936 | Let $ S $ be the set of all positive integers $ p $ for which there exists a positive integer $ q $ such that $ p < q $, $ pq = 12 $, and $ \gcd(p, q) = 1 $. Let $ c = |S| $. Determine the largest prime number $ n $ such that $ c \leq n \leq 10223 $. | 10,223 | graphs = [
Graph(
let={
"upper": Const(10223),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.239 | 2026-02-08T17:17:47.403995Z | {
"verified": true,
"answer": 10223,
"timestamp": "2026-02-08T17:17:47.642604Z"
} | eeeb6f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 540
},
"timestamp": "2026-02-16T09:24:49.844Z",
"answer": 10217
},
{
"id": 11,... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ef4882 | nt_count_divisible_and_v1_124444284_522 | Compute the number of integers $n$ such that $1 \leq n \leq 110190$, $10$ divides $n$, and
$$
n \equiv \sum_{k=0}^{5} (-1)^k \binom{5}{k} \pmod{15}.
$$ | 3,673 | graphs = [
Graph(
let={
"upper": Const(110190),
"d1": Const(10),
"d2": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Binom(n=Const(17), k=Const(17))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Re... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 961fba | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 2 | 4.064 | 2026-02-08T03:20:41.220697Z | {
"verified": true,
"answer": 3673,
"timestamp": "2026-02-08T03:20:45.284612Z"
} | 4bfb0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 619
},
"timestamp": "2026-02-09T18:48:12.214Z",
"answer": 3673
},
{
"id... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
ecb36b | nt_count_coprime_v1_153355830_463 | Let $\text{upper} = 85849$. Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 67$. Let $S$ be the set of all positive integers $n \leq 85849$ such that $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 81,331 | graphs = [
Graph(
let={
"upper": Const(85849),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(67)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_coprime_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 7.008 | 2026-02-08T03:07:09.049849Z | {
"verified": true,
"answer": 81331,
"timestamp": "2026-02-08T03:07:16.057946Z"
} | 1aa279 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 864
},
"timestamp": "2026-02-10T12:54:11.945Z",
"answer": 81331
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
58e174 | comb_count_permutations_fixed_v1_1978505735_1127 | Let $S$ be the set of all integers $t$ such that $10 \leq t \leq 24$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 2$, and $t = 4a + 6b$. Let $n = |S|$. Let $k = \sum_{k_1=0}^{7} (-1)^{k_1} \binom{7}{k_1}$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of de... | 73,313 | graphs = [
Graph(
let={
"_n": Const(98464),
"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 | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T15:51:11.300439Z | {
"verified": true,
"answer": 73313,
"timestamp": "2026-02-08T15:51:11.303936Z"
} | 1e6d89 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 1576
},
"timestamp": "2026-02-24T18:49:35.134Z",
"answer": 71313
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"s... | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
ac9808 | geo_count_lattice_triangle_v1_1218484723_337 | Let $R = |133 \cdot 144 + 44 \cdot (-256)|$, $S = \gcd(133, 256) + \gcd(|44 - 133|, |144 - 256|) + \gcd(44, 144)$, and $T = \frac{R + 2 - S}{2}$. Compute $|T|$. | 3,942 | graphs = [
Graph(
let={
"_m": Const(60),
"_n": Const(102),
"area_2x": Abs(arg=Sum(Mul(Const(value=133), Const(value=144)), Mul(Const(value=44), Sub(left=Const(value=0), right=Const(value=256))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=133)), b=Abs(arg=Cons... | GEOM | NT | COUNT | sympy | B3 | [
"B3/POLY4_MIN"
] | 7bbe22 | geo_count_lattice_triangle_v1 | null | 2 | 0 | [
"B3",
"POLY4_MIN"
] | 2 | 0.014 | 2026-02-25T02:03:07.949924Z | {
"verified": true,
"answer": 3942,
"timestamp": "2026-02-25T02:03:07.964066Z"
} | 5da9a8 | 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": 1117
},
"timestamp": "2026-03-10T09:36:33.812Z",
"answer": 3942
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY4_MIN",
"status": "ok_later"
}
] | {
"lo": -4.31,
"mid": -1.92,
"hi": 0.62
} | ||
080d7a | modular_count_residue_v1_865884756_3734 | Let $\text{upper} = 30625$ and $d_{\min}$ be the smallest divisor of $3246473$ that is at least $2$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n \equiv 12 \pmod{d_{\min}}$. Compute the remainder when $44121 \cdot \text{result}$ is divided by $61300$. | 17,121 | graphs = [
Graph(
let={
"_n": Const(61300),
"upper": Const(30625),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3246473))))),
"r": Const(12),
"result": CountOverSet(s... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.007 | 2026-02-08T17:33:31.236756Z | {
"verified": true,
"answer": 17121,
"timestamp": "2026-02-08T17:33:32.243334Z"
} | b9f321 | 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": 2255
},
"timestamp": "2026-02-18T04:02:59.328Z",
"answer": 17121
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
98b72d | algebra_poly_eval_v1_1125832087_1042 | Let $m = 4$ and $n = 7$. Let $b = 20$. Define $s$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $d$ be the smallest integer greater than or equal to 2 that divides 11025. Define
$$
\text{result} = \frac{28 \cdot b^s + 65 \cdot b^d - 4b^2 - 52b + n}{87}.
