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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a1ed0d | modular_sum_quadratic_residues_v1_1353956133_406 | Let $p$ be the largest prime number less than or equal to 277. Define $r = \frac{p(p-1)}{4}$. Compute the remainder when $20810 \cdot r$ is divided by 69449. | 7,107 | graphs = [
Graph(
let={
"_n": Const(69449),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(277)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T11:26:14.932514Z | {
"verified": true,
"answer": 7107,
"timestamp": "2026-02-08T11:26:14.933637Z"
} | a32655 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 1154
},
"timestamp": "2026-02-14T13:44:13.880Z",
"answer": 7107
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d85969 | diophantine_fbi2_count_v1_971394319_275 | Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 2423$. Let $d$ be an integer satisfying $2 \leq d \leq 51$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 52$. Let $r$ be the number of such integers $d$. Compute the remainder when $42695 \cdot r$ is divided by $80618$. | 28,632 | graphs = [
Graph(
let={
"_n": Const(51),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2423)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), ... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.007 | 2026-02-08T12:56:17.591967Z | {
"verified": true,
"answer": 28632,
"timestamp": "2026-02-08T12:56:17.599442Z"
} | afc411 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1363
},
"timestamp": "2026-02-15T08:04:41.497Z",
"answer": 28632
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3ad4b1 | nt_sum_divisors_mod_v1_1915831931_2455 | Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. For each such pair, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma$ denote the sum of all positive divisors of $n$. Compute the value of $\sigma \mod 11321$. | 2,880 | 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(176400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11321... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T16:51:10.329960Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T16:51:10.335625Z"
} | eae59e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1198
},
"timestamp": "2026-02-17T15:15:13.205Z",
"answer": 2880
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
495569 | comb_count_partitions_v1_784195855_5092 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 17$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $n_2$ be the number of elements in $T$. Define $v = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $S$ be the set of all ordered pairs $(x_1, ... | 31,185 | graphs = [
Graph(
let={
"_n": Const(39),
"n2": 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(... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING",
"COMB1/BINOMIAL_ALTERNATING"
] | 1b81bd | comb_count_partitions_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"LIN_FORM"
] | 3 | 0.003 | 2026-02-08T07:39:46.893588Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T07:39:46.896310Z"
} | 65b0c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 335,
"completion_tokens": 1721
},
"timestamp": "2026-02-24T08:20:07.210Z",
"answer": 31185
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": ... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
810688 | antilemma_sum_equals_v1_1918700295_2727 | Compute the number of ordered pairs of positive integers $(i, j)$ such that $i + j = 39$, $1 \leq i \leq 37$, and $1 \leq j \leq 38$. | 37 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(39)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(37)), right=IntegerRange(start=Const(1), end=Const(38))))),
},
... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.091 | 2026-02-08T08:10:56.347515Z | {
"verified": true,
"answer": 37,
"timestamp": "2026-02-08T08:10:56.438769Z"
} | e2dfb2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 356
},
"timestamp": "2026-02-24T09:00:18.656Z",
"answer": 37
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
c08ed9 | comb_count_permutations_fixed_v1_655260480_2221 | Let $n = 7$. Let $S$ be the set of all ordered pairs $(k_1, j)$ where $k_1 \in \{1, 2\}$ and $j \in \{1, 2, 3\}$. Define
$$
k = \frac{3}{9} \sum_{(k_1, j) \in S} k_1.
$$
Define
$$
\text{result} = \binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements. Let $Q = \text{result}$. Comp... | 315 | graphs = [
Graph(
let={
"n": Const(7),
"k": Div(Mul(Const(3), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k1"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.003 | 2026-02-08T16:37:22.771313Z | {
"verified": true,
"answer": 315,
"timestamp": "2026-02-08T16:37:22.774685Z"
} | d221cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 985
},
"timestamp": "2026-02-24T21:45:53.786Z",
"answer": 315
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma"... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
994a2d_n | alg_sum_powers_v1_1218484723_623 | A solar panel array is to be arranged as a rectangle with area $1600225$ square units using only whole-number side lengths. The installation team wants to minimize the total perimeter, so they choose dimensions $x$ and $y$ that minimize $x + y$. Meanwhile, a sensor logs the sum of squares of the first $1490$ positive i... | 53,671 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_powers_v1 | null | 4 | null | [
"B3"
] | 1 | 0.061 | 2026-02-25T02:22:36.241928Z | null | 3e0c4b | 994a2d | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T15:42:01.512Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
612441_l | algebra_quadratic_discriminant_v1_124444284_7950 | Let $a = 1$, $b = 2$, and $c = 1$. Define the discriminant $D = b^2 - 4ac$. Let $r = 1$ if $D > 0$, and $r = 0$ otherwise. Let $s = 1$ if $$D = \sum_{k=0}^{9} (-1)^k \binom{9}{k},$$ and $s = 0$ otherwise. Define $t = 2r + s$. Compute $t$ multiplied by the number of lattice points $(x, y)$ such that $1 \leq x \leq 26$ a... | 0 | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"BINOMIAL_ALTERNATING"
] | f28f83 | algebra_quadratic_discriminant_v1 | affine_mod | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | 2 | 0.003 | 2026-02-08T09:28:49.153663Z | {
"verified": false,
"answer": 5954,
"timestamp": "2026-02-08T09:28:49.156249Z"
} | b4951e | 612441 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 607
},
"timestamp": "2026-02-24T11:18:53.865Z",
"answer": 5954
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | |
f3aca9 | lin_form_endings_v1_784195855_5967 | Let $a = 40$ and $b = 32$. Define $s = \gcd(a, b)$. Let $k = 180$ and compute $m = \left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$. Compute the value of $14288 \cdot m$ modulo $59394$. | 49,020 | graphs = [
Graph(
let={
"a_coeff": Const(40),
"b_coeff": Const(32),
"k_val": Const(180),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:13:57.789641Z | {
"verified": true,
"answer": 49020,
"timestamp": "2026-02-08T08:13:57.791108Z"
} | d90c44 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 493
},
"timestamp": "2026-02-13T15:58:24.150Z",
"answer": 49020
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c1a4f7 | nt_count_coprime_and_v1_798873815_301 | Let $k_1 = 11$ and let $k_2$ be the largest prime number less than or equal to $14$. Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 24886$, $\gcd(n, 11) = \sum_{d \mid \gcd(15, 22)} \mu(d)$, and $\gcd(n, k_2) = 1$, where $\mu$ denotes the M\"obius function. Let $N = |S|$, the number of elements in... | 20,532 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": Const(24886),
"k1": Const(11),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=Solut... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"MAX_PRIME_BELOW"
] | f86db3 | nt_count_coprime_and_v1 | null | 7 | 0 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 2 | 2.56 | 2026-02-08T02:33:03.288528Z | {
"verified": true,
"answer": 20532,
"timestamp": "2026-02-08T02:33:05.848713Z"
} | 3091ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 3993
},
"timestamp": "2026-02-08T19:19:54.005Z",
"answer": 20532
},
{
"... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "n... | {
"lo": 1.3,
"mid": 4.19,
"hi": 6.61
} | ||
44ccde | nt_count_divisible_and_v1_458359167_1185 | Let $N$ be the largest integer such that $1 \leq N \leq 53220$. Determine the number of positive integers $n \leq N$ that are divisible by 6 and satisfy
$$
n \equiv \sum_{d \mid 6} \mu(d) \pmod{10},
$$
where $\mu$ denotes the Möbius function. Compute this count. | 1,774 | graphs = [
Graph(
let={
"upper": Const(53220),
"d1": Const(6),
"d2": Const(10),
"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("d1")), Const(0)), Eq(M... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"MOBIUS_SUM"
] | 518e32 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"MOBIUS_SUM"
] | 1 | 3.161 | 2026-02-08T04:28:52.421030Z | {
"verified": true,
"answer": 1774,
"timestamp": "2026-02-08T04:28:55.582469Z"
} | 8e13ca | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 541
},
"timestamp": "2026-02-18T11:44:06.178Z",
"answer": 1774
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
49fabd | comb_sum_binomial_row_v1_1520064083_7054 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. Compute $k^n$, where $k$ is the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 6$ and $\gcd(p, q) = 1$. | 16,384 | graphs = [
Graph(
let={
"_n": Const(49),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T08:43:45.027855Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T08:43:45.029963Z"
} | d34d5b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 511
},
"timestamp": "2026-02-15T20:20:03.204Z",
"answer": 4782969
},
{
"id": ... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
e61ab6 | alg_poly_preperiod_count_v1_1218484723_3363 | For each non-negative integer $a$ with $0 \leq a \leq 69945$, define $N = (a^2 + a) \bmod 41$, $M = (N^2 + N) \bmod 41$, $R = (M^2 + M) \bmod 41$, and $S = (R^2 + R) \bmod 41$. Find the number of such $a$ for which $S = M$ and $R \neq M€. | 10,236 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a")), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1")), modulus=Const(41)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2")), modulus=Const(41)),
"p4"... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.019 | 2026-02-25T05:02:49.214118Z | {
"verified": true,
"answer": 10236,
"timestamp": "2026-02-25T05:02:49.232814Z"
} | cc4ce4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 11749
},
"timestamp": "2026-03-29T09:50:30.674Z",
"answer": 10236
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
35ca15 | antilemma_k2_v1_898971024_289 | Let $n = 166$. Define
$$
x = \sum_{k=1}^{166} \phi(k) \left\lfloor \frac{166}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute $x$. | 13,861 | graphs = [
Graph(
let={
"_n": Const(166),
