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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
e95c28_l | antilemma_cartesian_v1_1520064083_3432 | Let $n = 32$. Let $x$ be the number of ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 12$ and $1 \leq b \leq 31$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive integers such that $x_1$ and $x_2$ are odd and $x_1 + x_2 = n$. Let $y$ be the number of elements in $S$. Compute $x + (... | 65,908 | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_CARTESIAN"
] | 392991 | antilemma_cartesian_v1 | mod_exp | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T05:39:08.859716Z | {
"verified": false,
"answer": 388,
"timestamp": "2026-02-08T05:39:08.860857Z"
} | 1a0840 | e95c28 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 800
},
"timestamp": "2026-02-24T04:16:47.107Z",
"answer": 65908
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |
947a1b | algebra_quadratic_discriminant_v1_717093673_4224 | Let $a = -10$, $b = 1$, and $c = -5$. Compute the discriminant $D = b^2 - 4ac$. Define $\alpha = 1$ if $D > 0$ and $0$ otherwise. Define $\beta = 1$ if $D = 0$ and $0$ otherwise. Let $r = 2\alpha + \beta$. Compute $10 - r$. | 10 | graphs = [
Graph(
let={
"a": Const(-10),
"b": Const(1),
"c": Const(-5),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Con... | NT | null | COMPUTE | sympy | K2 | [
"COPRIME_PAIRS/COPRIME_PAIRS",
"LIN_FORM"
] | d27ef1 | algebra_quadratic_discriminant_v1 | negation_mod | 2 | 0 | [
"COPRIME_PAIRS",
"K2",
"LIN_FORM"
] | 3 | 0.04 | 2026-02-08T18:06:17.297704Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T18:06:17.337371Z"
} | ff4cc7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 229
},
"timestamp": "2026-02-16T12:06:13.490Z",
"answer": 10
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"sta... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c86fde | algebra_quadratic_discriminant_v1_1978505735_2277 | Let $c = 2$. Let $m$ be the number of integers $t$ with $14 \leq t \leq 44$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 6$, and $t = 10a + 4b$. Let $a = -2$, $b = -16$, $c = -32$, and let $D = b^2 - 4ac$. Define $r = 2$ if $D > 0$, $r = 1$ if $D = 0$, and $r = 0$ otherwise. Let $p$... | 1 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(n... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | dbd266 | algebra_quadratic_discriminant_v1 | bell_mod | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.01 | 2026-02-08T16:48:37.379194Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:48:37.388695Z"
} | 4c4c2d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 528
},
"timestamp": "2026-02-16T07:53:53.726Z",
"answer": 1
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c92d52 | modular_count_residue_v1_153355830_1711 | Let $m = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 450$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be the number of elements in $S$. Compute the number of positive integers $n \leq 76176$ suc... | 7,618 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(76176),
"m": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"r": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"K2"
] | 5d07bf | modular_count_residue_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 5.392 | 2026-02-08T06:34:57.850216Z | {
"verified": true,
"answer": 7618,
"timestamp": "2026-02-08T06:35:03.242458Z"
} | b024d4 | 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": 1653
},
"timestamp": "2026-02-13T01:49:30.269Z",
"answer": 7618
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
611525 | geo_count_lattice_triangle_v1_124444284_5007 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3600$. Define $A = |128s + 22 \cdot (-4)|$. Let $B = \gcd(120, 4) + \gcd(|22 - 120|, |128 - 4|) + \gcd(22, C)$, where $C$ is the number of positive integers $p$ for which there exists a positive integer $q > p$ ... | 7,633 | graphs = [
Graph(
let={
"_m": Const(128),
"_n": Const(4),
"area_2x": Abs(arg=Sum(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Mul(Var(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.008 | 2026-02-08T06:20:45.458216Z | {
"verified": true,
"answer": 7633,
"timestamp": "2026-02-08T06:20:45.466247Z"
} | c82d47 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 779
},
"timestamp": "2026-02-15T17:26:35.725Z",
"answer": 8719
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
aafdc2 | antilemma_sum_factor_cartesian_v1_784195855_721 | Let $d$ be a positive divisor of $\gcd(7, 11)$. Define
$$
\mu = \sum_{d \mid \gcd(7,11)} \mu(d),
$$
where $\mu(d)$ is the M\"obius function.
Let $P$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 16$ and $1 \leq j \leq 16$ such that the above sum $\mu$ is nonzero. Let $x$ be the sum of $i \cd... | 18,496 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=7), b=Const(value=11)), var='d', expr=MoebiusMu(n=Var(name='d'))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(1... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME"
] | 1428b5 | antilemma_sum_factor_cartesian_v1 | null | 2 | 0 | [
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T04:33:57.087099Z | {
"verified": true,
"answer": 18496,
"timestamp": "2026-02-08T04:33:57.087920Z"
} | 669a2b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 609
},
"timestamp": "2026-02-18T12:03:09.820Z",
"answer": 18496
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V5",
"st... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
a7b722 | alg_poly4_sum_v1_1218484723_4091 | Let
$$M = \min\{64b_1^{3} - 144a_1b_1^{2} + 108a_1^{2}b_1 + 98a_1^{3} : 1 \le a_1 \le 29,\ 1 \le b_1 \le 29\}.$$
Consider all ordered pairs $(a,b)$ of positive integers with
$$1 \le a \le M \quad \text{and} \quad 1 \le b \le 126.$$
Compute the remainder when
$$\sum_{(a,b)} \bigl(81b^{4} + 54a^{2}b^{2} + 17a^{4} + 108... | 274 | graphs = [
Graph(
let={
"_n": Const(12),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")])... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | alg_poly4_sum_v1 | null | 7 | 0 | [
"POLY3_MIN"
] | 1 | 0.045 | 2026-02-25T05:44:14.218102Z | {
"verified": true,
"answer": 274,
"timestamp": "2026-02-25T05:44:14.263241Z"
} | e35bbd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 7454
},
"timestamp": "2026-03-29T13:43:42.651Z",
"answer": 73673
},
{
... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
a3c56d | nt_count_with_divisor_count_v1_1520064083_5160 | Let $n$ be a positive integer such that $1 \leq n \leq 41616$ and the number of positive divisors of $n$ is exactly $14$. Compute the number of such integers $n$. | 134 | graphs = [
Graph(
let={
"upper": Const(41616),
"div_count": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_1",
"ONE_PHI_2"
] | 6e9723 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM",
"ONE_PHI_1",
"ONE_PHI_2"
] | 3 | 4.671 | 2026-02-08T06:39:18.721577Z | {
"verified": true,
"answer": 134,
"timestamp": "2026-02-08T06:39:23.392179Z"
} | f76015 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 2019
},
"timestamp": "2026-02-13T03:01:03.599Z",
"answer": 134
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
0abf33 | nt_sum_divisors_range_v1_124444284_1461 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Define $u$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Compute the sum of the number of positive divisors of $n$ for all integers $n$ from $1$ to $u$, inclusive. That is, evaluate
\[
\sum_{n=1}^{u} \tau(n... | 43,776 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"result": S... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.364 | 2026-02-08T03:54:21.026251Z | {
"verified": true,
"answer": 43776,
"timestamp": "2026-02-08T03:54:21.390494Z"
} | 4f931e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 5417
},
"timestamp": "2026-02-10T14:47:59.751Z",
"answer": 43776
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
080701 | antilemma_sum_equals_v1_1125832087_490 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 45$, $1 \leq i \leq 44$, and $1 \leq j \leq 45$. | 44 | graphs = [
Graph(
let={
"_n": Const(45),
"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(44)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.007 | 2026-02-08T03:07:26.383651Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T03:07:26.390481Z"
} | 7e72fb | 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": 316
},
"timestamp": "2026-02-10T13:02:27.573Z",
"answer": 44
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
e87919 | sequence_count_fib_divisible_v1_1820931509_274 | Let $n = 51442$ and $u = 645$. Let $r$ be the number of positive integers $k \leq u$ such that the $k$-th Fibonacci number is divisible by 13. Let $c$ be the sum of all real solutions $x$ to the equation $x^2 - 1891x - 47900 = 0$. Compute the remainder when $c \cdot r$ is divided by $n$. | 19,646 | graphs = [
Graph(
let={
"_n": Const(51442),
"upper": Const(645),
"d": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | e2aa68 | sequence_count_fib_divisible_v1 | affine_mod | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.029 | 2026-02-08T11:27:54.837350Z | {
"verified": true,
"answer": 19646,
"timestamp": "2026-02-08T11:27:54.866672Z"
} | c1fbbe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1659
},
"timestamp": "2026-02-14T14:39:32.769Z",
"answer": 19646
},
... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