$$
Let $... | 30,807 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(7),
"b": Const(20),
"result": Div(Sum(Mul(Const(28), Pow(Ref("b"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.008 | 2026-02-08T03:28:14.042836Z | {
"verified": true,
"answer": 30807,
"timestamp": "2026-02-08T03:28:14.050646Z"
} | 674c76 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 2777
},
"timestamp": "2026-02-10T14:30:41.756Z",
"answer": 30807
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
268fd3 | nt_count_coprime_v1_655260480_1481 | Let $S$ be the set of all pairs $(a, b)$ of positive integers with $a \leq 28$, $b \leq 7$, and $21a + 15b$ in the interval $[36, 693]$. Let $P$ be the number of distinct values of $21a + 15b$ as $(a, b)$ ranges over $S$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy... | 24,686 | graphs = [
Graph(
let={
"upper": Const(57600),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("t"),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | nt_count_coprime_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 8.396 | 2026-02-08T16:09:31.363326Z | {
"verified": true,
"answer": 24686,
"timestamp": "2026-02-08T16:09:39.759534Z"
} | 791cef | 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": 4151
},
"timestamp": "2026-02-16T21:39:35.831Z",
"answer": 24686
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6eaafb | comb_factorial_compute_v1_1218484723_1350 | Let $n$ be the number of positive integers $k \le 29$ such that $\gcd(k, 30) = 1$. Let $M = n!$. Find the remainder when $17689 - M$ is divided by $88862$. | 66,231 | graphs = [
Graph(
let={
"_n": Const(17689),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(29)), Eq(GCD(a=Var("n1"), b=Const(30)), Const(1))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Sub(R... | COMB | NT | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | comb_factorial_compute_v1 | null | 3 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-25T03:04:04.353887Z | {
"verified": true,
"answer": 66231,
"timestamp": "2026-02-25T03:04:04.355302Z"
} | f6b418 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 715
},
"timestamp": "2026-03-10T06:37:44.669Z",
"answer": 66231
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
f5c1ba | comb_factorial_compute_v1_677425708_3399 | Let $n = 8$. Compute the remainder when
$$
\left|\left\{ n \in \mathbb{Z} \mid 1 \leq n \leq 29999 \text{ and } n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3} \right\}\right| - n!