"x": Summation(var="k", start=Const(1), end=Const(166), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T15:20:02.630591Z | {
"verified": true,
"answer": 13861,
"timestamp": "2026-02-08T15:20:02.631995Z"
} | 75685f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 613
},
"timestamp": "2026-02-16T03:13:45.990Z",
"answer": 13861
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b9f316 | geo_count_lattice_triangle_v1_677425708_1985 | Let $A = (0,0)$, $B = (105,196)$, and $C = (222,360)$. The area of triangle $ABC$ is $\frac{1}{2} \times \text{area}_{2x}$, where $\text{area}_{2x} = |105 \cdot 360 - 222 \cdot (-196)|$. Let $b$ be the number of lattice points on the boundary of triangle $ABC$, which is given by
\[
b = \gcd(105,196) + \gcd(222-105,360-... | 2,850 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=105), Const(value=360)), Mul(Const(value=222), Sub(left=Const(value=0), right=Const(value=196))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=105)), b=Abs(arg=Const(value=196))), GCD(a=Abs(arg=Sub(left=Const(value=222), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.006 | 2026-02-08T04:42:08.680722Z | {
"verified": true,
"answer": 2850,
"timestamp": "2026-02-08T04:42:08.686472Z"
} | 010dd8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 1209
},
"timestamp": "2026-02-10T04:01:21.966Z",
"answer": 2850
},
{
"i... | 1 | [] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||||
298da8 | nt_lcm_compute_v1_1456120455_104 | Let $a = 1107$ and $b = 1047$. Compute $\text{lcm}(a, b)$. Let $T$ be the set of all integers $t$ such that $44 \leq t \leq 21080$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 810$, $1 \leq b \leq 656$, and $t = 9a + 21b + 14$. Let $c$ be the number of elements in $T$. Let $d$ be the number of posi... | 34,640 | graphs = [
Graph(
let={
"a": Const(1107),
"b": Const(1047),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), r... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"C2"
] | 2baf72 | nt_lcm_compute_v1 | two_moduli | 7 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T02:53:45.477589Z | {
"verified": true,
"answer": 34640,
"timestamp": "2026-02-08T02:53:45.480151Z"
} | 7bd0a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:54:10.571Z",
"answer": 47332
},
{
... | 0 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"... | {
"lo": 4.62,
"mid": 6.54,
"hi": 9.53
} | ||
0f1c0d | alg_poly4_count_v1_601307018_2008 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 35$ such that $10a^2 + 25b^2 - 18ab \le 4525$. Let $T = \sum_{\substack{(a_2, b_2, c) \,\text{with}\\ a_2^2 + b_2^2 + c^2 = a_2b_2 + b_2c + ca_2 \\ 5a_2 + 7b_2 + 6c = 198 \\ a_2, b_2, c \ge 1}} a_2^2 + b_2^2 + c^2$. Let $Q$ be the... | 363 | graphs = [
Graph(
let={
"_m": Const(337),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Leq(Sum(Mul(Const(10), Pow(Var("a"), Const(2))),... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/SUM_SQUARES_IDENTITY"
] | c5cc1d | alg_poly4_count_v1 | null | 8 | 0 | [
"QF_PSD_COUNT_LEQ",
"SUM_SQUARES_IDENTITY"
] | 2 | 1.384 | 2026-03-10T02:44:40.514259Z | {
"verified": true,
"answer": 363,
"timestamp": "2026-03-10T02:44:41.897985Z"
} | 3a70cd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 339,
"completion_tokens": 4962
},
"timestamp": "2026-04-18T16:01:08.837Z",
"answer": 363
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok_later"
}
] | {
"lo": 1.36,
"mid": 4.42,
"hi": 6.81
} | ||
172682 | modular_sum_quadratic_residues_v1_1874849503_1507 | Let $m = 2$. Define $a_n = 1$ if $\gcd\left(n, t\right) = 1$ for some integer $t$ such that $10 \leq t \leq 42$ and there exist positive integers $a \leq 3$, $b \leq 7$ satisfying $t = 7a + 3b$; otherwise, let $a_n = 0$. Let $n$ be the number of positive integers $n$ with $1 \leq n \leq m$ such that $a_n = 1$. Let $p$ ... | 3,164 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(GCD(a=Var("n"), b=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), ... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/C4/MIN_PRIME_FACTOR"
] | 4a5635 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"C4",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.007 | 2026-02-08T13:56:40.617350Z | {
"verified": true,
"answer": 3164,
"timestamp": "2026-02-08T13:56:40.624773Z"
} | abe364 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 7627
},
"timestamp": "2026-02-11T08:07:04.738Z",
"answer": 3164
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
dd199d | alg_poly_orbit_count_v1_1419126231_486 | Let $N \equiv a^3 - 3a \pmod{83}$, $M \equiv N^3 - 3N \pmod{83}$, and $R \equiv M^3 - 3M \pmod{83}$. Find the number of non-negative integers $a$ with $0 \le a \le 61917$ such that $R = a$, $N \ne a$, and $M \ne a$. | 8,952 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-3), Var("a"))), modulus=Const(83)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-3), Ref("p1"))), modulus=Const(83)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(-3), R... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.014 | 2026-02-25T10:01:19.719906Z | {
"verified": true,
"answer": 8952,
"timestamp": "2026-02-25T10:01:19.734236Z"
} | bab876 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 23031
},
"timestamp": "2026-03-30T08:44:36.649Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
c4d5fc | antilemma_k2_v1_124444284_8748 | Compute $\sum_{k=1}^{320} \phi(k) \left\lfloor \frac{320}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. | 51,360 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(320), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(320), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T11:53:31.350934Z | {
"verified": true,
"answer": 51360,
"timestamp": "2026-02-08T11:53:31.351423Z"
} | 8fd2ed | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 1263
},
"timestamp": "2026-02-14T20:16:48.485Z",
"answer": 51360
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"stat... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f88365 | nt_count_divisible_and_v1_124444284_253 | Let $d_1 = \sum_{k=1}^{2} k$ and $d_2 = 10$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq 74520$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Let $k$ be the number of elements in $S$. Compute the smallest positive integer $m$ such that the $m$-th Fibonacci number is divisibl... | 570 | graphs = [
Graph(
let={
"upper": Const(74520),
"d1": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")), expr=Var("k")),
"d2": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Ge... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 2a57af | nt_count_divisible_and_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 6.017 | 2026-02-08T03:06:43.370725Z | {
"verified": true,
"answer": 570,
"timestamp": "2026-02-08T03:06:49.387696Z"
} | fbda91 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 2469
},
"timestamp": "2026-02-09T15:11:50.046Z",
"answer": 570
},
{
"id... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6b5a6c | antilemma_k3_v1_865884756_6410 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $42804$, where $\phi$ denotes Euler's totient function. | 42,804 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=42804), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T19:11:02.983219Z | {
"verified": true,
"answer": 42804,
"timestamp": "2026-02-08T19:11:02.983794Z"
} | fb382e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 664
},
"timestamp": "2026-02-18T21:35:26.252Z",
"answer": 42804
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4d48a0 | nt_sum_divisors_mod_v1_124444284_2191 | Let $n$ be the sum of all positive integers $x \leq 160$ such that $x$ is divisible by the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ satisfying $xy = 1600$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by 10427. | 744 | graphs = [
Graph(
let={
"_n": Const(160),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(... | NT | null | COMPUTE | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 138b1a | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.007 | 2026-02-08T04:30:36.462550Z | {
"verified": true,
"answer": 744,
"timestamp": "2026-02-08T04:30:36.469480Z"
} | 3f3980 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 761
},
"timestamp": "2026-02-10T16:58:10.586Z",
"answer": 744
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
8de734 | nt_count_coprime_and_v1_784195855_10154 | Let $k_1 = 3$ and let $k_2$ be the largest prime number $n$ such that $2 \leq n \leq 9$. Determine the number of positive integers $n$ such that $1 \leq n \leq 36202$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 20,687 | graphs = [
Graph(
let={
"upper": Const(36202),
"k1": Const(3),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.764 | 2026-02-08T17:28:28.824913Z | {
"verified": true,
"answer": 20687,
"timestamp": "2026-02-08T17:28:32.588810Z"
} | 0e0e60 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1265
},
"timestamp": "2026-02-18T03:10:17.993Z",
"answer": 20687
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
34dd8b | nt_count_digit_sum_v1_1918700295_916 | Let $ S $ be the set of all integers $ t $ with $ 18 \le t \le 36 $ for which there exist integers $ a $ and $ b $ such that $ 1 \le a \le 5 $, $ 1 \le b \le 3 $, and $ t = 2a + 5b + 11 $. Let $ s $ be the number of elements in $ S $. Determine the number of positive integers $ n $ with $ 1 \le n \le 99999 $ such that ... | 3,246 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 4.034 | 2026-02-08T05:23:43.406827Z | {
"verified": true,
"answer": 3246,
"timestamp": "2026-02-08T05:23:47.441089Z"
} | 58e564 | 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": 2019
},
"timestamp": "2026-02-12T07:51:50.553Z",
"answer": 3246
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
16fcc8 | comb_count_surjections_v1_865884756_179 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 7$, $1 \le j \le 8$, and $i + j = 8$. Let $k = 3$ and define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q = 17711 - \text{result}$. Find the value of $Q$. | 15,905 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(8))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.018 | 2026-02-08T15:15:00.601536Z | {
"verified": true,
"answer": 15905,
"timestamp": "2026-02-08T15:15:00.619571Z"
} | 6d9bc1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1232
},
"timestamp": "2026-02-10T05:09:31.776Z",
"answer": 15905
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
b523ed | algebra_quadratic_discriminant_v1_48377204_1872 | Let $a = -10$, $b$ be the largest prime number less than or equal to 5, and $c = 2$. Compute the value of $b^2 - 4ac$. | 105 | graphs = [
Graph(
let={
"a": Const(-10),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"c": Const(2),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c")... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.025 | 2026-02-08T16:27:48.538631Z | {