033beb_l | diophantine_fbi2_min_v1_1116507919_508 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Define $m$ to be the minimum element of $T$. Let $D$ be the set of all integers $d$ such that $m \leq d \leq 45$, $d$ divides 35, and $\frac{35}{d} \geq 4$. Determine ... | 53,299 | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T02:37:38.612899Z | {
"verified": false,
"answer": 53199,
"timestamp": "2026-02-08T02:37:38.617944Z"
} | 0b2661 | 033beb | legacy_text | CC BY 4.0 | [
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} | |
84b945 | nt_min_with_divisor_count_v1_677425708_3527 | Let $n = 44121$ and let $u = 28561$. Define $d$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 4500$. Let $S$ be the set of all integers $k$ such that $1 \le k \le u$ and the number of positive divisors of $k$ is equal to $d$. Deter... | 81,976 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(28561),
"div_count": 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=45... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.374 | 2026-02-08T05:47:42.360730Z | {
"verified": true,
"answer": 81976,
"timestamp": "2026-02-08T05:47:43.735190Z"
} | a7ffb0 | CC BY 4.0 | [
{
"id": 5,
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"score": 3,
"correct": {
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},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 5792
},
"timestamp": "2026-02-12T15:09:28.179Z",
"answer": 81976
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
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},
{
"lemma": "K15",
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{
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{
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},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
39d9a4 | nt_count_divisible_and_v1_2051736721_5530 | Let $d_1$ be the number of integers $j$ with $0 \leq j \leq 1156$ such that $\binom{1156}{j}$ is odd. Let $d_2 = 12$. Let $r$ be the number of positive integers $n$ with $1 \leq n \leq 106440$ such that $n$ is divisible by both $d_1$ and $d_2$. Compute $r + \phi(|r| + 1) + \tau(|r| + 1)$, where $\phi$ denotes Euler's t... | 6,657 | graphs = [
Graph(
let={
"upper": Const(106440),
"d1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1156)), Eq(Mod(value=Binom(n=Const(1156), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_divisible_and_v1 | null | 6 | 0 | [
"V8"
] | 1 | 3.275 | 2026-02-08T18:39:08.724133Z | {
"verified": true,
"answer": 6657,
"timestamp": "2026-02-08T18:39:11.999125Z"
} | 160471 | CC BY 4.0 | [
{
"id": 5,
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"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2387
},
"timestamp": "2026-02-18T18:26:03.386Z",
"answer": 6657
},
{... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1004f8 | comb_binomial_compute_v1_1978505735_6512 | Let $N$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 168$ and $16$ divides the $n_1$-th Fibonacci number. Let $n = N$ and $k = 8$. Compute $\binom{n}{k}$, and let $R$ be the absolute value of this binomial coefficient. Find the $R \bmod 11$-th Bell number. | 1 | graphs = [
Graph(
let={
"_n": Const(168),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Divides(divisor=Const(16), dividend=Fibonacci(arg=Var(name='n1')))))),
"k": Const(8),
"result": Binom... | COMB | NT | COMPUTE | sympy | B1 | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_binomial_compute_v1 | null | 5 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.025 | 2026-02-08T19:38:38.288791Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T19:38:38.314114Z"
} | 95b831 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2084
},
"timestamp": "2026-02-18T23:06:24.444Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
980f82 | geo_count_lattice_triangle_v1_151522320_1192 | Let $c = 100$. Let $m$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 137$ and $1 \leq i, j \leq 137$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 4624$. Define $\text{area}_{2x} = |225 \cdot 128 + 100 \cdot (-n)|$. Let $\te... | 88,194 | graphs = [
Graph(
let={
"_c": Const(100),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(137)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(137)), right=IntegerRange(start=Const(1), end... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/B3",
"B3/MAX_DIVISOR"
] | 317518 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"COUNT_SUM_EQUALS",
"MAX_DIVISOR"
] | 3 | 0.014 | 2026-02-08T03:50:02.664314Z | {
"verified": true,
"answer": 88194,
"timestamp": "2026-02-08T03:50:02.677973Z"
} | 9bceaa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 337,
"completion_tokens": 1205
},
"timestamp": "2026-02-10T15:52:12.430Z",
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{
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{
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},
{
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{
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{
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},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemm... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
d98315 | antilemma_sum_equals_v1_124444284_5009 | Let $N$ be the number of elements in the Cartesian product of the sets $\{1, 2, 3, 4, 5\}$ and $\{1, 2, \dots, 9\}$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 43$, $1 \leq j \leq 44$, and $i + j = N$. | 43 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(9)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.053 | 2026-02-08T06:20:45.492853Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T06:20:45.546271Z"
} | b888da | 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": 818
},
"timestamp": "2026-02-24T06:02:22.336Z",
"answer": 43
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
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"status": "no"
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{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
f763b3 | nt_count_primes_v1_153355830_2763 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $P$.
Determine the number of prime numbers $n$ such that $L \leq n \leq 40320$. Let $k$ be this count.
Find the smallest positive int... | 252 | graphs = [
Graph(
let={
"upper": Const(40320),
"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 | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.977 | 2026-02-08T07:20:09.512549Z | {
"verified": true,
"answer": 252,
"timestamp": "2026-02-08T07:20:11.489408Z"
} | bd30f0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 2442
},
"timestamp": "2026-02-13T10:03:19.445Z",
"answer": 252
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c82b99 | antilemma_cartesian_v1_1874849503_975 | Compute the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 13$ and $1 \leq b \leq 15$. Let this number be $x$. Compute $x + \left(2^{(x \bmod 16)} \bmod 63805\right)$. | 203 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(15)))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(16))), modulus=Const(63805))),
},... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T13:29:41.090696Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T13:29:41.091350Z"
} | 781b24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 262
},
"timestamp": "2026-02-09T23:14:54.020Z",
"answer": 203
},
{
"id"... | 1 | [
{
"lemma": "C2",
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},
{
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{
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{
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"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
b6a079 | nt_sum_gcd_range_mod_v1_124444284_7259 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 144$. Let $k = 240$ and $M = 11287$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Compute the remainder when $\text{sum}$ is divided by $M$. | 1,404 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(144)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(240),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.239 | 2026-02-08T08:58:50.097864Z | {
"verified": true,
"answer": 1404,
"timestamp": "2026-02-08T08:58:50.336738Z"
} | be3f67 | 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": 2566
},
"timestamp": "2026-02-13T23:40:55.018Z",
"answer": 1404
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
58fe18 | comb_count_permutations_fixed_v1_124444284_861 | Let $m = 2$. Let $N$ be the set of prime numbers $n$ satisfying $m \leq n \leq 9$. Let $d_{\max}$ be the largest element of $N$. Define $n$ to be the sum of $\varphi(d)$ over all positive divisors $d$ of $d_{\max}$, where $\varphi$ denotes Euler's totient function. Let $k = 1$. Define $\text{result} = \binom{n}{k} \cdo... | 9,719 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(44121),
"n": SumOverDivisors(n=MaxOverSet(set=SolutionsSet(var=Var(name='n'), condition=And(Geq(left=Var(name='n'), right=Ref(name='_m')), Leq(left=Var(name='n'), right=Const(value=9)), IsPrime(arg=Var(name='n'))))), var... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K3"
] | 6b6e89 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"K3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T03:33:11.090286Z | {
"verified": true,
"answer": 9719,
"timestamp": "2026-02-08T03:33:11.093148Z"
} | 789ae3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 1384
},
"timestamp": "2026-02-09T23:07:35.176Z",
"answer": 9719
},
{
"i... | 1 | [
{
"lemma": "C2",