$$
is divided by $70857$. | 40,536 | graphs = [
Graph(
let={
"_n": Const(70857),
"n": Const(8),
"result": Factorial(Ref("n")),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(29999)), Congruent(a=Var(name='n'), b=Floor(arg=... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | fba717 | comb_factorial_compute_v1 | negation_mod | 4 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T05:41:21.409690Z | {
"verified": true,
"answer": 40536,
"timestamp": "2026-02-08T05:41:21.411042Z"
} | c41ebe | 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": 1394
},
"timestamp": "2026-02-12T12:28:18.104Z",
"answer": 40536
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
9a4e30 | nt_min_coprime_above_v1_717093673_3878 | Let $m$ be the largest prime number such that $2 \le m \le 81$. Let $S$ be the set of all integers $n_1$ such that $86436 < n_1 \le 86525$ and $\gcd(n_1, m) = 1$. Compute the minimum element of $S$. | 86,437 | graphs = [
Graph(
let={
"_n": Const(2),
"start": Const(86436),
"upper": Const(86525),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(81)), IsPrime(Var("n"))))),
"result": MinOverSet(... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.011 | 2026-02-08T17:55:09.081025Z | {
"verified": true,
"answer": 86437,
"timestamp": "2026-02-08T17:55:09.091560Z"
} | b461de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 835
},
"timestamp": "2026-02-18T10:16:18.486Z",
"answer": 86437
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
226857_n | alg_qf_psd_min_v1_1218484723_3257 | A robotic arm on an assembly line has four adjustable joints controlled by integer-valued parameters $a$, $b$, $c$, and $d$, each ranging from 1 to 15. The energy cost of a configuration is given by
$$
4140b^2 - 552cd + 4232a^2 - 1840ac + 2576c^2 + S \cdot d^2 - 920ad + 1656bc + 5888ab + 2024bd,
$$
where $S$ is the m... | 20,424 | ALG | null | COMPUTE | sympy | STARS_BARS | [
"B3"
] | 0cd20d | alg_qf_psd_min_v1 | null | 4 | null | [
"B3",
"STARS_BARS"
] | 2 | 1.884 | 2026-02-25T04:57:24.897946Z | null | e6d94a | 226857 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 13574
},
"timestamp": "2026-03-30T19:55:04.944Z",
"answer": 20424
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
bfa361 | sequence_count_fib_divisible_v1_548369836_19 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 123904$. Let $d = 8$. Compute the number of positive integers $n$ such that $1 \leq n \leq s$ and $d$ divides the $n$-th Fibonacci number. | 117 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(123904)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(8... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.03 | 2026-02-08T02:42:48.963303Z | {
"verified": true,
"answer": 117,
"timestamp": "2026-02-08T02:42:48.993015Z"
} | f70bf0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 2826
},
"timestamp": "2026-02-08T19:43:05.052Z",
"answer": 117
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
40ccdc | modular_min_modexp_v1_798873815_242 | Let $a = 5$ and $b = 173$. Let $m$ be the number of prime numbers $n$ such that $2 \leq n \leq 5189$. Find the smallest positive integer $x$ with $1 \leq x \leq 115$ such that
$$
5^x \equiv 173 \pmod{m}.
$$ | 31 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(5),
"b": Const(173),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(5189)), IsPrime(Var("n"))))),
"upper": Const(115),
"res... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | modular_min_modexp_v1 | null | 7 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.008 | 2026-02-08T02:31:39.668985Z | {
"verified": true,
"answer": 31,
"timestamp": "2026-02-08T02:31:39.677276Z"
} | fff4f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T14:24:47.317Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 3.46,
"mid": 4.99,
"hi": 6.52
} | ||
f61a67 | modular_modexp_compute_v1_1248542787_48 | Let $e$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 16000000$. Compute the remainder when $13^e$ is divided by $60000$. | 1 | graphs = [
Graph(
let={
"a": Const(13),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16000000)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:55:22.330426Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T02:55:22.331627Z"
} | 31bc5a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1828
},
"timestamp": "2026-02-08T23:53:48.282Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.67,
"hi": -2.19
} | ||
3b8339 | comb_count_partitions_v1_2051736721_2601 | Let $S$ be the set of all integers $t$ such that $15 \le t \le 138$ and there exist positive integers $a$ and $b$ with $1 \le a \le 10$, $1 \le b \le 8$, and $t = 9a + 6b$. Let $n$ be the number of elements in $S$. Compute the number of integer partitions of $n$. | 37,338 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:48:48.826071Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T16:48:48.827140Z"