"verified": true,
"answer": 105,
"timestamp": "2026-02-08T16:27:48.563360Z"
} | 7f5b78 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 150
},
"timestamp": "2026-02-16T07:26:40.163Z",
"answer": 89
},
{
"id": 11,
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
47a375 | algebra_poly_eval_v1_717093673_4112 | Let $a = 16$. Compute the value of $5a^3 + 2a^2 + a + p$, where $p$ is the largest prime number not exceeding $6$. Let $Q$ be the remainder when this value is multiplied by $26820$ and then divided by $97433$. Find the value of $Q$. | 16,188 | graphs = [
Graph(
let={
"_n": Const(6),
"a": Const(16),
"result": Sum(Mul(Const(5), Pow(Ref("a"), Const(3))), Mul(Const(2), Pow(Ref("a"), Const(2))), Ref("a"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPri... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T18:03:00.591875Z | {
"verified": true,
"answer": 16188,
"timestamp": "2026-02-08T18:03:00.593846Z"
} | e4867f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1608
},
"timestamp": "2026-02-18T12:25:27.430Z",
"answer": 16188
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0d878f | nt_sum_divisors_mod_v1_784195855_4632 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14400$. Compute the sum of all positive divisors of $n$, and then find the remainder when this sum is divided by $10691$. | 744 | graphs = [
Graph(
let={
"_n": Const(14400),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T07:13:34.788490Z | {
"verified": true,
"answer": 744,
"timestamp": "2026-02-08T07:13:34.792704Z"
} | 294fa4 | 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": 1833
},
"timestamp": "2026-02-13T08:58:23.285Z",
"answer": 744
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
4ce8a1 | comb_binomial_compute_v1_153355830_602 | Let $n = 16$. Let $k$ be the number of elements in the Cartesian product of the sets $\{1, 2, 3\}$ and $\{1, 2, 3\}$. Compute $\binom{n}{k}$. | 11,440 | graphs = [
Graph(
let={
"n": Const(16),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_binomial_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:10:39.243434Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T03:10:39.244396Z"
} | 21670c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 637
},
"timestamp": "2026-02-23T23:14:22.261Z",
"answer": 11440
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
8ad392 | diophantine_sum_product_min_v1_865884756_899 | Let $S = 128$. Let $P$ be the number of positive integers $n \leq 42804$ such that $9$ divides the $n$-th Fibonacci number. Let $r$ be the smallest positive integer $x \leq 127$ such that $x(S - x) = P$. Compute
$$
r + \phi(|r| + 1) + \tau(|r| + 1),
$$
where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes... | 61 | graphs = [
Graph(
let={
"_n": Const(9),
"S": Const(128),
"P": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(42804)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": MinOve... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | diophantine_sum_product_min_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.015 | 2026-02-08T15:40:49.456429Z | {
"verified": true,
"answer": 61,
"timestamp": "2026-02-08T15:40:49.471867Z"
} | e22547 | 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": 1854
},
"timestamp": "2026-02-16T10:56:19.346Z",
"answer": 61
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
38f3c3 | comb_count_surjections_v1_2051736721_2269 | Let $S$ be the set of all ordered pairs of positive odd integers $(x_{11}, x_{21})$ such that $x_{11} + x_{21} = 24$. Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = |S|$. Let $k = 3$ and define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of th... | 3,493 | 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")), CountOverSet(set=SolutionsSet(v... | COMB | NT | COUNT | sympy | COMB1 | [
"COMB1/COMB1",
"ONE_FACTORIAL_0"
] | 70e38d | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1",
"ONE_FACTORIAL_0"
] | 2 | 0.005 | 2026-02-08T16:33:23.894700Z | {
"verified": true,
"answer": 3493,
"timestamp": "2026-02-08T16:33:23.899805Z"
} | ddd722 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 5890
},
"timestamp": "2026-02-17T06:34:15.306Z",
"answer": 3493
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c80cc2 | nt_count_primes_v1_784195855_8065 | Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $T$. Define $S$ as the set of all prime numbers $n$ such that $m \leq n \leq 36100$. Compute the number of elements in $S$. Multi... | 52,782 | graphs = [
Graph(
let={
"upper": Const(36100),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.533 | 2026-02-08T10:45:54.889187Z | {
"verified": true,
"answer": 52782,
"timestamp": "2026-02-08T10:45:56.422265Z"
} | ab8545 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 2209
},
"timestamp": "2026-02-14T08:33:57.529Z",
"answer": 52782
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"stat... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
39baf3 | comb_factorial_compute_v1_458359167_725 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18900$, $\gcd(p, q) = 1$, and $p < q$. Compute $n!$. | 40,320 | 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=18900)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T03:31:29.137827Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T03:31:29.139349Z"
} | 0df135 | 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": 2617
},
"timestamp": "2026-02-10T14:42:23.569Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.15,
"hi": 0.25
} | ||
964400 | nt_count_digit_sum_v1_1116507919_327 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 3$ and $1 \leq j \leq 12$ such that $\gcd(i,j) = 1$. Let $t$ be the number of elements in $S$. Let $U = 99999$. Compute the number of positive integers $n$ such that $1 \leq n \leq U$ and the sum of the digits of $n$ equals $t$. Le... | 2,280 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": 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(3)), right=IntegerRange(start=... | NT | null | COUNT | sympy | B3 | [
"B3",
"COUNT_COPRIME_GRID"
] | 776b20 | nt_count_digit_sum_v1 | negation_mod | 6 | 0 | [
"B3",
"COUNT_COPRIME_GRID"
] | 2 | 3.593 | 2026-02-08T02:31:31.384164Z | {
"verified": true,
"answer": 2280,
"timestamp": "2026-02-08T02:31:34.976726Z"
} | 0d3e97 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 2869
},
"timestamp": "2026-02-08T19:23:03.094Z",
"answer": 2280
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},... | {
"lo": -1.73,
"mid": 0.31,
"hi": 2.19
} | ||
f4c362 | nt_count_divisors_in_range_v1_784195855_9066 | Let $n = 45360$ and $a = 54$. Define $b$ to be the number of integers $t$ such that $9 \leq t \leq 965$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 149$, $1 \leq b' \leq 55$, and $t = 5a' + 4b'$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $R$ be this c... | 94,324 | graphs = [
Graph(
let={
"n": Const(45360),
"a": Const(54),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=C... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.012 | 2026-02-08T16:30:51.792872Z | {
"verified": true,
"answer": 94324,
"timestamp": "2026-02-08T16:30:51.804859Z"
} | fcfe93 | 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": 4272
},
"timestamp": "2026-02-17T05:31:57.269Z",
"answer": 94324
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09b17b | antilemma_k3_v1_865884756_902 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $94550$, where $\phi$ denotes Euler's totient function. Compute $x$. | 94,550 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=94550), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T15:40:49.633725Z | {
"verified": true,
"answer": 94550,
"timestamp": "2026-02-08T15:40:49.634154Z"
} | bb4581 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 85,
"completion_tokens": 530
},
"timestamp": "2026-02-16T10:55:46.046Z",
"answer": 94550
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8109e5 | nt_count_with_divisor_count_v1_717093673_0 | Let $ A $ be the number of positive integers $ n $ such that $ 1 \leq n \leq 11111 $ and $ n $ has exactly 3 positive divisors. Let $ B $ be the number of ordered pairs $ (x_1, x_2) $ of positive odd integers such that $ x_1 + x_2 = 3872 $. Compute $ B - A $. | 1,909 | graphs = [
Graph(
let={
"_n": Const(3872),
"upper": Const(11111),
"div_count": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | nt_count_with_divisor_count_v1 | negation_mod | 5 | 0 | [
"COMB1"
] | 1 | 0.875 | 2026-02-08T15:08:39.608139Z | {
"verified": true,
"answer": 1909,
"timestamp": "2026-02-08T15:08:40.483611Z"
} | a08790 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 835
},
"timestamp": "2026-02-16T00:31:35.113Z",
"answer": 1909
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
46a5fd | comb_bell_compute_v1_168721529_2059 | Let $n$ be the number of positive integers $k$ with $1 \le k \le 108$ such that the $k$-th Fibonacci number is divisible by $16$. Let $r$ be the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Let $Q$ be the remainder when $44121 \cdot r$ is divided by $58831$. Compute $Q$. | 25,958 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(108)), Divides(divisor=Const(16), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Bell(Ref("n")),
"Q": ... | COMB | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_bell_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T14:04:28.790733Z | {
"verified": true,
"answer": 25958,
"timestamp": "2026-02-08T14:04:28.793507Z"
} | c4ae9d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2632
},
"timestamp": "2026-02-10T01:29:49.529Z",
"answer": 25958
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
9c61bf | nt_min_coprime_above_v1_784195855_838 | Let $ S $ be the set of all integers $ t $ such that $ 10 \leq t \leq 2185 $ and $ t = 3a + 7b $ for some integers $ a $ and $ b $ with $ 1 \leq a \leq 152 $ and $ 1 \leq b \leq 247 $. Let $ \text{upper} $ be the number of elements in $ S $. Let $ \text{start} = 1849 $ and $ \text{modulus} = 305 $. Let $ T $ be the set... | 1,851 | graphs = [
Graph(
let={
"start": Const(1849),
"upper": 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=152)), Geq... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.047 | 2026-02-08T04:38:56.697041Z | {
"verified": true,
"answer": 1851,
"timestamp": "2026-02-08T04:38:56.744520Z"
} | 4b7b5d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 6669
},
"timestamp": "2026-02-10T17:28:19.991Z",
"answer": 1851
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
82039d | geo_count_lattice_triangle_v1_784195855_2352 | Let $A = |100 \cdot 169 + 233 \cdot (-120)|$. Let $B$ be the sum of the following three greatest common divisors:
- $\gcd(|n|, 120)$, where $n$ is the number of prime integers from 2 to 541, inclusive;
- $\gcd(|233 - 100|, |169 - \sum_{k=1}^{15} k|)$;
- $\gcd(|-233|, |-169|)$.