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},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4e5d39_l | modular_modexp_compute_v1_1116507919_496 | Let $a = 7$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 250000$. Define $s_{\min}$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $e$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s_{\min}$. Let $m = 219... | 44,121 | NT | null | COMPUTE | sympy | B3 | [
"B3/COMB1"
] | e26f7e | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.002 | 2026-02-08T02:35:54.277832Z | {
"verified": false,
"answer": 16593,
"timestamp": "2026-02-08T02:35:54.279825Z"
} | 7d3247 | 4e5d39 | legacy_text | CC BY 4.0 | [
{
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"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 6246
},
"timestamp": "2026-02-08T19:38:19.629Z",
"answer": 16593
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{
"... | 1 | [
{
"lemma": "B3",
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},
{
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},
{
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},
{
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"status": "no"
},
{
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"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": 1.1,
"mid": 2.78,
"hi": 4.36
} | |
62db94 | sequence_count_fib_divisible_v1_784195855_9923 | Let $T$ be the set of all positive integers $t$ such that $24 \leq t \leq 2916$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 14$, $1 \leq b \leq 186$, and $t = 9a + 15b$. Let $u$ be the number of elements in $T$. Determine the value of $u$, and then compute the number of positive integers $n$ such ... | 239 | graphs = [
Graph(
let={
"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=14)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.13 | 2026-02-08T17:18:41.747526Z | {
"verified": true,
"answer": 239,
"timestamp": "2026-02-08T17:18:41.877362Z"
} | 78e943 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 4880
},
"timestamp": "2026-02-18T00:20:36.639Z",
"answer": 239
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f441f7 | nt_count_digit_sum_v1_865884756_733 | Let $a$ and $b$ be positive integers such that $1 \le a \le 7$, $1 \le b \le 4$, and define $t = 9a + 12b$. Let $S$ be the set of all integers $t$ satisfying $21 \le t \le 111$. Let $N$ be the number of elements in $S$. Compute the number of positive integers $n \le 99999$ such that the sum of the decimal digits of $n$... | 8,127 | 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=7)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 3.782 | 2026-02-08T15:34:54.664020Z | {
"verified": true,
"answer": 8127,
"timestamp": "2026-02-08T15:34:58.446205Z"
} | 76b9ad | 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": 2928
},
"timestamp": "2026-02-16T08:48:17.154Z",
"answer": 8127
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
547faf | nt_count_divisible_and_v1_1742523217_4981 | Let $d_1$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $d_2 = 12$. Let $N$ be the number of positive integers $n$ such that $1 \le n \le 164916$, $n \equiv \sum_{k=0}^{6} (-1)^k \binom{6}{k} \pmod{d_1}$, and $n \equiv 0 \pmod{d_2}$. Compute $N$. | 4,581 | graphs = [
Graph(
let={
"upper": Const(164916),
"d1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y"))... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"B1"
] | 6d96ac | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B1",
"BINOMIAL_ALTERNATING"
] | 2 | 9.919 | 2026-02-08T10:41:59.538057Z | {
"verified": true,
"answer": 4581,
"timestamp": "2026-02-08T10:42:09.456976Z"
} | 499cbe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1027
},
"timestamp": "2026-02-24T12:13:38.501Z",
"answer": 4581
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"stat... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
6df606 | comb_sum_binomial_row_v1_1520064083_5893 | Let $m = 660$. Define $t$ to be the number of positive integers $k$ such that $1 \leq k \leq m$ and $55$ divides $k$. Let $n$ be the largest prime number satisfying $2 \leq n \leq t$. Now, let $S$ be the set of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) =... | 2,048 | graphs = [
Graph(
let={
"_m": Const(660),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_m")), Divi... | NT | null | SUM | sympy | C2 | [
"C2/MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 300618 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"C2",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T07:42:22.804309Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T07:42:22.807066Z"
} | 439a8b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 512
},
"timestamp": "2026-02-15T19:02:35.495Z",
"answer": 177147
},
{
"id": 1... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e499fc | geo_count_lattice_rect_v1_124444284_2907 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 441$ and $0 \leq y \leq 110$. | 49,062 | graphs = [
Graph(
let={
"a": Const(441),
"b": Const(110),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T05:04:10.994549Z | {
"verified": true,
"answer": 49062,
"timestamp": "2026-02-08T05:04:10.996883Z"
} | 974d0c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 264
},
"timestamp": "2026-02-24T02:35:18.638Z",
"answer": 49062
},
{
"i... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
4bc187 | alg_poly4_sum_v1_1218484723_806 | Let $M$ be the minimum value of $x + y$ over all positive integers $x, y$ such that $xy = 389376$. Let $P$ be the minimum value of $x_1 + y_1$ over all positive integers $x_1, y_1$ such that $x_1 y_1 = 65536$. Let $q = \max\{ n : 2 \leq n \leq \max\{ x_2 y_2 : x_2, y_2 > 0,\ x_2 + y_2 = 20 \},\ n \text{ prime} \}$. Fin... | 57,932 | graphs = [
Graph(
let={
"_c": Const(313),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(389376)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B1 | [
"B1/MAX_PRIME_BELOW",
"B3/B3"
] | f208d0 | alg_poly4_sum_v1 | null | 7 | 0 | [
"B1",
"B3",
"MAX_PRIME_BELOW"
] | 3 | 0.237 | 2026-02-25T02:32:16.537364Z | {
"verified": true,
"answer": 57932,
"timestamp": "2026-02-25T02:32:16.774667Z"
} | 297edf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 12442
},
"timestamp": "2026-03-10T01:53:46.127Z",
"answer": 62612
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELO... | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
2e1775 | nt_sum_over_divisible_v1_717093673_2995 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 188$. Define $\text{upper}$ to be the maximum value of $xy$ over all such pairs. Let $S'$ be the set of all positive integers $n$ such that $1 \le n \le \text{upper}$ and $n$ is divisible by $104$. Let $\sigma$ be the sum of all ele... | 65,670 | graphs = [
Graph(
let={
"_n": Const(98829),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(188)))), expr=Mul(Var("x"), Var("y")... | NT | null | SUM | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"B1"
] | 1 | 1.12 | 2026-02-08T17:19:06.675544Z | {
"verified": true,
"answer": 65670,
"timestamp": "2026-02-08T17:19:07.795324Z"
} | 7b946f | 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": 1367
},
"timestamp": "2026-02-18T00:19:17.071Z",
"answer": 65670
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
48f0b0 | nt_sum_over_divisible_v1_1248542787_84 | Let $\mathcal{N}$ be the set of all positive integers $n$ such that $1 \le n \le 9409$ and $n \equiv \sum_{k=0}^{9} (-1)^k \binom{9}{k} \pmod{138}$. Compute the sum of all elements in $\mathcal{N}$. Let $F_n$ denote the $n$-th Fibonacci number. Let $c$ be the number of positive integers $n$ such that $1 \le n \le 20586... | 30,871 | graphs = [
Graph(
let={
"_n": Const(59753),
"upper": Const(9409),
"divisor": Const(138),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Sum... | COMB | NT | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"BINOMIAL_ALTERNATING"
] | 8715d3 | nt_sum_over_divisible_v1 | affine_mod | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.301 | 2026-02-08T02:56:26.184659Z | {
"verified": true,
"answer": 30871,
"timestamp": "2026-02-08T02:56:26.485344Z"
} | 829511 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 2988
},
"timestamp": "2026-02-09T00:09:51.995Z",
"answer": 30871
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": 1.42,
"mid": 3.26,
"hi": 4.99
} | ||
9a4d63 | algebra_poly_eval_v1_601307018_2199 | Let $y = 17$ and define
$$
R = y^4 - 2y^3 + y^2 + \left|\left\{ (a, b) \in \mathbb{Z}^2 : 1 \le a \le b \le 10,\ -64ab + 32a^2 + S \cdot b^2 = 32 \right\}\right| \cdot y - 9,
$$
where
$$
S = \left|\left\{ (a_1, b_1) \in \mathbb{Z}^2 : 1 \le a_1, b_1 \le 35,\ 68a_1^3b_1 + 68a_1b_1^3 + 17a_1^4 + 17b_1^4 + 102a_1^2b_1^2 =... | 84,215 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(10),
"y": Const(17),
"result": Sum(Pow(Ref("y"), Ref("_m")), Mul(Const(-2), Pow(Ref("y"), Const(3))), Pow(Ref("y"), Const(2)), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condi... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_ORBIT"
] | a035de | algebra_poly_eval_v1 | null | 6 | 0 | [
"POLY4_COUNT",
"QF_PSD_ORBIT"
] | 2 | 0.016 | 2026-03-10T02:53:29.411519Z | {
"verified": true,
"answer": 84215,
"timestamp": "2026-03-10T02:53:29.427275Z"
} | 8268f4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 336,
"completion_tokens": 3428
},
"timestamp": "2026-03-29T04:37:27.284Z",
"answer": 19771
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
a41f05 | algebra_quadratic_discriminant_v1_1439011603_2274 | Let $a = -6$, $b = -8$, and $c = 4$. Define $m$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Define $n$ to be the number of positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 \cdot q ... | 160 | graphs = [