} | 08daca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 4050
},
"timestamp": "2026-02-17T12:02:45.649Z",
"answer": 37338
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c5177e | comb_count_surjections_v1_124444284_2957 | Let $n = 4$ and $k = 3$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ is the Stirling number of the second kind. Let $c$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 14112$. Compute $c$ minus the value of $k! \cdot S(n, k)$. | 7,020 | graphs = [
Graph(
let={
"n": Const(4),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')),... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_count_surjections_v1 | negation_mod | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T05:05:57.354554Z | {
"verified": true,
"answer": 7020,
"timestamp": "2026-02-08T05:05:57.357017Z"
} | 8b4656 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 607
},
"timestamp": "2026-02-24T02:41:04.336Z",
"answer": 7020
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"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": "no"
}... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
7a4310 | nt_sum_divisors_compute_v1_784195855_5953 | Let $n = 70756$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Let $k$ be the number of integers $j$ with $0 \leq j \leq 1112$ such that $\binom{1112}{j}$ is odd. Let $c = k + 1$. Let $p$ and $q$ be positive integers such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $B$ be the number of such pa... | 45,809 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Const(70756),
"result": SumDivisors(n=Ref("n")),
"_c": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1112)), Eq(Mod(value=Binom(n=Const(1112), k=Var("j"))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"V8"
] | 859a49 | nt_sum_divisors_compute_v1 | quadratic_mod | 6 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.005 | 2026-02-08T08:13:37.997448Z | {
"verified": true,
"answer": 45809,
"timestamp": "2026-02-08T08:13:38.002297Z"
} | 4aff06 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 2344
},
"timestamp": "2026-02-13T15:55:23.127Z",
"answer": 45809
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
84ca61_n | alg_qf_psd_orbit_v1_1218484723_4319 | An audio engineer is designing paired speaker settings. Each configuration is described by two positive integers $(a,b)$ with $1 \le a \le b$. The second setting $b$ cannot exceed the total number of distinct sound levels $t$ that can be produced by the formula $t = 8a + 14b$ using integers $a,b$ with $1 \le a \le 10$,... | 5 | ALG | null | COUNT | sympy | SUM_SQUARES_IDENTITY | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | alg_qf_psd_orbit_v1 | null | 7 | null | [
"LIN_FORM",
"MIN_PRIME_FACTOR",
"SUM_SQUARES_IDENTITY"
] | 3 | 0.341 | 2026-02-25T05:56:53.443312Z | null | dfeef6 | 84ca61 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T21:30:10.513Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
c37d1f | comb_sum_binomial_mod_v1_655260480_1784 | Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 12769$. Let $m$ be the minimum value of $x + y$ over all pairs $(x, y) \in T$. For each integer $k$ from $27$ to $211$ inclusive, and each integer $j$ from $1$ to $10$ inclusive, compute $\binom{m}{k}$. Let $S$ be the sum of all these... | 76,234 | graphs = [
Graph(
let={
"_n": Const(50),
"sum": Div(Mul(Const(5), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(27), end=Const(211)), right=IntegerRange(start=Const(1), e... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/SUM_INDEPENDENT"
] | 3674a2 | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"B3",
"SUM_INDEPENDENT"
] | 2 | 0.033 | 2026-02-08T16:22:15.155432Z | {
"verified": true,
"answer": 76234,
"timestamp": "2026-02-08T16:22:15.188529Z"
} | a3705c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 23617
},
"timestamp": "2026-02-24T20:41:30.735Z",
"answer": 31623
},
{
... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok_later"
}
] | {
"lo": 4.28,
"mid": 7.01,
"hi": 10
} | ||
6f3d9e | lin_form_endings_v1_124444284_5242 | Let $a = 9$, $b = 12$, $A = 50$, and $B = 49$. Let $g = \gcd(a, b)$. Define $$s = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.$$ Let $k = 5150$ and $M = 56983$. Compute the remainder when $k \cdot s$ is divided by $M$. | 41,510 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(12),
"A_val": Const(50),
"B_val": Const(49),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), Re... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:28:40.663169Z | {
"verified": true,
"answer": 41510,
"timestamp": "2026-02-08T06:28:40.664754Z"
} | 6fdc3e | 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": 801
},
"timestamp": "2026-02-13T01:08:01.530Z",
"answer": 41510