Compute $\frac{A + 2 - B}{2}$. | 5,517 | graphs = [
Graph(
let={
"_c": Const(169),
"_m": Const(15),
"_n": Const(169),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Ref(name='_c')), Mul(Const(value=233), Sub(left=Const(value=0), right=Const(value=120))))),
"boundary": Sum(GCD(a=Abs(arg=Coun... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2",
"COUNT_PRIMES"
] | c8a900 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"COUNT_PRIMES",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.027 | 2026-02-08T05:41:51.238627Z | {
"verified": true,
"answer": 5517,
"timestamp": "2026-02-08T05:41:51.265276Z"
} | 86c290 | 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": 843
},
"timestamp": "2026-02-12T13:06:21.205Z",
"answer": 5517
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"stat... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5939ba | algebra_quadratic_discriminant_v1_655260480_5092 | Let $a = 3$, $b = 0$, and $n = 4$. Define $c$ to be the number of integers $t$ such that $7 \leq t \leq 20$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 2$, $1 \leq b' \leq 5$, and $t = 5a' + 2b'$. Let $r = b^2 - n \cdot a \cdot c$. Compute the remainder when $32811 \cdot r$ is divided by $53977... | 3,001 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(3),
"b": Const(0),
"c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T18:16:18.461286Z | {
"verified": true,
"answer": 3001,
"timestamp": "2026-02-08T18:16:18.463881Z"
} | 508e0c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2698
},
"timestamp": "2026-02-18T15:46:03.691Z",
"answer": 3001
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b96e36 | modular_min_linear_v1_458359167_4007 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1630729$.
Let $a$ be the number of positive integers at most $n$ whose digit sum is even.
Let $m$ be the total number of ordered pairs $(i, j)$ such that $1 \leq i \leq 27$ and $1 \leq j \leq 107$.
Find the smallest ... | 2,399 | 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(1630729)))), expr=Sum(Var("x"), Var("y")))),
"a": CountOver... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"B3/L3B"
] | 3defda | modular_min_linear_v1 | null | 6 | 0 | [
"B3",
"COUNT_CARTESIAN",
"L3B"
] | 3 | 0.133 | 2026-02-08T11:28:31.483550Z | {
"verified": true,
"answer": 2399,
"timestamp": "2026-02-08T11:28:31.616401Z"
} | 7a8061 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 2643
},
"timestamp": "2026-02-14T14:29:38.159Z",
"answer": 2399
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f867c0 | diophantine_product_count_v1_458359167_3558 | Let $A$ be the set of all positive integers $n$ such that $n \leq 120$ and $n$ is divisible by 60. Let $m$ be the sum of all elements in $A$. Let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $n$ be the maximum value of $xy$ as $(x, y)$ ranges over $B$. Let $C$ be the set ... | 14 | graphs = [
Graph(
let={
"_m": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(120)), Eq(Mod(value=Var("n"), modulus=Const(60)), Const(0))))),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")])... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B1/B3"
] | cf3329 | diophantine_product_count_v1 | null | 7 | 0 | [
"B1",
"B3",
"SUM_DIVISIBLE"
] | 3 | 0.015 | 2026-02-08T08:24:32.254815Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T08:24:32.269865Z"
} | 13436b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 1467
},
"timestamp": "2026-02-13T18:41:25.944Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
dafaa7 | antilemma_k3_v1_1918700295_3557 | Compute the value of $\sum_{d \mid 89140} \phi(d)$, where $\phi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $89140$. | 89,140 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=89140), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T08:42:01.985646Z | {
"verified": true,
"answer": 89140,
"timestamp": "2026-02-08T08:42:01.986120Z"
} | 9bfd8f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 420
},
"timestamp": "2026-02-15T20:20:25.679Z",
"answer": 89140
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
1d87a1 | modular_min_linear_v1_717093673_1554 | Let $a = 20799$ and $m = 58207$. Let $b$ be the number of positive integers $k$ such that $1 \le k \le 250371$ and $81$ divides $k$. Determine the value of the smallest positive integer $x$ such that $1 \le x \le m$ and $ax \equiv b \pmod{m}$. | 51,555 | graphs = [
Graph(
let={
"a": Const(20799),
"b": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(250371)), Divides(divisor=Const(81), dividend=Var("k"))), domain='positive_integers')),
"m": Const(58207),
"r... | ALG | NT | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | modular_min_linear_v1 | null | 5 | 0 | [
"C2"
] | 1 | 2.337 | 2026-02-08T16:10:15.239728Z | {
"verified": true,
"answer": 51555,
"timestamp": "2026-02-08T16:10:17.576272Z"
} | bfd66a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 2827
},
"timestamp": "2026-02-16T22:00:50.967Z",
"answer": 51555
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c41bf | antilemma_k2_v1_1520064083_1492 | Compute
$$
\sum_{k=1}^{289} \phi(k) \left\lfloor \frac{289}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $x$ be the value of this sum. Find the remainder when $19079 \cdot x$ is divided by $50110$. | 445 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(289), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(289), Var("k"))))),
"Q": Mod(value=Mul(Const(19079), Ref("x")), modulus=Const(50110)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T04:02:21.004209Z | {
"verified": true,
"answer": 445,
"timestamp": "2026-02-08T04:02:21.004668Z"
} | a5eee6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 7064
},
"timestamp": "2026-02-10T16:33:54.439Z",
"answer": 445
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
498520 | comb_count_partitions_v1_349078426_579 | Let $n$ be the number of positive integers $t$ with $21 \leq t \leq 70$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 15$ and $1 \leq b \leq 4$, such that $t = 2a + 7b + 12$. Let $\text{result}$ be the number of integer partitions of $n$. Compute $\text{result}$. | 75,175 | 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=15)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:09:11.336666Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T13:09:11.339776Z"
} | d81cf4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2107
},
"timestamp": "2026-02-24T17:21:02.671Z",
"answer": 75127
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
2d5b90 | alg_poly3_min_v1_1218484723_7716 | Let $A$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 30$ such that $13a_1^2 + 2b_1^2 - 2a_1b_1 \le 962$. Find the minimum value of $3297a^3 + 24021a^2b - 9891ab^2 + 71592b^3$ over all positive integers $a$, $b$ with $1 \le a \le A$ and $1 \le b \le 155$. | 89,019 | graphs = [
Graph(
let={
"_n": Const(71592),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_min_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.055 | 2026-02-25T09:13:48.562230Z | {
"verified": true,
"answer": 89019,
"timestamp": "2026-02-25T09:13:48.617313Z"
} | 55f2ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 4435
},
"timestamp": "2026-03-30T06:04:12.902Z",
"answer": 89019
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
288398 | nt_count_divisible_and_v1_2080023795_14 | Let $m=9$ and $n=8$. Let $d_1$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = m$.