Graph(
let={
"a": Const(-6),
"b": Const(-8),
"c": Const(4),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.006 | 2026-02-08T16:39:41.944298Z | {
"verified": true,
"answer": 160,
"timestamp": "2026-02-08T16:39:41.950306Z"
} | 9d6216 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2113
},
"timestamp": "2026-02-17T10:04:51.836Z",
"answer": 160
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
830bbd | nt_max_prime_below_v1_1353956133_168 | Let $Q$ be the largest prime number less than or equal to $11551$. Find the remainder when $|Q|$ is divided by $58849$. | 11,551 | graphs = [
Graph(
let={
"upper": Const(11551),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Abs(arg=Ref(name='result')), modulus=Const(58849)),
},
... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.722 | 2026-02-08T11:20:09.408595Z | {
"verified": true,
"answer": 11551,
"timestamp": "2026-02-08T11:20:12.130584Z"
} | 599595 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 1157
},
"timestamp": "2026-02-14T11:46:56.842Z",
"answer": 11551
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
53e21b | antilemma_cartesian_v1_1520064083_691 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 39$ and $1 \leq j \leq 46$. Compute
$$
x + \phi(|x| + 0!) + \tau(|x| + 1),
$$
where $\phi(n)$ denotes the number of positive integers at most $n$ that are relatively prime to $n$, and $\tau(n)$ denotes the number of positive divisors of $n$. | 3,230 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(39)), right=IntegerRange(start=Const(1), end=Const(46)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Factorial(Const(0)))), NumDivisors(n=Sum(Abs(arg=Ref(name='x... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | cb6f65 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 2 | 0.001 | 2026-02-08T03:32:59.449266Z | {
"verified": true,
"answer": 3230,
"timestamp": "2026-02-08T03:32:59.450300Z"
} | 274b1c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 848
},
"timestamp": "2026-02-10T14:57:43.780Z",
"answer": 3230
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
72a0f0 | comb_catalan_compute_v1_1918700295_888 | Let $T$ be the set of all positive integers $t$ such that $36 \le t \le 6249$ and there exist positive integers $a \le 264$, $b \le 47$ satisfying $t = 21a + 15b$. Let $\#T$ denote the number of elements in $T$. Let $C_{10}$ be the 10th Catalan number. Compute the remainder when $\#T - C_{10}$ is divided by $96423$, wh... | 80,651 | 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=264)), Geq(left=Var(name='b'), right=Const(valu... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 866223 | comb_catalan_compute_v1 | negation_mod | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T05:23:12.260436Z | {
"verified": true,
"answer": 80651,
"timestamp": "2026-02-08T05:23:12.264288Z"
} | 3bc3dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 10818
},
"timestamp": "2026-02-24T03:24:43.268Z",
"answer": 81675
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
c1e47e | geo_count_lattice_triangle_v1_153355830_405 | Let $A$ be twice the area of the triangle with vertices at $(113, 3)$, $(121, 169)$, and $(0, 0)$, which can be computed as $|113 \cdot 169 + 121 \cdot (-3)|$. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each edge of the triangle: $\gcd(|113|, |3|) +... | 17,062 | graphs = [
Graph(
let={
"_n": Const(22),
"area_2x": Abs(arg=Sum(Mul(Const(value=113), Const(value=169)), Mul(Const(value=121), Sub(left=Const(value=0), right=Const(value=3))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=113)), b=Abs(arg=Const(value=3))), GCD(a=Abs(arg=Sub... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.008 | 2026-02-08T03:05:19.263723Z | {
"verified": true,
"answer": 17062,
"timestamp": "2026-02-08T03:05:19.271744Z"
} | 36d5cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 2458
},
"timestamp": "2026-02-10T12:39:40.288Z",
"answer": 17062
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
dba5d9 | nt_sum_divisors_compute_v1_1742523217_2978 | Let $n = 70000$. Let $\text{result}$ be the sum of all positive divisors of $n$. Let $p$ be the largest prime number less than or equal to $11$. Compute the Bell number $B_k$, where $k$ is the remainder when $|\text{result}|$ is divided by $p$. | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(70000),
"result": SumDivisors(n=Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(11)), I... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_divisors_compute_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T05:29:34.603369Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T05:29:34.604897Z"
} | 2c1848 | 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": 1153
},
"timestamp": "2026-02-12T09:10:45.602Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
1413a4 | sequence_lucas_compute_v1_349078426_329 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 56$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 11$, and $t = 6a + 4b$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_m = L_{m-1} + L_{m-2}$ for $m \geq 3$. Compute the remainder ... | 59,211 | graphs = [
Graph(
let={
"_n": Const(79464),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:56:41.253714Z | {
"verified": true,
"answer": 59211,
"timestamp": "2026-02-08T12:56:41.254894Z"
} | 3e5ee7 | 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": 3093
},
"timestamp": "2026-02-15T08:29:32.898Z",
"answer": 59211
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b87e10 | antilemma_k2_v1_124444284_7834 | Let $n = 245$. Consider the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 245$ and $1 \leq j \leq 7$. For each such $k$, define a term $\varphi(k) \left\lfloor \frac{n}{k} \right\rfloor$, where $\varphi$ is Euler's totient function. Let $T$ be the sum of this term over all such pairs. ... | 203 | graphs = [
Graph(
let={
"_n": Const(245),
"x": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Pow(Const(84), Const(0)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(245)), right=IntegerRange(sta... | NT | COMB | COMPUTE | sympy | K2 | [
"SUM_INDEPENDENT",
"IDENTITY_POW_ZERO",
"K2"
] | 1d9bfe | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_POW_ZERO",
"K2",
"SUM_INDEPENDENT"
] | 3 | 0.03 | 2026-02-08T09:23:18.154956Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T09:23:18.185177Z"
} | 9e117c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1359
},
"timestamp": "2026-02-14T03:41:22.643Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status"... | {
"lo": -5.49,
"mid": 0.2,
"hi": 6.27
} | ||
4c7b97 | alg_qf_psd_orbit_v1_1218484723_4675 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a \le b \le c \le 55$ such that $14a^2 + 14b^2 + 14c^2 + 2ab + 2bc + 2ac = 53654$. | 9 | graphs = [
Graph(
let={
"_m": Const(53654),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(55)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"C5/QF_PSD_DISTINCT"
] | e025da | alg_qf_psd_orbit_v1 | null | 4 | 0 | [
"C5",
"MAX_PRIME_BELOW",
"QF_PSD_DISTINCT"
] | 3 | 1.458 | 2026-02-25T06:21:17.949428Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-25T06:21:19.407256Z"
} | 31d1c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 23597
},
"timestamp": "2026-03-29T16:57:50.877Z",
"answer": 2
},
{
"i... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma"... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
2f80c8 | alg_linear_system_2x2_v1_1218484723_7445 | Let $\det = -20 \cdot (-19) - (-17) \cdot 20$. Let $M = -310980 \cdot (-19) - (-280497) \cdot \left|\{ (a, b) : a \geq 1, a \leq 20, b \geq 1, b \leq 20, -189 \cdot a^{3} = -12096 \}\right|$ and $R = -20 \cdot (-280497) - (-17) \cdot (-310980)$. Compute $\frac{M}{\det} + \frac{R}{\det}$. | 16,447 | graphs = [
Graph(
let={
"_n": Const(3),
"num_x": Sub(Mul(Const(-310980), Const(-19)), Mul(Const(-280497), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Co... | ALG | null | COMPUTE | sympy | C3 | [
"POLY3_COUNT"
] | 355dbe | alg_linear_system_2x2_v1 | null | 3 | 0 | [
"C3",
"POLY3_COUNT"
] | 2 | 0.037 | 2026-02-25T08:52:52.076125Z | {
"verified": true,
"answer": 16447,
"timestamp": "2026-02-25T08:52:52.113527Z"
} | 7ce005 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 1093
},
"timestamp": "2026-03-30T04:36:17.453Z",
"answer": 16447
},
{
"... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
6593ca | nt_count_coprime_and_v1_1440796553_1083 | Let $k_1 = 3$ and let $k_2$ be the largest prime number between $2$ and $5$, inclusive. Determine the number of positive integers $n \leq 47561$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 25,366 | graphs = [
Graph(
let={
"upper": Const(47561),
"k1": Const(3),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition... | NT | null | COUNT | sympy | LTE_SUM | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"LTE_SUM",
"MAX_PRIME_BELOW"
] | 2 | 8.07 | 2026-02-08T12:10:35.894391Z | {
"verified": true,
"answer": 25366,
"timestamp": "2026-02-08T12:10:43.964361Z"
} | 292101 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 654
},
"timestamp": "2026-02-14T22:51:55.033Z",
"answer": 25366
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
adfdac | comb_bell_compute_v1_1470522791_468 | Let $k$ be a positive integer. Define $m$ to be the number of positive integers $k$ from $1$ to $568320$ that are divisible by $120$.
Let $j$ be a nonnegative integer. Define $n$ to be the number of integers $j$ with $0 \leq j \leq 4736$ such that the binomial coefficient $\binom{m}{j}$ is odd.