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7c5265 | modular_sum_quadratic_residues_v1_1439011603_1216 | Let $p$ be the number of integers $t$ such that $7 \leq t \leq 123$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 44$, $1 \leq b \leq 7$, and $t = 2a + 5b$. Define $\text{result} = \frac{p(p-1)}{4}$. Compute the remainder when $44121 \cdot \text{result}$ is divided by $69430$. | 44,544 | graphs = [
Graph(
let={
"_n": Const(69430),
"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=44)), Geq(left=V... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T15:58:46.163447Z | {
"verified": true,
"answer": 44544,
"timestamp": "2026-02-08T15:58:46.165281Z"
} | 06e6fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2957
},
"timestamp": "2026-02-16T18:35:04.178Z",
"answer": 44544
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
27a640 | nt_min_coprime_above_v1_1431428450_88 | Let $n = 359$. Define $\mathcal{D}$ as the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $S$ be the set of all integers $k$ such that $15625 < k \leq 15994$ and $\gcd(k, \mathcal{D}) = 1$. Compute the smallest element of $S$. | 15,626 | graphs = [
Graph(
let={
"_n": Const(359),
"start": Const(15625),
"upper": Const(15994),
"modulus": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var(... | NT | null | EXTREMUM | sympy | K3 | [
"K3"
] | 54c41e | nt_min_coprime_above_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.045 | 2026-02-08T13:10:58.524977Z | {
"verified": true,
"answer": 15626,
"timestamp": "2026-02-08T13:10:58.569858Z"
} | 5af1cc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 915
},
"timestamp": "2026-02-15T11:07:12.713Z",
"answer": 15626
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
fa2ab6 | nt_gcd_compute_v1_784195855_73 | Let $n_1$ be the number of integers $n$ with $1 \leq n \leq 426$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $s = \mu(n_1)^2$, where $\mu$ denotes the Möbius function. Let $n = 974947$ and $f = \mu(n)^2$. Define $a = 619576 \cdot s + f$ and $b = 1161705$. Let $d = \gcd(a, b)$. Compute the ... | 29,791 | graphs = [
Graph(
let={
"n1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(426)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"s": Pow(MoebiusMu(n=Ref(name... | NT | null | COMPUTE | sympy | L3C | [
"L3C/MOBIUS_SQUAREFREE"
] | 964e96 | nt_gcd_compute_v1 | null | 5 | 2 | [
"L3C",
"MOBIUS_SQUAREFREE"
] | 2 | 0.002 | 2026-02-08T02:56:52.723750Z | {
"verified": true,
"answer": 29791,
"timestamp": "2026-02-08T02:56:52.726029Z"
} | f60adc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 3603
},
"timestamp": "2026-02-08T22:33:02.505Z",
"answer": 29791
},
{
... | 1 | [
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CON... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
5f42e3 | modular_count_residue_v1_1439011603_2381 | Let $m = 5$ and $r = 4$. Consider the set of all positive integers $n$ such that $1 \leq n \leq 88209$ and $n \equiv r \pmod{m}$. Let $A$ be the number of elements in this set.
Let $T$ be the set of all positive integers $t$ such that $9 \leq t \leq 1956$ and there exist positive integers $a$ and $b$ with $1 \leq a \l... | 56,137 | graphs = [
Graph(
let={
"upper": Const(88209),
"m": Const(5),
"r": Const(4),
"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/K3"
] | 94828b | modular_count_residue_v1 | negation_mod | 5 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 4.756 | 2026-02-08T16:45:14.359877Z | {
"verified": true,
"answer": 56137,
"timestamp": "2026-02-08T16:45:19.116286Z"
} | 23831b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 4013
},
"timestamp": "2026-02-17T11:35:59.630Z",
"answer": 56137
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e17339 | comb_bell_compute_v1_1820931509_195 | Let $n$ be the number of positive integers $k \leq 33$ such that $3$ divides $k$ and $\gcd(k, 35) = 1$. Compute the Bell number $B_n$, which counts the number of partitions of an $n$-element set. | 4,140 | graphs = [
Graph(
let={
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(33)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"result": Bell(Ref("n"))... | NT | COMB | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | comb_bell_compute_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.003 | 2026-02-08T11:24:23.662247Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T11:24:23.664905Z"
} | 5c4913 | 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": 700
},
"timestamp": "2026-02-14T13:10:43.740Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c75a14 | diophantine_sum_product_min_v1_898971024_691 | Let $S = 16$ and $P = 64$. Determine the value of $x$, where $x$ is a positive integer satisfying $1 \leq x \leq 15$ and
$$
x(S - x) = P.
$$
If multiple solutions exist, take the smallest such $x$.