Consider all integers $t$ for which there exist integers $a$ and $b$ satisfying
\[1 \le a \le 6, \quad 1 \le b \le 8, \quad 24 \le t \le 162, \quad t = 15a + 9b.\]
Let $N$ be the number ... | 1,927 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": Const(8),
"upper": Const(46248),
"d1": 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"... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_SUM/SUM_DIVISIBLE",
"B3"
] | 895e54 | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"MOBIUS_SUM",
"SUM_DIVISIBLE"
] | 4 | 3.189 | 2026-02-08T11:30:07.821954Z | {
"verified": true,
"answer": 1927,
"timestamp": "2026-02-08T11:30:11.011111Z"
} | 661a0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 397,
"completion_tokens": 2534
},
"timestamp": "2026-02-08T20:35:47.611Z",
"answer": 1927
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"l... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
0f7d16 | comb_count_surjections_v1_1439011603_1328 | Let $n = 7$ and $k = 6$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 51$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 6a + 9b$. Compute the Bell number of the r... | 203 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM"
] | 1ae498 | comb_count_surjections_v1 | bell_mod | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.019 | 2026-02-08T16:01:59.653982Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T16:01:59.672863Z"
} | d1a5c5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 1049
},
"timestamp": "2026-02-24T19:39:30.465Z",
"answer": 203
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
a62893 | antilemma_sum_equals_v1_784195855_7888 | Let $n = 17$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 16$, $1 \leq j \leq 17$, and $i + j = n$. | 16 | graphs = [
Graph(
let={
"_n": Const(17),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.027 | 2026-02-08T09:36:22.145669Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T09:36:22.172393Z"
} | 55000b | 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": 243
},
"timestamp": "2026-02-24T11:34:42.569Z",
"answer": 16
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
b8130b | nt_num_divisors_compute_v1_153355830_1713 | Let $n = 66564$. Compute the number of positive divisors of $n$. | 27 | graphs = [
Graph(
let={
"n": Const(66564),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/LIOUVILLE_ONE",
"EULER_TOTIENT_SUM"
] | 457fb8 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"EULER_TOTIENT_SUM",
"LIOUVILLE_ONE",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-02-08T06:35:14.410364Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T06:35:14.420022Z"
} | a81cb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 454
},
"timestamp": "2026-02-13T01:47:27.109Z",
"answer": 27
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
87cada | sequence_fibonacci_compute_v1_153355830_688 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 48$.
Compute the $n$th Fibonacci number. | 46,368 | graphs = [
Graph(
let={
"_n": Const(48),
"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")), Re... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T04:08:01.950580Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T04:08:01.952048Z"
} | 87eca0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1072
},
"timestamp": "2026-02-10T15:30:24.559Z",
"answer": 46368
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
ee2c29_n | comb_count_partitions_v1_1419126231_1020 | A composer plans a musical suite with $n$ movements, where $n = 1 + 3 + 9 + 27$. Each movement has a duration of one unit, and the suite is divided into contiguous sections such that the sum of durations in each section forms a non-increasing sequence (e.g., 3+3+2+1). The number of distinct ways to structure the suite ... | 69,562 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_partitions_v1 | null | 3 | null | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T10:31:39.080379Z | null | d1d3da | ee2c29 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 11243
},
"timestamp": "2026-03-31T04:14:38.788Z",
"answer": 69562
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
db0f20 | nt_count_phi_equals_v1_2051736721_4209 | Let $T$ be the set of all integers $t$ such that $10 \leq t \leq 3621$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 206$, $1 \leq b \leq 429$, and $t = 3a + 7b$. Let $U$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 7$ and $1 \leq j \leq 9$ such that $\gcd(i, j) = 1$. Let... | 30,841 | graphs = [
Graph(
let={
"_m": Const(91699),
"_n": Const(61064),
"upper": 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')... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 66e6c4 | nt_count_phi_equals_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 0.576 | 2026-02-08T17:48:41.747569Z | {
"verified": true,
"answer": 30841,
"timestamp": "2026-02-08T17:48:42.323308Z"
} | f2a895 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 6056
},
"timestamp": "2026-02-18T08:35:07.934Z",
"answer": 30841
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0aadac | nt_count_gcd_equals_v1_1520064083_4689 | Let $k$ be the number of integers $t$ such that $10 \leq t \leq 336$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 42$, $1 \leq b \leq 30$, and $t = 3a + 7b$. Let $d$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 16$ such that $\gcd(i, j) = 1$. Determine the value... | 274 | graphs = [
Graph(
let={
"upper": Const(14365),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=42)), Geq(lef... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 66e6c4 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 1.11 | 2026-02-08T06:23:06.803632Z | {
"verified": true,
"answer": 274,
"timestamp": "2026-02-08T06:23:07.913876Z"
} | 9a9517 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 5452
},
"timestamp": "2026-02-12T23:31:56.755Z",
"answer": 274
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
999fcb_n | comb_count_partitions_v1_1218484723_3827 | A tilemaker produces rectangular tiles whose side lengths are integers between 1 and 8 for one dimension and 1 and 7 for the other. The perimeter of each tile is $2(a + b)$, but due to a labeling error, each tile is marked with the value $8a + 6b$ instead. The quality inspector records every distinct value of this inco... | 44,583 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-25T05:28:31.402444Z | null | f85fa0 | 999fcb | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T20:42:12.329Z",
"answer": 53174
},
{
... | 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": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
83abfc | sequence_lucas_compute_v1_655260480_4407 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 32$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 5$, and $t = 3a + 4b$. Let $L_n$ denote the $n$-th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $4... | 87,947 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:55:46.211950Z | {
"verified": true,
"answer": 87947,
"timestamp": "2026-02-08T17:55:46.213078Z"
} | 53b3b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 2217
},
"timestamp": "2026-02-18T09:44:44.883Z",
"answer": 87947
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
93dc95 | antilemma_cartesian_v1_124444284_8381 | Let $x$ be the number of ordered pairs $(m, n)$ such that $1 \leq m \leq 34$ and $1 \leq n \leq 47$. Let $S$ be the set of all positive integers $t$ satisfying the following conditions:
- $10 \leq t \leq 10748$,
- there exist positive integers $a$ and $b$ such that $1 \leq a \leq 638$, $1 \leq b \leq 1366$, and $t = 4... | 35,870 | graphs = [
Graph(
let={
"_n": Const(51459),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(34)), right=IntegerRange(start=Const(1), end=Const(47)))),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), ... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_CARTESIAN"
] | 35a59e | antilemma_cartesian_v1 | affine_mod | 4 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T09:40:09.795701Z | {
"verified": true,
"answer": 35870,
"timestamp": "2026-02-08T09:40:09.797441Z"
} | 12fc69 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 12093
},
"timestamp": "2026-02-24T11:40:50.821Z",
"answer": 35870
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
a91aea | comb_binomial_compute_v1_124444284_5676 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 36$. Let $k$ be the largest prime number $p$ such that $2 \le p \le 10$. Compute $\binom{n}{k}$. | 792 | graphs = [
Graph(
let={
"_m": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"_n": Const(2),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/B3/MAX_PRIME_BELOW"
] | f211b4 | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.004 | 2026-02-08T06:46:09.651817Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T06:46:09.656051Z"
} | 55f5c8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 460
},
"timestamp": "2026-02-15T17:45:20.947Z",
"answer": 792
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
1667be | algebra_vieta_sum_v1_1742523217_2255 | Let $B$ be the set of all integers $t$ such that $9 \leq t \leq 40$ and there exist positive integers $a \leq 4$, $b \leq 5$ satisfying $t = 5a + 4b$. Let $c$ be the number of elements in $B$. Let $S$ be the set of all real numbers $x$ such that
$$
2x^3 + c x^2 - 98x - 980 = 0.