Let $\text{result}$ be... | 77,056 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4736)), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Con... | COMB | NT | COMPUTE | sympy | C2 | [
"C2/V8"
] | 3477ff | comb_bell_compute_v1 | null | 7 | 0 | [
"C2",
"V8"
] | 2 | 0.004 | 2026-02-08T13:01:55.889442Z | {
"verified": true,
"answer": 77056,
"timestamp": "2026-02-08T13:01:55.893255Z"
} | 8256e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 2644
},
"timestamp": "2026-02-15T08:41:17.007Z",
"answer": 77056
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b52e17 | nt_max_prime_below_v1_1520064083_2359 | Let $n$ range over the positive integers. Define $k_0$ to be the number of positive integers $k$ such that $1 \leq k \leq 256$ and $128$ divides $k$. Let $S$ be the set of all prime numbers $n$ such that $n \geq k_0$ and $n \leq 39340$. Find the maximum value of $S$. | 39,323 | graphs = [
Graph(
let={
"_n": Const(256),
"upper": Const(39340),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Co... | NT | null | EXTREMUM | sympy | C2 | [
"C2"
] | 9685eb | nt_max_prime_below_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.934 | 2026-02-08T04:40:55.779751Z | {
"verified": true,
"answer": 39323,
"timestamp": "2026-02-08T04:40:56.713694Z"
} | 6d3452 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 4688
},
"timestamp": "2026-02-11T21:49:27.931Z",
"answer": 39323
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
91b46b | diophantine_fbi2_min_v1_677425708_4290 | Let $k = 360$. Let $\text{upper}$ be the number of integers $t$ with $14 \leq t \leq 764$ for which there exist positive integers $a \leq 13$ and $b \leq 110$ such that $t = 8a + 6b$. Let $\text{result}$ be the smallest integer $d$ such that $2 \leq d \leq \text{upper}$, $d$ divides $k$, and $k/d \geq 4$. Let $c = 7435... | 14,870 | graphs = [
Graph(
let={
"k": Const(360),
"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=13)), Geq(left=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.026 | 2026-02-08T06:31:54.473038Z | {
"verified": true,
"answer": 14870,
"timestamp": "2026-02-08T06:31:54.498691Z"
} | 6b25c2 | 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": 4273
},
"timestamp": "2026-02-13T01:36:00.016Z",
"answer": 14870
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
8a40c9 | nt_sum_divisors_mod_v1_717093673_3058 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. For each such pair, compute $x + y$, and let $n$ be the minimum value among these sums. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10253$. | 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(10253... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T17:21:15.331328Z | {
"verified": true,
"answer": 2880,
"timestamp": "2026-02-08T17:21:15.336008Z"
} | 232162 | 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": 1617
},
"timestamp": "2026-02-18T00:26:39.241Z",
"answer": 2880
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6ccc4 | alg_qf_psd_min_v1_601307018_5443 | Let $T = \{ v \mid 1 \leq v \leq 5185,\ \text{there exist integers } a, b \text{ with } 1 \leq a, b \leq 17 \text{ such that } 20a^2 - 36ab + 17b^2 = v \}$. Find the minimum value of $126171a^2 - 252342ab + 182247b^2$ over all positive integers $a, b$ with $1 \leq a \leq |T|$ and $1 \leq b \leq 206$. | 56,076 | graphs = [
Graph(
let={
"_n": Const(206),
"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=Var("v"), condition=And(Geq(Var("v"), Const(1)), Leq(Var("v"... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_min_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 1.062 | 2026-03-10T06:03:47.837043Z | {
"verified": true,
"answer": 56076,
"timestamp": "2026-03-10T06:03:48.898591Z"
} | 87ee62 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2948
},
"timestamp": "2026-04-19T02:08:06.862Z",
"answer": 56076
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -6.2,
"mid": -2.86,
"hi": 0.46
} | ||
89e814 | modular_inverse_v1_1440796553_718 | Let $a = 734$ and $m = 1303$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 34596$. Let $s_{\min}$ be the minimum value of $x + y$ over all $(x, y) \in S$. Let $\text{upper}$ be the sum of all positive integers $n \leq s_{\min}$ such that $n$ is divisible by $62$. Let $\text{resu... | 20,153 | graphs = [
Graph(
let={
"a": Const(734),
"m": Const(1303),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive... | NT | null | EXTREMUM | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 138b1a | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.055 | 2026-02-08T11:56:12.008021Z | {
"verified": true,
"answer": 20153,
"timestamp": "2026-02-08T11:56:12.063340Z"
} | cf07ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 2190
},
"timestamp": "2026-02-14T20:47:31.868Z",
"answer": 20153
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
85d7e4 | nt_count_intersection_v1_1918700295_2013 | Let $N = 20000$. Compute the number of positive integers $n \le N$ such that $11$ divides $n$ and $\gcd(n, 12) = 1$. Let $m$ be this count. Let $M$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 170$. Compute $M - m$. | 6,619 | graphs = [
Graph(
let={
"_n": Const(170),
"N": Const(20000),
"a": Const(11),
"b": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Va... | NT | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | nt_count_intersection_v1 | negation_mod | 5 | 0 | [
"B1"
] | 1 | 0.644 | 2026-02-08T07:36:49.958233Z | {
"verified": true,
"answer": 6619,
"timestamp": "2026-02-08T07:36:50.602230Z"
} | 8bd399 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 992
},
"timestamp": "2026-02-13T11:27:56.311Z",
"answer": 6619
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
e22677 | nt_count_intersection_v1_971394319_1532 | Let $ N = 100000 $, and let $ a $ be the smallest divisor of $ 3675 $ that is at least $ 2 $. Compute the number of positive integers $ n \leq N $ such that $ a $ divides $ n $ and $ \gcd(n, 10) = 1 $. Let this count be $ c $. Compute $ c + \phi(|c| + 1) + \tau(|c| + 1) $, where $ \phi $ denotes Euler's totient functio... | 19,398 | graphs = [
Graph(
let={
"N": Const(100000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3675))))),
"b": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 5.364 | 2026-02-08T13:43:20.756888Z | {
"verified": true,
"answer": 19398,
"timestamp": "2026-02-08T13:43:26.120460Z"
} | 52a066 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1662
},
"timestamp": "2026-02-15T20:18:20.597Z",
"answer": 19398
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f92f28 | antilemma_k2_v1_865884756_6330 | Let $$
x = \sum_{k=1}^{63} \phi(k) \left\lfloor \frac{63}{k} \right\rfloor,$$ where $\phi(n)$ denotes Euler's totient function. Compute the remainder when $59671 \cdot x$ is divided by $71498$. | 37,100 | graphs = [
Graph(
let={
"_n": Const(63),
"x": Summation(var="k", start=Const(1), end=Const(63), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(59671),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(71498)),
},
... | NT | COMB | COMPUTE | sympy | SUM_INDEPENDENT | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.009 | 2026-02-08T19:09:11.725159Z | {
"verified": true,
"answer": 37100,
"timestamp": "2026-02-08T19:09:11.734296Z"
} | 3daaf8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 4883
},
"timestamp": "2026-02-18T21:26:11.447Z",
"answer": 37100
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
04e839 | comb_count_permutations_fixed_v1_1439011603_1968 | Let $n = 7$ and let $N = 4235$. Let $k$ be the smallest divisor of $N$ that is at least $2$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remainder when this value is multiplied by $52775$ and then divided by $55343$. Find the value of... | 1,415 | graphs = [
Graph(
let={
"_n": Const(4235),
"n": Const(7),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T16:25:46.769949Z | {
"verified": true,
"answer": 1415,
"timestamp": "2026-02-08T16:25:46.772367Z"
} | f327a4 | 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": 750
},
"timestamp": "2026-02-17T03:54:38.727Z",
"answer": 1415
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3dd885 | nt_count_gcd_equals_v1_1440796553_420 | Let $n = 2$ and let $k$ be the largest prime number $p$ such that $n \leq p \leq s$, where $s$ is the sum of all positive integers at most $52$ that are divisible by $13$. Let $d = 1$ and let $u = 38416$. Compute the number of positive integers $m$ such that $1 \leq m \leq u$ and $\gcd(m, k) = d$. | 38,114 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(38416),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(52)), E... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MAX_PRIME_BELOW"
] | caf344 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 2 | 5.811 | 2026-02-08T11:46:41.492161Z | {
"verified": true,
"answer": 38114,
"timestamp": "2026-02-08T11:46:47.303311Z"
} | c8c5dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 981
},
"timestamp": "2026-02-14T18:23:12.544Z",
"answer": 38114
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
db84b0 | diophantine_sum_product_min_v1_1915831931_4048 | Let $S = 52$. Let $P$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 114244$. Let $r$ be the smallest positive integer $x_1$ with $1 \leq x_1 \leq 51$ such that $x_1(S - x_1) = P$. Define $Q = 17956 - r$. Compute $Q$. | 17,930 | graphs = [
Graph(
let={
"S": Const(52),
"P": 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(114244)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.015 | 2026-02-08T18:05:40.642128Z | {
"verified": true,
"answer": 17930,
"timestamp": "2026-02-08T18:05:40.657484Z"
} | adc79f | 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": 765
},
"timestamp": "2026-02-18T13:06:38.116Z",
"answer": 17930
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fddeb2 | comb_binomial_compute_v1_48377204_766 | Let $n$ be the largest prime number such that $2 \leq n \leq 14$. Compute $\binom{n}{6}$. | 1,716 | graphs = [
Graph(
let={
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(14)), IsPrime(Var("n1"))))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:41:28.390006Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T15:41:28.391883Z"