Find the value of $x$. | 8 | graphs = [
Graph(
let={
"S": Const(16),
"P": Const(64),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Summation(var="k", start=Const(1), end=Const(5), expr=Var("k"))), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Re... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.004 | 2026-02-08T15:35:54.248435Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T15:35:54.252629Z"
} | 3904d3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 335
},
"timestamp": "2026-02-16T06:09:48.105Z",
"answer": 8
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
48234c | modular_sum_quadratic_residues_v1_601307018_6340 | Let $p = 521$. Compute $$\frac{p(p - 1)}{\min\left\{ 41a^2 - 62ab + \left|\left\{ (a_1, b_1) : a_1 \geq 1,\ a_1 \leq 25,\ b_1 \geq 1,\ b_1 \leq 25,\ 16b_1^2 = 784 \right\}\right| \cdot b^2 : (a, b),\ 1 \leq a \leq 5,\ 1 \leq b \leq 5 \right\}}.$$ | 67,730 | graphs = [
Graph(
let={
"_n": Const(5),
"p": Const(521),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(5)), Geq(Var("b")... | NT | null | SUM | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/QF_PSD_MIN"
] | 2a0653 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_MIN"
] | 2 | 0.009 | 2026-03-10T06:59:41.664475Z | {
"verified": true,
"answer": 67730,
"timestamp": "2026-03-10T06:59:41.673656Z"
} | 537cc3 | 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": 1745
},
"timestamp": "2026-04-19T04:10:12.870Z",
"answer": 67730
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
},
{
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
751b29 | alg_poly4_count_v1_1218484723_1126 | Let $E$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 20$ satisfying
$$
97a_1^4 - 292a_1^3b_1 + 510a_1^2b_1^2 - 316a_1b_1^3 + 82b_1^4 = 4205601.
$$
Find the number $Q$ of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 91$ such that
$$
16a^4 + 384a^2b^2 + 512... | 26 | graphs = [
Graph(
let={
"_n": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(91)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(91)), Eq(Sum(Mul(Const(384), Pow(Var("a"), Const(2))... | ALG | null | COUNT | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_poly4_count_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 1.979 | 2026-02-25T02:52:34.465707Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-25T02:52:36.444588Z"
} | 0d947a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T05:38:27.388Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.76,
"mid": 6.79,
"hi": 9.83
} | ||
57c312_n | comb_count_partitions_v1_1218484723_4813 | A puzzle designer creates tiles labeled with integers from 12 to 56. A tile labeled $t$ is valid if $t = 5a + 2b + 5$ for some integers $a$ between 1 and 7 and $b$ between 1 and 8. Let $n$ be the number of valid tiles. The designer then builds a tower using $n$ identical blocks, stacking them into any number of non-inc... | 25,933 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T06:27:23.659022Z | null | b05b31 | 57c312 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 5404
},
"timestamp": "2026-03-30T22:23:22.393Z",
"answer": 25933
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
775f36 | nt_min_crt_v1_124444284_2722 | Let $m = 3$ and $k = 7$. Let $S$ be the set of all ordered pairs $(k, j)$ with $1 \le k \le 2$ and $1 \le j \le 9$. For each such pair, define $f(k, j) = \phi(k) \left\lfloor \frac{d}{k} \right\rfloor$, where $d$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, ... | 10 | graphs = [
Graph(
let={
"m": Const(3),
"k": Const(7),
"a": Const(1),
"b": Div(Mul(Const(8), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2",
"SUM_INDEPENDENT"
] | fcc213 | nt_min_crt_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"K2",
"SUM_INDEPENDENT"
] | 3 | 0.094 | 2026-02-08T04:54:03.880481Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T04:54:03.974444Z"
} | c237c2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 1444
},
"timestamp": "2026-02-11T22:42:32.326Z",
"answer": 10
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma":... | {
"lo": -3.45,
"mid": 1.13,
"hi": 6
} | ||
4e4d3b | modular_modexp_compute_v1_1874849503_841 | Let $e$ be the number of positive integers $n$ such that $1 \leq n \leq 22242$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Compute the remainder when $29^e$ is divided by $88209$. | 2,359 | graphs = [
Graph(
let={
"_n": Const(22242),
"a": Const(29),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Con... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | modular_modexp_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T13:20:00.220543Z | {
"verified": true,
"answer": 2359,
"timestamp": "2026-02-08T13:20:00.222236Z"
} | 9272e8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2823
},
"timestamp": "2026-02-09T21:36:20.418Z",
"answer": 2359