$$
Let $\text{result}$ be the product of... | 43,694 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=2), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b')... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T04:38:39.982619Z | {
"verified": true,
"answer": 43694,
"timestamp": "2026-02-08T04:38:39.990950Z"
} | 06fa3a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 2125
},
"timestamp": "2026-02-11T21:43:10.802Z",
"answer": 43694
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e2b2b7 | modular_inverse_v1_1470522791_1130 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 3969$. Let $m = 137$. Find the smallest positive integer $x \leq 136$ such that $ax \equiv 1 \pmod{m}$. | 112 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3969)))), expr=Sum(Var("x"), Var("y")))),
"m": Const(137),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T13:26:49.928910Z | {
"verified": true,
"answer": 112,
"timestamp": "2026-02-08T13:26:49.938614Z"
} | 6336bb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1314
},
"timestamp": "2026-02-15T15:38:50.731Z",
"answer": 112
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1a4faf | comb_count_permutations_fixed_v1_655260480_5739 | Let $t = \sum_{k=0}^{5} (-1)^k \binom{5}{k}$ and $c = \sum_{k=0}^{6} (-1)^k \binom{6}{k}$. Let $k$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 5$ and $1 \leq j \leq 5$ such that $i + j = 7$. Define $\text{result} = \binom{8}{k} \cdot !(8 - k)$, where $!(8 - k)$ denotes the subfactorial of $8 ... | 60,075 | graphs = [
Graph(
let={
"n2": Const(5),
"t": 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(5),
"b": Const(1),
"n1": Sum(Ref("a"), Ref("b")),
"c": Sum... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | b9499e | comb_count_permutations_fixed_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.014 | 2026-02-08T18:38:43.678551Z | {
"verified": true,
"answer": 60075,
"timestamp": "2026-02-08T18:38:43.692651Z"
} | f0eff6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1355
},
"timestamp": "2026-02-18T18:15:16.921Z",
"answer": 60075
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
9b723a | geo_count_lattice_triangle_v1_1218484723_710 | Let $M = \left|136 \cdot S + 30 \cdot (-276)\right|$, where $S = \left|\{ v \in [49, 19600] : \exists\, a,b \in \{1,\dots,20\} \text{ such that } 9a^2 + 24ab + 16b^2 = v \}\right|$. Let $R = \gcd(136, 276) + \gcd(|30 - 136|, |128 - 276|) + \gcd(|0 - 30|, |0 - 128|)$. Compute $\frac{M + 2 - R}{2}$. | 4,561 | graphs = [
Graph(
let={
"_n": Const(136),
"area_2x": Abs(arg=Sum(Mul(Const(value=136), CountOverSet(set=SolutionsSet(var=Var(name='v'), condition=And(Geq(left=Var(name='v'), right=Const(value=49)), Leq(left=Var(name='v'), right=Const(value=19600)), Exists(var=Tuple(elements=[Var(name... | GEOM | NT | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.005 | 2026-02-25T02:27:18.574178Z | {
"verified": true,
"answer": 4561,
"timestamp": "2026-02-25T02:27:18.579272Z"
} | 527abd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T01:00:17.072Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 2.74,
"mid": 4.78,
"hi": 6.68
} | ||
fdc496 | modular_sum_quadratic_residues_v1_1978505735_1852 | Let $x$ and $y$ be positive integers such that $xy = 42436$. Define $s$ to be the minimum value of $x + y$ over all such pairs. Let $p$ be the largest prime number at most $s$. Compute the remainder when $10723 \cdot \frac{p(p-1)}{4}$ is divided by $83590$. | 52,024 | graphs = [
Graph(
let={
"_m": Const(4),
"_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(42436)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T16:28:46.333989Z | {
"verified": true,
"answer": 52024,
"timestamp": "2026-02-08T16:28:46.338427Z"
} | ff0e14 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2556
},
"timestamp": "2026-02-17T05:00:28.969Z",
"answer": 52024
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
62d6f5 | nt_count_gcd_equals_v1_1248542787_284 | Let $k = 353$. Let $d$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 706$. Determine the number of positive integers $n \leq 50000$ such that $\gcd(n, k) = d$. | 141 | graphs = [
Graph(
let={
"upper": Const(50000),
"k": Const(353),
"d": 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')... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 4.771 | 2026-02-08T03:02:40.459459Z | {
"verified": true,
"answer": 141,
"timestamp": "2026-02-08T03:02:45.229961Z"
} | 5336eb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 781
},
"timestamp": "2026-02-09T02:21:23.346Z",
"answer": 141
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.67,
"hi": -2.17
} | ||
f67315 | nt_count_with_divisor_count_v1_784195855_341 | Let $A$ be the number of positive integers $n \leq 20164$ such that $n$ has exactly 13 positive divisors. Let $p$ be the largest prime number less than or equal to 254. Compute the value of $$
A \bmod p + 5003 \cdot (A \bmod 397).
$$ | 5,004 | graphs = [
Graph(
let={
"upper": Const(20164),
"div_count": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"Q": Sum(Mod(valu... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_with_divisor_count_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.926 | 2026-02-08T03:06:35.260912Z | {
"verified": true,
"answer": 5004,
"timestamp": "2026-02-08T03:06:36.187164Z"
} | af68f6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 813
},
"timestamp": "2026-02-10T16:13:05.865Z",
"answer": 5004
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b3927a | nt_count_with_divisor_count_v1_458359167_101 | Let $n$ be a positive integer. Define $d(n)$ to be the number of positive divisors of $n$. Let $p$ be the largest prime number satisfying $2 \leq p \leq 3$. Compute the number of positive integers $n \leq 32768$ such that $d(n) = p$. Let this count be $C$. Find the remainder when $47403 \cdot C$ is divided by $63592$. | 19,574 | graphs = [
Graph(
let={
"upper": Const(32768),
"div_count": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Co... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.387 | 2026-02-08T02:59:25.209886Z | {
"verified": true,
"answer": 19574,
"timestamp": "2026-02-08T02:59:27.596495Z"
} | df3334 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1124
},
"timestamp": "2026-02-10T12:02:14.378Z",
"answer": 19574
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
c00af4 | comb_sum_binomial_row_v1_1520064083_4216 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $|P|$ denote the number of elements in $P$. Compute $|P|^{12}$. | 4,096 | graphs = [
Graph(
let={
"n": Const(12),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T06:08:40.554205Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T06:08:40.555295Z"
} | d2f43a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 385
},
"timestamp": "2026-02-19T00:35:54.399Z",
"answer": 1
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
5243fe | nt_count_coprime_and_v1_458359167_2412 | Let $n$ be a positive integer such that $1 \leq n \leq 27419$, $\gcd(n, 3) = 1$, and $\gcd(n, 11) = 1$. Let $A$ be the number of such integers $n$. Let $d$ be the smallest divisor of $20449$ that is at least $2$. Compute the Bell number $B_r$, where $r$ is the remainder when $|A|$ is divided by $d$. Determine the value... | 4,140 | graphs = [
Graph(
let={
"upper": Const(27419),
"k1": Const(3),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_coprime_and_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.975 | 2026-02-08T05:24:10.549630Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T05:24:13.524694Z"
} | 0bffe7 | 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": 950
},
"timestamp": "2026-02-12T08:03:40.189Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
391884 | nt_count_divisible_v1_124444284_70 | Let $U = 80656$. Let $D$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 9$, $1 \le b \le 3$, $10 \le t \le 48$, and $t = 3a + 7b$. Let $d$ be the number of elements in $D$. Let $T$ be the set of all integers $n$ such that $\phi(2) \le n \le U$ and $n$ is divisible b... | 2,987 | graphs = [
Graph(
let={
"upper": Const(80656),
"divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_2"
] | 9858be | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM",
"ONE_PHI_2"
] | 2 | 3.151 | 2026-02-08T02:56:46.322711Z | {
"verified": true,
"answer": 2987,
"timestamp": "2026-02-08T02:56:49.473277Z"
} | ab8a37 | 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": 3888
},
"timestamp": "2026-02-09T13:34:36.168Z",
"answer": 2987
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"statu... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
bbf71c | nt_sum_gcd_range_mod_v1_458359167_2232 | Let $N$ be the number of prime numbers less than or equal to $17569$. Let $k = 540$ and $M = 11743$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Find the remainder when $\text{sum}$ is divided by $M$. | 9,725 | graphs = [
Graph(
let={
"_n": Const(17569),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k": Const(540),
"M": Const(11743),
"sum": Summation(var="n", start=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"COUNT_PRIMES"
] | 07c874 | nt_sum_gcd_range_mod_v1 | null | 3 | 0 | [
"COUNT_PRIMES",
"LIN_FORM"
] | 2 | 1.157 | 2026-02-08T05:13:31.023770Z | {
"verified": true,
"answer": 9725,
"timestamp": "2026-02-08T05:13:32.180579Z"
} | 824af6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 3280
},
"timestamp": "2026-02-12T05:57:00.415Z",
"answer": 9725
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
97df85 | comb_count_surjections_v1_1918700295_3640 | Let $T$ be the set of integers $t$ such that $5 \leq t \leq 14$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j$ equals the number of element... | 150 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=... | 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 | 0.017 | 2026-02-08T08:47:40.263589Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T08:47:40.280403Z"
} | e5aeb5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 1260
},
"timestamp": "2026-02-24T09:59:21.233Z",
"answer": 150
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
a4702b_n | geo_visible_lattice_v1_1218484723_4599 | A city planner designs a grid park of size $157 \times 157$, with trees planted at each lattice point $(x,y)$. A tree at $(x,y)$ is visible from the origin if $\gcd(x,y) = 1$. Let $N$ be the number of such visible trees. The planner organizes a festival where attendees are assigned to groups in every possible way — the... | 52 | GEOM | GEOM | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | null | null | null | 2.357 | 2026-02-25T06:16:14.019591Z | null | 5b3b37 | a4702b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 24697
},
"timestamp": "2026-03-30T21:59:01.581Z",
"answer": 52
},
{
"id... | 1 | [] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |||
4d6cc5 | modular_mod_compute_v1_1978505735_4350 | Let $m$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = s$, where $s$ is the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1,y_1)$ of positive integers such that $x_1 y_1 = p$, where $p$ is the maximum value of $x_2 y_2$ over all ordered pairs $(x_2,y_2)$ of... | 68,415 | graphs = [
Graph(
let={
"_m": Const(172),
"_n": Const(77196),
"a": Const(111),
"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")... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3/B1"
] | 644515 | modular_mod_compute_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.01 | 2026-02-08T18:11:43.577847Z | {
"verified": true,
"answer": 68415,
"timestamp": "2026-02-08T18:11:43.587792Z"
} | 8b911d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2070
},
"timestamp": "2026-02-18T14:40:21.140Z",
"answer": 68415
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
351f6f | comb_catalan_compute_v1_655260480_6015 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 17$ and there exist positive integers $a \leq 3$, $b \leq 4$ satisfying $t = 3a + 2b$. Let $n$ be the number of elements in $T$. Compute the remainder when $22604 \cdot C_n$ is divided by $94341$, where $C_n$ denotes the $n$-th Catalan number. | 5,759 | graphs = [
Graph(
let={
"_n": Const(94341),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:46:40.484732Z | {
"verified": true,
"answer": 5759,
"timestamp": "2026-02-08T18:46:40.487220Z"
} | 795add | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2096
},
"timestamp": "2026-02-18T19:30:30.335Z",
"answer": 5759
},
{... | 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": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
8cf102 | modular_inverse_v1_548369836_294 | Let $a = 462$ and $m = 601$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 90000$. Define $u$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $T$ be the set of all integers $x$ with $1 \le x \le u$ such that
$$
462x \equiv 1 \pmod{601}.