} | d6a339 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 768
},
"timestamp": "2026-02-16T11:18:19.689Z",
"answer": 1716
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b2ae49 | comb_count_partitions_v1_124444284_6636 | Let $n = 45$. Let $p$ be the largest prime number such that $2 \leq p \leq n$. Let $r = p(p)$, the number of integer partitions of $p$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $r + 2$. | 7,720 | graphs = [
Graph(
let={
"_n": Const(45),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Partition(arg=Ref(name='n')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_partitions_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T08:33:41.431397Z | {
"verified": true,
"answer": 7720,
"timestamp": "2026-02-08T08:33:41.432824Z"
} | 614fe2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 2668
},
"timestamp": "2026-02-13T19:37:33.983Z",
"answer": 7720
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
43c02c | sequence_lucas_compute_v1_1742523217_1715 | Let $n = 19$. Define $\ell$ to be the $n$th Lucas number. Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 11$, and let $m$ be the maximum element of $S$. Let $Q$ be the remainder when the $|\ell| \bmod m$th Bell number is divided by $90303$. Find the value of $Q$. | 25,672 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(19),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | sequence_lucas_compute_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:06:50.327978Z | {
"verified": true,
"answer": 25672,
"timestamp": "2026-02-08T04:06:50.329167Z"
} | cb72f0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1094
},
"timestamp": "2026-02-10T15:50:14.643Z",
"answer": 25672
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b45cd2 | sequence_fibonacci_compute_v1_1520064083_4113 | Let $n = 10$. Define $m$ to be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = n$. Let $F_m$ denote the $m$-th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $44121 \cdot F_m$ is divided by $66128$. | 8,729 | graphs = [
Graph(
let={
"_n": Const(10),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T06:05:15.744678Z | {
"verified": true,
"answer": 8729,
"timestamp": "2026-02-08T06:05:15.745542Z"
} | b2bb1a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1594
},
"timestamp": "2026-02-12T19:16:14.996Z",
"answer": 8729
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
dd1557 | comb_count_permutations_fixed_v1_1440796553_635 | Let $n = 9$ and $m = 5$. Let $k$ be the sum of $\phi(d)$ over all positive divisors $d$ of $m$, where $\phi$ denotes Euler's totient function. Compute the value of
$$
\binom{n}{k} \cdot !(n - k),
$$
where $!t$ denotes the number of derangements of $t$ elements.\n\nFind the value of this number. | 1,134 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Const(9),
"k": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
... | NT | COMB | COUNT | sympy | K3 | [
"K3"
] | 54c41e | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T11:54:46.642495Z | {
"verified": true,
"answer": 1134,
"timestamp": "2026-02-08T11:54:46.644074Z"
} | 163ee6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 463
},
"timestamp": "2026-02-16T03:26:47.877Z",
"answer": 1134
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
f4f5e1 | nt_count_with_divisor_count_v1_1248542787_599 | Let $d$ be the number of integers $t$ such that $27 \leq t \leq 46$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 7a + 2b + 18$. Let $m$ be the number of positive integers $n$ with $1 \leq n \leq 12100$ such that the number of positive divisors of $n$ is equal to $d$. Compute
... | 696 | graphs = [
Graph(
let={
"upper": Const(12100),
"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(name='a'), right=Const(value=2)), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.483 | 2026-02-08T03:15:15.478510Z | {
"verified": true,
"answer": 696,
"timestamp": "2026-02-08T03:15:15.961562Z"
} | 6bdc0b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 2444
},
"timestamp": "2026-02-09T06:01:52.440Z",
"answer": 696
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
f13af8 | algebra_poly_eval_v1_1978505735_2297 | Let $k = 13$. Let $c$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 26$. Compute the value of
$$
\frac{10 \cdot k^5 + c \cdot k^4 - 37 \cdot k^3 - 62 \cdot k^2 + 75 \cdot k + 27}{133}.
$$ | 30,026 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(13),
"result": Div(Sum(Mul(Const(10), Pow(Ref("k"), Ref("_n"))), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), ... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | algebra_poly_eval_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T16:49:01.815695Z | {
"verified": true,
"answer": 30026,
"timestamp": "2026-02-08T16:49:01.818488Z"
} | fa351b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1207
},
"timestamp": "2026-02-17T12:36:21.495Z",
"answer": 30026
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f97f92 | comb_sum_binomial_row_v1_1918700295_1867 | Let $n$ be the largest prime number less than or equal to $16$. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(16)), IsPrime(Var("n"))))),
"result": Pow(Ref("_n"), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:07:47.207562Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T06:07:47.208813Z"
} | 0aa013 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 207
},
"timestamp": "2026-02-15T17:07:05.823Z",
"answer": 8192
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
698d68 | algebra_vieta_sum_v1_1742523217_5360 | Let $f(x) = -x^4 - 7x^3 + 40x^2 + kx - 480$, where $k$ is the number of integers $t$ with $7 \leq t \leq 206$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 12$, $1 \leq b \leq 73$, and $$t = 5a + 2b.$$
Let $R$ be the set of all real roots of the equation $f(x) = 0$. Compute the remainder... | 32,484 | graphs = [
Graph(
let={
"_n": Const(2),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=-1), Pow(base=Var(name='x'), exp=Const(value=4))), Mul(Const(value=-7), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=40), Pow(ba... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_vieta_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.015 | 2026-02-08T10:56:23.357288Z | {
"verified": true,
"answer": 32484,
"timestamp": "2026-02-08T10:56:23.372472Z"
} | 88aeb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 4360
},
"timestamp": "2026-02-14T09:41:29.502Z",
"answer": 32484
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d6bc11 | nt_count_divisible_v1_898971024_1041 | Let $t$ be an integer such that $14 \leq t \leq 76$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 5$, $1 \leq b \leq 6$, and $t = 8a + 6b$. Let $d$ be the number of such values of $t$. Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 36100$ and $n \equiv 0 \pmod{d}$. Let $r$ be the ... | 63,302 | graphs = [
Graph(
let={
"_n": Const(31354),
"upper": Const(36100),
"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... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.196 | 2026-02-08T15:54:09.511174Z | {
"verified": true,
"answer": 63302,
"timestamp": "2026-02-08T15:54:10.707625Z"
} | d199c9 | 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": 2725
},
"timestamp": "2026-02-16T15:52:30.019Z",
"answer": 63302
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
88b4c4 | antilemma_k3_v1_1918700295_3787 | Let
\[x = \sum_{d \mid 48651} \varphi(d),\]
where $\varphi$ denotes Euler's totient function. Let $n=67$.
Let $T$ be the set of all integers $u$ such that
\[u^2 - 67u - 12218 = 0,\]
and assume this set is nonempty. Define
\[Q = x + \varphi\left(\left|x\right| + \frac{n}{\sum_{u \in T} 1}\right) + \tau\left(\left|x\rig... | 72,981 | graphs = [
Graph(
let={
"_n": Const(67),
"x": SumOverDivisors(n=Const(value=48651), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Div(Ref("_n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), ... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/IDENTITY_DIV_SELF",
"K3"
] | 4df488 | antilemma_k3_v1 | arith_invariants | 6 | 0 | [
"IDENTITY_DIV_SELF",
"K3",
"VIETA_SUM"
] | 3 | 0.001 | 2026-02-08T08:56:56.389616Z | {
"verified": true,
"answer": 72981,
"timestamp": "2026-02-08T08:56:56.391066Z"
} | 20d34e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 3173
},
"timestamp": "2026-02-13T22:46:01.972Z",
"answer": 72981
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
063bc9 | nt_count_divisible_v1_1520064083_1661 | Let $m = 28$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Define $n$ to be the maximum value of $x \cdot y$ over all such pairs. Let $d$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $x \cdot y = n$. Compute the number of po... | 1,575 | graphs = [
Graph(
let={
"_m": Const(28),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisible_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 4.226 | 2026-02-08T04:11:06.239862Z | {
"verified": true,
"answer": 1575,
"timestamp": "2026-02-08T04:11:10.465606Z"
} | 62a3c1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 839
},
"timestamp": "2026-02-10T15:48:20.139Z",
"answer": 1575
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
82690d | nt_count_intersection_v1_458359167_1167 | Let $p$ be the largest prime number such that $2 \leq p \leq 52$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 79524$. Let $t$ be the minimum value of $x + y$ over all such pairs. Let $b$ be the number of positive integers $k$ such that $1 \leq k \leq t$ and $p$ divides $k$. Let... | 606 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(52)), IsPrime(Var("n"))))),
"N": Const(20000),
"a": Const(11),
"b": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C2",
"B3/C2"
] | 1b02bb | nt_count_intersection_v1 | null | 7 | 0 | [
"B3",
"C2",
"MAX_PRIME_BELOW"
] | 3 | 1.301 | 2026-02-08T04:25:50.498577Z | {
"verified": true,
"answer": 606,
"timestamp": "2026-02-08T04:25:51.799194Z"
} | ca9008 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 1173
},
"timestamp": "2026-02-10T16:28:43.719Z",
"answer": 606
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
eae36c | comb_catalan_compute_v1_349078426_1705 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 9$. Let $c = 65887$. Compute the remainder when $c \cdot C_n$ is divided by $52782$, where $C_n$ denotes the $n$th Catalan number. | 10,640 | graphs = [