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
6ea5e3 | nt_min_with_divisor_count_v1_1874849503_1159 | Let $A$ be the set of all positive integers $n$ such that $n \leq 72361$ and $n$ has exactly 8 positive divisors. Let $a$ be the smallest element of $A$.\\
Let $B$ be the set of all positive integers $x$ and $y$ such that $xy = 3600$. Define $s = x + y$ for each such pair. Let $m$ be the minimum value of $s$ over all ... | 2,496 | graphs = [
Graph(
let={
"upper": Const(72361),
"div_count": Const(8),
"result": MinOverSet(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"))))),
"_c": SumOverSet(set... | NT | null | EXTREMUM | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 0d839b | nt_min_with_divisor_count_v1 | negation_mod | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 3.141 | 2026-02-08T13:39:11.596120Z | {
"verified": true,
"answer": 2496,
"timestamp": "2026-02-08T13:39:14.736747Z"
} | 44e580 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 1731
},
"timestamp": "2026-02-10T01:47:52.906Z",
"answer": 2496
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
19d5d7 | alg_poly3_count_v1_1218484723_2924 | Let $R$ be the minimum value of $35a^3 + 33ab^2 + 9b^3 + 51a^2b$ over positive integers $a, b$ with $1 \le a, b \le 11$. Let $S = \min\{ 16a_3^3 + 12a_3^2b_3 + b_3^3 + 6a_3b_3^2 : a_3, b_3 \ge 1,\ 1 \le a_3, b_3 \le 14 \}$. Let $T = \left|\left\{ (a_2, b_2) : 1 \le a_2, b_2 \le 35,\ R a_2^3 + 128b_2^3 + 384a_2^2b_2 + 3... | 103 | graphs = [
Graph(
let={
"_c": Const(84),
"_m": Const(3),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(11)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(11)))), expr=S... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"POLY3_MIN/POLY3_COUNT"
] | fd477e | alg_poly3_count_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"POLY3_MIN",
"QF_PSD_DISTINCT"
] | 3 | 2.635 | 2026-02-25T04:40:48.732602Z | {
"verified": true,
"answer": 103,
"timestamp": "2026-02-25T04:40:51.367216Z"
} | f8af80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 399,
"completion_tokens": 3413
},
"timestamp": "2026-03-29T07:17:55.724Z",
"answer": 103
},
{
"id... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
0bf2a6 | nt_min_coprime_above_v1_677425708_1992 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 5625$. Let $m$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all integers $n$ such that $70756 < n \leq 70916$ and $\gcd(n, m) = \phi(2)$, where $\phi$ denotes Euler's totient function. Determine the value... | 70,757 | graphs = [
Graph(
let={
"start": Const(70756),
"upper": Const(70916),
"modulus": 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")), Co... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"ONE_PHI_2",
"B3"
] | 0519c9 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3",
"ONE_PHI_2"
] | 2 | 0.016 | 2026-02-08T04:42:12.426568Z | {
"verified": true,
"answer": 70757,
"timestamp": "2026-02-08T04:42:12.442719Z"
} | d5e4fa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1282
},
"timestamp": "2026-02-10T04:07:37.392Z",
"answer": 70757
},
{
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
2c7edb | lin_form_endings_v1_784195855_8145 | Let $a = 42$ and $b = 24$. Let $d$ be the greatest common divisor of $a$ and $b$. Let $k = 15024$ and let $s = k \cdot d$. Compute the remainder when $s$ is divided by $73473$. | 16,671 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(24),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(15024),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(73473),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T15:54:52.841765Z | {
"verified": true,
"answer": 16671,
"timestamp": "2026-02-08T15:54:52.842186Z"
} | e0a16a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 486
},
"timestamp": "2026-02-16T06:36:56.702Z",
"answer": 16671
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b6f212 | alg_poly_preperiod_count_v1_601307018_6470 | For each non-negative integer $a$ with $0 \le a \le 26519$, define $N = a^2 + 8 \bmod 17$, $M = N^2 + 8 \bmod 17$, $R = M^2 + 8 \bmod 17$, and $S = R^2 + 8 \bmod 17$. Let $Q$ be the number of values of $a$ such that $S = M$ and $R \ne M$. Find $Q$. | 9,360 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(8)), modulus=Const(17)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(8)), modulus=Const(17)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(8)), modulus=Const(17)),
"p4": ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.028 | 2026-03-10T07:07:45.433842Z | {
"verified": true,
"answer": 9360,
"timestamp": "2026-03-10T07:07:45.461726Z"
} | 1d3076 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 3294
},
"timestamp": "2026-04-19T04:30:44.630Z",
"answer": 9360
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} |
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