$$
Determine the value ... | 147 | graphs = [
Graph(
let={
"a": Const(462),
"m": Const(601),
"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(90000)))),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.027 | 2026-02-08T02:51:29.000558Z | {
"verified": true,
"answer": 147,
"timestamp": "2026-02-08T02:51:29.027568Z"
} | 9a0989 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1460
},
"timestamp": "2026-02-08T20:17:51.709Z",
"answer": 147
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -1.89,
"mid": 0.13,
"hi": 1.92
} | ||
ae30bc | antilemma_sum_primes_v1_151522320_129 | Let $x$ be the sum of all prime numbers $n$ such that $2 \leq n \leq 4$. Compute the remainder when $38599 \cdot x$ is divided by $57796$. | 19,607 | graphs = [
Graph(
let={
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(4)), IsPrime(Var("n"))))),
"Q": Mod(value=Mul(Const(38599), Ref("x")), modulus=Const(57796)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_PRIMES | [
"SUM_PRIMES"
] | 83231d | antilemma_sum_primes_v1 | null | 2 | 0 | [
"SUM_PRIMES"
] | 1 | 0.001 | 2026-02-08T02:59:57.033038Z | {
"verified": true,
"answer": 19607,
"timestamp": "2026-02-08T02:59:57.033769Z"
} | a88088 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 274
},
"timestamp": "2026-02-08T23:31:11.769Z",
"answer": 19607
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
ae5fbe | nt_count_gcd_equals_v1_1915831931_1788 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 2809$. Let $d = 53$. Determine the number of positive integers $n$ such that $1 \leq n \leq 39601$ and $\gcd(n, k) = d$. | 374 | graphs = [
Graph(
let={
"upper": Const(39601),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2809)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 3.441 | 2026-02-08T16:27:31.555337Z | {
"verified": true,
"answer": 374,
"timestamp": "2026-02-08T16:27:34.996157Z"
} | dc2043 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1014
},
"timestamp": "2026-02-17T03:39:38.387Z",
"answer": 374
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"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
} | ||
f26e46 | modular_modexp_compute_v1_1520064083_2604 | Let $a = 19$, $m = 6660$, and $n = 6301$. Let $d$ be the number of positive integers $k$ such that $1 \leq k \leq m$ and $222$ divides $k$. Let $e$ be the number of positive integers $n$ such that $1 \leq n \leq n$ and $\gcd(n, d) = 1$. Let $r = a^e \bmod 69696$. Find the smallest positive integer $Q$ such that the $Q$... | 1,980 | graphs = [
Graph(
let={
"_m": Const(6660),
"_n": Const(6301),
"a": Const(19),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=CountOverSet(set=SolutionsSet(var=Var("k"), con... | NT | null | COMPUTE | sympy | C2 | [
"C2/C4"
] | 90526d | modular_modexp_compute_v1 | null | 7 | 0 | [
"C2",
"C4"
] | 2 | 0.005 | 2026-02-08T04:53:00.355761Z | {
"verified": true,
"answer": 1980,
"timestamp": "2026-02-08T04:53:00.360785Z"
} | d53ef2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 3540
},
"timestamp": "2026-02-11T22:24:34.469Z",
"answer": 1980
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemm... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
44bf91 | sequence_count_fib_divisible_v1_124444284_835 | Let $\text{upper}$ be the number of integers $t$ such that $22 \le t \le 1540$ and there exist positive integers $a$ and $b$ with $1 \le a \le 38$, $1 \le b \le 126$, and $t = 14a + 8b$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \le n \le \text{upper}$ and the $n$-th Fibonacci number is di... | 197 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": 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=38)), Geq(left=V... | NT | null | COUNT | sympy | C5 | [
"C5",
"LIN_FORM"
] | 029967 | sequence_count_fib_divisible_v1 | digits_weighted_mod | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.036 | 2026-02-08T03:32:54.299583Z | {
"verified": true,
"answer": 197,
"timestamp": "2026-02-08T03:32:54.335271Z"
} | 7ff2c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 316,
"completion_tokens": 3314
},
"timestamp": "2026-02-09T22:47:38.176Z",
"answer": 197
},
{
"id... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lem... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
ccadaa | algebra_vieta_sum_v1_971394319_261 | Let $r_1$ and $r_2$ be the roots of the equation $x^2 + 5x + 6 = 0$. Let $p$ be the product of all values of $x$ that satisfy this equation. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|p| + 2$. | 6 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=2)), Mul(Const(value=5), Var(name='x')), Const(value=6)), right=Const(value=0)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name=... | NT | null | COMPUTE | sympy | B3 | [
"COMB1"
] | 567f58 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"B3",
"COMB1"
] | 2 | 0.062 | 2026-02-08T12:55:07.325826Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T12:55:07.387623Z"
} | 6de1b6 | 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": 462
},
"timestamp": "2026-02-15T08:05:22.527Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9cc6f0 | sequence_fibonacci_compute_v1_1520064083_7646 | Let $n = 23$. Define $F_n$ to be the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $S = \sum_{k=1}^{35} k$. Compute the remainder when $S - F_n$ is divided by $78612$. | 50,585 | graphs = [
Graph(
let={
"n": Const(23),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sub(Summation(var="k", start=Const(1), end=Const(35), expr=Var("k")), Ref("result")), modulus=Const(78612)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 5c63b0 | sequence_fibonacci_compute_v1 | negation_mod | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T09:13:50.286632Z | {
"verified": true,
"answer": 50585,
"timestamp": "2026-02-08T09:13:50.287283Z"
} | af0347 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 614
},
"timestamp": "2026-02-14T01:37:24.218Z",
"answer": 50585
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
36ee58 | algebra_poly_eval_v1_349078426_319 | Let $m = 70652$ and $z$ be the smallest integer $d \geq 2$ that divides $77077$. Let $A$ be the number of integers $t$ with $34 \leq t \leq 61$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 6a + 9b + 19$. Let $B$ be the number of positive integers $p$ for which there exi... | 61,199 | graphs = [
Graph(
let={
"_m": Const(70652),
"_n": Const(2),
"z": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77077))))),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("t")... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS",
"LIN_FORM"
] | 860791 | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.008 | 2026-02-08T12:55:51.841389Z | {
"verified": true,
"answer": 61199,
"timestamp": "2026-02-08T12:55:51.849777Z"
} | 793116 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1480
},
"timestamp": "2026-02-15T08:28:27.972Z",
"answer": 61199
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
73d464 | nt_count_digit_sum_v1_153355830_2449 | Let $S$ be the set of all integers $t$ with $11 \leq t \leq 56$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 7$, $1 \leq b \leq 4$, and $t = 4a + 7b$. Let $T$ be the number of elements in $S$.