Graph(
let={
"_n": Const(9),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(nam... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T13:51:15.486585Z | {
"verified": true,
"answer": 10640,
"timestamp": "2026-02-08T13:51:15.488560Z"
} | 8b1e4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1802
},
"timestamp": "2026-02-24T19:07:02.092Z",
"answer": 10640
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
a8c024 | comb_count_surjections_v1_1874849503_1073 | Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 28$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 ... | 1,806 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(28))))),
"_n... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COMB1/COMB1"
] | b2c526 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.025 | 2026-02-08T13:33:29.478381Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T13:33:29.503678Z"
} | b72924 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1711
},
"timestamp": "2026-02-10T00:39:56.047Z",
"answer": 1806
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
ebfdf4 | antilemma_k2_v1_655260480_1893 | Compute the value of $\sum_{k=1}^{310} \phi(k) \left\lfloor \frac{310}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Find the value of this sum. | 48,205 | graphs = [
Graph(
let={
"_n": Const(310),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(310), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.003 | 2026-02-08T16:27:32.214838Z | {
"verified": true,
"answer": 48205,
"timestamp": "2026-02-08T16:27:32.217720Z"
} | defbf4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 536
},
"timestamp": "2026-02-17T03:17:06.688Z",
"answer": 48205
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d2636 | comb_bell_compute_v1_865884756_2692 | Let $n = 9$. Define $r$ to be the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. Let $Q$ be the remainder when $91684 \cdot r$ is divided by $85381$. Find the value of $Q$. | 9,800 | graphs = [
Graph(
let={
"n": Const(9),
"result": Bell(Ref("n")),
"_c": Const(91684),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(85381)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/B1"
] | 844731 | comb_bell_compute_v1 | null | 3 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.019 | 2026-02-08T16:53:28.434557Z | {
"verified": true,
"answer": 9800,
"timestamp": "2026-02-08T16:53:28.453838Z"
} | 1343f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 3644
},
"timestamp": "2026-02-17T14:39:44.339Z",
"answer": 9800
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETI... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
a2fe8d | diophantine_product_count_v1_1440796553_429 | Let $k = 360$ and let $u = 340$. Consider the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Compute the number of elements in this set. | 22 | graphs = [
Graph(
let={
"k": Const(360),
"upper": Const(340),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"K3"
] | 54c41e | diophantine_product_count_v1 | null | 3 | 0 | [
"K3",
"MAX_PRIME_BELOW"
] | 2 | 0.146 | 2026-02-08T11:47:11.919325Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T11:47:12.065394Z"
} | f850d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1099
},
"timestamp": "2026-02-14T19:14:01.194Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8e9e2c | comb_bell_compute_v1_124444284_1585 | Let $u$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 7$. Let $n_2 = u + 1$. Define
\[
w = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
\]
Let $a = 2$, $b = 1$, and $n_1 = a + b$. Define
\[
v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
\]
Let $B_n$ denote the $n$th Be... | 76,448 | graphs = [
Graph(
let={
"_n": Const(71965),
"u": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_bell_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.003 | 2026-02-08T04:01:45.091943Z | {
"verified": true,
"answer": 76448,
"timestamp": "2026-02-08T04:01:45.094904Z"
} | 12ea46 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 326,
"completion_tokens": 2564
},
"timestamp": "2026-02-11T15:47:56.511Z",
"answer": 76448
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INT... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
a5b7b0 | algebra_vieta_sum_v1_1978505735_4021 | Let $f(x) = x^4 - 6x^3 - 109x^2 + 474x + m$, where $m$ is the minimum value of $x_1 + y$ over all ordered pairs $(x_1, y)$ of positive integers such that $x_1 y = 1166400$. Find the product of all real roots of the equation $f(x) = 0$. | 2,160 | graphs = [
Graph(
let={
"_n": Const(2),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=4)), Mul(Const(value=-6), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=-109), Pow(base=Var(name='x'), ex... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_vieta_sum_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T17:58:54.157898Z | {
"verified": true,
"answer": 2160,
"timestamp": "2026-02-08T17:58:54.167967Z"
} | 88fd47 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1474
},
"timestamp": "2026-02-18T10:41:21.452Z",
"answer": 2160
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
22de2f | geo_count_lattice_triangle_v1_2051736721_2743 | Let $A$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 144$, and let $s_1 = \min\{x_1 + y_1 \mid (x_1, y_1) \in A\}$. Let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s_1$, and let $P = \max\{xy \mid (x, y) \in B\}$. Let $T$ be the set of a... | 25,011 | graphs = [
Graph(
let={
"_c": Const(128),
"_m": Const(300),
"_n": Const(19),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=128)), Mul(Const(value=300), Sub(left=Const(value=0), right=Const(value=19))))),
"boundary": Sum(GCD(a=Abs(arg=Max... | NT | null | COUNT | sympy | B3 | [
"B3/B1",
"LIN_FORM"
] | 1550c9 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.017 | 2026-02-08T16:52:31.835292Z | {
"verified": true,
"answer": 25011,
"timestamp": "2026-02-08T16:52:31.851846Z"
} | 9d457b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 360,
"completion_tokens": 5318
},
"timestamp": "2026-02-17T14:47:19.268Z",
"answer": 25011
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
14b246 | antilemma_product_of_sums_v1_168721529_2003 | Let $n = 28$. Define
$$
A = \left( \sum_{k=1}^{n} k \right) \left( \sum_{(i,j) \in S} ij \right),
$$
where $S$ is the set of all ordered pairs $(i,j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 6$. Let $N$ be the number of positive integers $k \leq 582420$ such that $30$ divides the $k$-th Fibonacci number. Compute the ... | 29,532 | graphs = [
Graph(
let={
"_n": Const(28),
"x": Mul(Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=Const(2)), domain=CartesianProduct(left=IntegerRange(start=Con... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"PRODUCT_OF_SUMS",
"ONE_PHI_2"
] | e353af | antilemma_product_of_sums_v1 | affine_mod | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"ONE_PHI_2",
"PRODUCT_OF_SUMS"
] | 3 | 0.003 | 2026-02-08T14:03:06.263866Z | {
"verified": true,
"answer": 29532,
"timestamp": "2026-02-08T14:03:06.266623Z"
} | 6aa2eb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 7661
},
"timestamp": "2026-02-10T00:51:42.990Z",
"answer": 29532
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"sta... | {
"lo": -6.5,
"mid": -0.21,
"hi": 5.94
} | ||
eedc91 | antilemma_sum_equals_v1_458359167_1066 | Let $m = 21023$ and let $n$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 5$ and $1 \leq j \leq 8$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 39$, $1 \leq j \leq 40$, and $i + j = n$. Define $Q$ to be the remainder when $m \cdot x$ is divided by $5236... | 34,467 | graphs = [
Graph(
let={
"_m": Const(21023),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(8)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.033 | 2026-02-08T04:15:41.053593Z | {
"verified": true,
"answer": 34467,
"timestamp": "2026-02-08T04:15:41.086951Z"
} | fffdaa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1253
},
"timestamp": "2026-02-24T00:28:28.089Z",
"answer": 34467
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
4303f6 | nt_sum_over_divisible_v1_153355830_962 | Let $n = 6134$. Let $p$ be the largest prime number less than or equal to $n$. Compute the sum of all positive integers $k$ such that $k \leq p$ and $k$ is divisible by 200. | 93,000 | graphs = [
Graph(
let={
"_n": Const(6134),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"divisor": Const(200),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | SUM | sympy | COMB1 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"COMB1",
"MAX_PRIME_BELOW"
] | 2 | 7.121 | 2026-02-08T04:19:59.469382Z | {
"verified": true,
"answer": 93000,
"timestamp": "2026-02-08T04:20:06.590154Z"
} | b0db13 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2383
},
"timestamp": "2026-02-10T16:08:55.436Z",
"answer": 93000
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
54ffa6 | nt_min_coprime_above_v1_1978505735_2574 | Let $n = 89110$, $a = 5776$, $b = 5809$, and $m = 23$. Define $r$ to be the smallest integer $n$ such that $a < n \leq b$ and $\gcd(n, m) = 1$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 64$. Define $P$ to be the maximum value of $xy$ over all pairs $(x, y) \in S$. Compute ... | 84,357 | graphs = [
Graph(
let={
"_n": Const(89110),
"start": Const(5776),
"upper": Const(5809),
"modulus": Const(23),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | d2b6e1 | nt_min_coprime_above_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 0.007 | 2026-02-08T16:57:52.080845Z | {
"verified": true,
"answer": 84357,
"timestamp": "2026-02-08T16:57:52.087516Z"
} | f58e60 | 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": 1040
},
"timestamp": "2026-02-17T18:29:21.275Z",
"answer": 84357
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a055e9_l | comb_count_partitions_v1_1520064083_3602 | Let $m = 5$. Define $S$ as the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 9$ and $1 \leq j \leq 10$. Let $T$ be the set of all values of $k$ that appear in the pairs in $S$. Compute the sum of all elements in $T$, multiply this sum by $m$, and divide the result by 50 to obtain a num... | 5 | COMB | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_ARITHMETIC"