Let $U$ be the set of all positive integers $n$ such that $1 \leq n \leq 99999$ and the sum of... | 19,351 | graphs = [
Graph(
let={
"_n": Const(54704),
"upper": Const(99999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(n... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 3.643 | 2026-02-08T07:08:29.448112Z | {
"verified": true,
"answer": 19351,
"timestamp": "2026-02-08T07:08:33.091402Z"
} | 2bbfe6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 3008
},
"timestamp": "2026-02-13T08:23:42.195Z",
"answer": 19351
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5d6fa5 | nt_max_prime_below_v1_784195855_1535 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 24$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $n \ge m$ and $n \le 19321$. | 19,319 | graphs = [
Graph(
let={
"upper": Const(19321),
"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 | 0.448 | 2026-02-08T05:07:48.169782Z | {
"verified": true,
"answer": 19319,
"timestamp": "2026-02-08T05:07:48.617524Z"
} | e67edc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 2886
},
"timestamp": "2026-02-11T22:56:48.468Z",
"answer": 19319
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
382098 | geo_visible_lattice_v1_1742523217_2241 | A lattice point $(x, y)$ is said to be visible from the origin if $\gcd(x, y) = 1$. Let $n = 169$. Compute the remainder when $71567$ times the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$ is divided by $85161$. | 49,225 | graphs = [
Graph(
let={
"n": Const(169),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(71567), Ref("result")), modulus=Const(85161)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.611 | 2026-02-08T04:37:28.646316Z | {
"verified": true,
"answer": 49225,
"timestamp": "2026-02-08T04:37:29.256833Z"
} | 852426 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 27988
},
"timestamp": "2026-02-24T01:30:53.766Z",
"answer": 49225
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
50bb50 | nt_count_coprime_v1_784195855_10277 | Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq 52441$ and $\gcd(n, 3) = 1$. Let $s$ be the number of positive integers $n$ such that $1 \leq n \leq 74425$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $d = s - r$. Compute the remainder when $d$ is divided by $96012$. | 67,816 | graphs = [
Graph(
let={
"upper": Const(52441),
"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")), Const(1))))),
"_c": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | fba717 | nt_count_coprime_v1 | negation_mod | 5 | 0 | [
"L3C"
] | 1 | 9.408 | 2026-02-08T17:33:07.206956Z | {
"verified": true,
"answer": 67816,
"timestamp": "2026-02-08T17:33:16.614531Z"
} | 890f3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 948
},
"timestamp": "2026-02-18T07:35:25.832Z",
"answer": 67816
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b4c7a3 | modular_inverse_v1_48377204_1409 | Let $a = 598$ and $m = 977$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 238144$. Find the smallest positive integer $x_1$ such that $1 \le x_1 \le s$ and $598x_1 \equiv 1 \pmod{977}$. | 116 | graphs = [
Graph(
let={
"a": Const(598),
"m": Const(977),
"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(238144))))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.062 | 2026-02-08T16:05:26.516440Z | {
"verified": true,
"answer": 116,
"timestamp": "2026-02-08T16:05:26.578939Z"
} | 60f786 | 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": 1860
},
"timestamp": "2026-02-16T21:07:37.098Z",
"answer": 116
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c352e6 | nt_lcm_compute_v1_1742523217_4558 | Let $m = 3$ and let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $2156$. Let $a$ be the number of positive integers $j$ such that $j \leq n$ and $j^m \leq 10021812416$. Let $b = 1620$ and let $\text{result} = \text{lcm}(a, b)$. Find the remainder when $65536 - \text{result}$ is divided by $92965$. | 29,041 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": SumOverDivisors(n=Const(value=2156), var='d', expr=EulerPhi(n=Var(name='d'))),
"a": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Ref("_m")), Con... | NT | null | COMPUTE | sympy | K3 | [
"K3/C3"
] | 712e3b | nt_lcm_compute_v1 | null | 6 | 0 | [
"C3",
"K3"
] | 2 | 0.002 | 2026-02-08T08:58:06.091533Z | {
"verified": true,
"answer": 29041,
"timestamp": "2026-02-08T08:58:06.093678Z"
} | c37d27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1479
},
"timestamp": "2026-02-13T22:36:25.505Z",
"answer": 29041
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
04816c | comb_bell_compute_v1_168721529_970 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 216$, and $\gcd(p, q) = 1$. Let $n$ be the largest integer $k$ such that $m^k$ divides $5^{64} - 3^{64}$. Compute the number of partitions of an $n$-element set. | 21,147 | graphs = [
Graph(
let={
"_m": Const(64),
"_n": Const(3),
"n": MaxKDivides(target=Sub(Pow(Const(5), Const(64)), Pow(Ref("_n"), Ref("_m"))), base=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LTE_DIFF_P2"
] | 287135 | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LTE_DIFF_P2"
] | 2 | 0.003 | 2026-02-08T13:21:48.987115Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T13:21:48.989848Z"
} | 70c5c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 2603
},
"timestamp": "2026-02-09T11:23:16.097Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
b0b952 | diophantine_product_count_v1_48377204_1015 | Let $k = 360$ and $u = 113$. Define $r$ to be the number of positive integers $x$ such that $1 \le x \le u$, $x$ divides $k$, and $\frac{k}{x} \le u$. Let $c$ be the minimum value of $x_1 + y$ over all ordered pairs $(x_1, y)$ of positive integers such that $x_1 y = 6002500$. Compute $c - r$. | 4,882 | graphs = [
Graph(
let={
"k": Const(360),
"upper": Const(113),
"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"
] | fc629c | diophantine_product_count_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-08T15:51:51.526061Z | {
"verified": true,
"answer": 4882,
"timestamp": "2026-02-08T15:51:51.539786Z"
} | 19f633 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 2837
},
"timestamp": "2026-02-16T14:57:29.256Z",
"answer": 4882
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
968734 | nt_count_gcd_equals_v1_1918700295_3730 | Determine the number of positive integers $n$ such that $1 \leq n \leq 32768$ and $\gcd(n, 248) = 124$. Compute $1225$ minus this number. | 1,093 | graphs = [
Graph(
let={
"upper": Const(32768),
"k": Const(248),
"d": Const(124),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
... | NT | null | COUNT | sympy | C3 | [
"C3/B3"
] | 9118ce | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B3",
"C3"
] | 2 | 3.342 | 2026-02-08T08:50:31.527593Z | {
"verified": true,
"answer": 1093,
"timestamp": "2026-02-08T08:50:34.869637Z"
} | c62ebe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 948
},
"timestamp": "2026-02-13T22:39:57.186Z",
"answer": 1093
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"le... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
eab50f | alg_poly_preperiod_count_v1_601307018_10487 | For a non-negative integer $a$, define a sequence by:
\[
N = (a^2 - 20) \bmod 67,\quad
M = (N^2 - 20) \bmod 67,\quad
R = (M^2 - 20) \bmod 67,\quad
S = (R^2 - 20) \bmod 67.
\]
Let $Q$ be the number of integers $a$ with $0 \le a \le 20836$ such that $S = M$ and $R \ne M$. Find $Q$. | 1,866 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-20)), modulus=Const(67)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-20)), modulus=Const(67)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-20)), modulus=Const(67)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.016 | 2026-03-10T10:57:49.140907Z | {
"verified": true,
"answer": 1866,
"timestamp": "2026-03-10T10:57:49.157036Z"
} | 1b9c0f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 5342
},
"timestamp": "2026-04-19T13:55:40.280Z",
"answer": 1866
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
a370d0 | v1_endings_v1_677425708_877 | Let $n = 47868$, $m = 22334$, and $p = 7$. Define $v_p(k!)$ to be the largest integer $e$ such that $p^e$ divides $k!$.
Let $a = v_p(n!)$, $b = v_p(m!)$, and $c = v_p((n - m)!)$, where $n - m = 25534$. Define $t = a + b - c$.
Find the remainder when $t$ is divided by $100000$. | 7,441 | graphs = [
Graph(
let={
"n_val": Const(47868),
"m_val": Const(22334),
"nm_val": Const(25534),
"p_val": Const(7),
"n_fact": Factorial(Ref("n_val")),
"m_fact": Factorial(Ref("m_val")),
"nm_fact": Factorial(Ref("nm_val")),
... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T03:50:03.478299Z | {
"verified": true,
"answer": 7441,
"timestamp": "2026-02-08T03:50:03.478881Z"
} | 452e0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 2513
},
"timestamp": "2026-02-09T13:44:31.388Z",
"answer": 7441
},
{
"i... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "n... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
c41668 | comb_catalan_compute_v1_2051736721_3725 | Let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $n$ be the number of such ordered pairs. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $18329 \cdot C_n$ is divided by 53085. | 22,349 | graphs = [
Graph(
let={
"_m": Const(18329),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(11)))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), conditi... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1"
] | 1007b3 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.004 | 2026-02-08T17:30:08.451708Z | {
"verified": true,
"answer": 22349,
"timestamp": "2026-02-08T17:30:08.456205Z"
} | b282e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1331
},
"timestamp": "2026-02-18T03:07:19.303Z",
"answer": 22349
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
d1f6da | nt_min_with_divisor_count_v1_1915831931_678 | Let $n = 44121$ and $U = 65536$. Define $T$ as the set of all integers $t$ such that $25 \leq t \leq 55$ and $t = 10a + 4b + 11$ for some integers $a \in \{1,2\}$ and $b \in \{1,2,3,4,5,6\}$. Let $d$ be the number of elements in $T$. Let $r$ be the smallest positive integer $n \leq U$ such that the number of positive d... | 72,436 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(65536),
"div_count": 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(na... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 3.053 | 2026-02-08T15:36:49.140614Z | {
"verified": true,
"answer": 72436,
"timestamp": "2026-02-08T15:36:52.193335Z"
} | 119ffa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1684
},
"timestamp": "2026-02-16T10:17:16.876Z",
"answer": 72436
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
727615 | nt_max_prime_below_v1_1742523217_1669 | Let $S$ be the set of all ordered pairs $(p, q)$ of positive integers such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Determine the largest prime number $n$ such that $k \leq n \leq 74529$. | 74,527 | graphs = [
Graph(
let={
"upper": Const(74529),
"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 | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.698 | 2026-02-08T04:06:03.991236Z | {
"verified": true,
"answer": 74527,
"timestamp": "2026-02-08T04:06:05.688920Z"
} | 134478 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 7637
},
"timestamp": "2026-02-10T15:18:15.712Z",
"answer": 74527
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
0147a8 | diophantine_fbi2_min_v1_2051736721_753 | Let $k = \sum_{k_1=1}^{8} \phi(k_1) \left\lfloor \frac{8}{k_1} \right\rfloor$, where $\phi$ denotes Euler's totient function. Find the smallest integer $d$ such that $5 \leq d \leq 46$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. | 6 | graphs = [
Graph(
let={
"_n": Const(8),
"k": Summation(var="k1", start=Const(1), end=Const(8), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_n"), Var("k1"))))),
"upper": Const(46),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"... | NT | null | EXTREMUM | sympy | B1 | [
"K2"
] | 6897ab | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B1",
"K2"
] | 2 | 0.087 | 2026-02-08T15:39:15.439658Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T15:39:15.526937Z"
} | 31ac3c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1165
},
"timestamp": "2026-02-16T11:09:30.585Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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