] | 9f7183 | comb_count_partitions_v1 | null | 7 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.001 | 2026-02-08T05:46:48.736243Z | {
"verified": false,
"answer": 89134,
"timestamp": "2026-02-08T05:46:48.737292Z"
} | b69ad2 | a055e9 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2802
},
"timestamp": "2026-02-24T04:27:58.720Z",
"answer": 5
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_IN... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | |
ff0aab | comb_factorial_compute_v1_1978505735_310 | Let $k$ be the largest integer such that $5^k \leq 119364$. Compute $k!$, the factorial of $k$. Let $Q$ be the remainder when $13164$ multiplied by this factorial is divided by $63157$. Compute $Q$. | 31,710 | graphs = [
Graph(
let={
"_n": Const(63157),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(5), Var("k")), Const(119364)))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(13164), Ref("result")), modulus=Ref("_n")),
},
... | ALG | COMB | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_factorial_compute_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T15:17:50.544537Z | {
"verified": true,
"answer": 31710,
"timestamp": "2026-02-08T15:17:50.545965Z"
} | b1b9b8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 977
},
"timestamp": "2026-02-24T20:13:48.035Z",
"answer": 31710
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
9e1787 | nt_sum_divisors_mod_v1_655260480_1054 | Let $m = 8100$ and $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $\sigma$ denote the sum of the positive divisors of $n$. Define $M = 11503$, and let $c$ be the number of integers $t$ satisfying $5 \le t \le 10005$ for which there exist positive integer... | 28,517 | graphs = [
Graph(
let={
"_m": Const(8100),
"_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("_m")))), expr... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 333563 | nt_sum_divisors_mod_v1 | quadratic_mod | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T15:52:55.889025Z | {
"verified": true,
"answer": 28517,
"timestamp": "2026-02-08T15:52:55.896933Z"
} | 6a0fb8 | 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": 4116
},
"timestamp": "2026-02-16T15:12:50.499Z",
"answer": 28517
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9f2ade | nt_min_with_divisor_count_v1_349078426_1167 | Let $N = 17$. Let $U$ be the number of nonnegative integers $j \leq 97191$ for which the binomial coefficient $\binom{97191}{j}$ is odd.\\
Let $d = 8$. Define $r$ to be the smallest positive integer $n \leq U$ that has exactly $d$ positive divisors.\\
Let $S$ be the set of all ordered pairs of positive integers $(x, ... | 3,012 | graphs = [
Graph(
let={
"_n": Const(17),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(97191)), Eq(Mod(value=Binom(n=Const(97191), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"V8"
] | e2d6ae | nt_min_with_divisor_count_v1 | quadratic_mod | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.174 | 2026-02-08T13:27:13.699827Z | {
"verified": true,
"answer": 3012,
"timestamp": "2026-02-08T13:27:13.873997Z"
} | 4e6da5 | 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": 2114
},
"timestamp": "2026-02-15T16:06:43.048Z",
"answer": 3012
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7b8e10 | nt_sum_totient_over_divisors_v1_784195855_2079 | Let $n$ be the smallest divisor of $5475599$ that is at least $2$. Compute the sum $\sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. | 2,339 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(5475599))))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T05:28:03.136341Z | {
"verified": true,
"answer": 2339,
"timestamp": "2026-02-08T05:28:03.139449Z"
} | f527a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 2319
},
"timestamp": "2026-02-12T09:17:45.604Z",
"answer": 2339
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
47f8d1 | sequence_fibonacci_compute_v1_601307018_8978 | Let $M$ be the number of integers $t$ such that $t = 4a + 6b + 12$ for some integers $a, b$ with $1 \le a \le 5$, $1 \le b \le 2$, and $22 \le t \le 44$. Let $C = \left| \{ n_1 \mid 1 \le n_1 \le 12680,\ M \mid n_1,\ \gcd(n_1, 21) = 1 \} \right|$. Let $n$ be the largest divisor of $C$ such that $1 \le n \le 25$. Comput... | 75,025 | graphs = [
Graph(
let={
"_c": Const(21),
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C5/MAX_DIVISOR"
] | 1566c4 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM",
"MAX_DIVISOR"
] | 3 | 0.007 | 2026-03-10T09:25:11.040901Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-03-10T09:25:11.048162Z"
} | 8926d1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 1778
},
"timestamp": "2026-04-19T10:17:43.013Z",
"answer": 75025
},
{
... | 2 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
14739b | algebra_poly_eval_v1_1419126231_1621 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ such that $50a^2 + 50b^2 = 16250$. Compute $6k^4 + 5k^3 - 10k^2 - 3k - 9$. | 8,469 | graphs = [
Graph(
let={
"_n": Const(20),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Eq(Sum(Mul(Const(50), Pow(Var("b"), Const(2))), Mu... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | algebra_poly_eval_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-02-25T11:09:29.538624Z | {
"verified": true,
"answer": 8469,
"timestamp": "2026-02-25T11:09:29.540598Z"
} | 8f9125 | 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": 1430
},
"timestamp": "2026-03-30T13:19:52.387Z",
"answer": 8469
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
18fab5 | nt_sum_divisors_mod_v1_1520064083_2362 | Let $n$ range over the positive integers. Define $S$ to be the set of all positive integers $n$ such that $1 \leq n \leq 24300$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = |S|$. Define $n_0 = \min\{x + y \mid (x, y... | 546 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(... | NT | null | COMPUTE | sympy | L3C | [
"L3C/B3"
] | 4d8a41 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3",
"L3C"
] | 2 | 0.002 | 2026-02-08T04:41:08.414954Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T04:41:08.416892Z"
} | 1b29c3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1604
},
"timestamp": "2026-02-11T21:49:22.326Z",
"answer": 546
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lem... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
1fc217 | nt_sum_divisors_mod_v1_1918700295_476 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 32400$. For each such pair, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $10247$. Determine the v... | 1,170 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10247)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:16:39.631361Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T03:16:39.632484Z"
} | 9f241d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1013
},
"timestamp": "2026-02-10T13:44:26.515Z",
"answer": 1170
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
0bd14e | nt_sum_divisors_mod_v1_1918700295_3430 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14400$. For each such pair, compute $x + y$. Let $n$ be the smallest value among all such sums. Define $\sigma$ to be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $11777$. | 744 | graphs = [
Graph(
let={
"n": SumOverDivisors(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Mul(Var(name='x'), Var(name='y')), right=Const(value=14400)))), expr=S... | NT | null | COMPUTE | sympy | B3 | [
"B3/K3"
] | 4a4ef2 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3",
"K3"
] | 2 | 0.002 | 2026-02-08T08:37:49.178893Z | {
"verified": true,
"answer": 744,
"timestamp": "2026-02-08T08:37:49.180451Z"
} | 92118f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1555
},
"timestamp": "2026-02-13T20:19:27.989Z",
"answer": 744
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
3a3637 | nt_count_coprime_and_v1_151522320_539 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 31447$, $\gcd(n, 3) = 1$, and $\gcd(n, 5) = 1$. Let $r$ be the number of elements in $A$.
Now, consider the set $T$ of all integers $t$ such that $8 \leq t \leq 30$ and there exist positive integers $a \leq 3$, $b \leq 5$ for which $t = 5a + 3b$... | 16,776 | graphs = [
Graph(
let={
"_n": Const(98752),
"upper": Const(31447),
"k1": Const(3),
"k2": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 812dee | nt_count_coprime_and_v1 | mod_exp | 6 | 0 | [
"LIN_FORM"
] | 1 | 5.362 | 2026-02-08T03:22:15.493781Z | {
"verified": true,
"answer": 16776,
"timestamp": "2026-02-08T03:22:20.855723Z"
} | ad37ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 1218
},
"timestamp": "2026-02-10T14:14:46.633Z",
"answer": 16776
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
2d2b44 | geo_count_lattice_triangle_v1_349078426_1352 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(100,64)$, and $(81,240)$, multiplied by $2$. Let $B$ be the number of lattice points on the boundary of this triangle, computed using the formula
\[
B = \gcd(100, 64) + \gcd(|81 - 100|, |240 - 64|) + \gcd(81, 240).
\]
Let $N = \frac{A + 2 - B}{2}$. Compute t... | 21,861 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=240)), Mul(Const(value=81), Sub(left=Const(value=0), right=Const(value=64))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=64))), GCD(a=Abs(arg=Sub(left=Const(value=81), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.01 | 2026-02-08T13:34:04.560136Z | {
"verified": true,
"answer": 21861,
"timestamp": "2026-02-08T13:34:04.570334Z"
} | 061a3a | 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": 1670
},
"timestamp": "2026-02-15T17:57:15.465Z",
"answer": 21861
},
... | 1 | [] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||||
9aeeac | nt_num_divisors_compute_v1_1440796553_1006 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 50$. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $50049 \cdot d(n)$ is divided by $51536$. | 44,101 | graphs = [
Graph(
let={
"_n": Const(50),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T12:05:38.913300Z | {
"verified": true,
"answer": 44101,
"timestamp": "2026-02-08T12:05:38.914248Z"
} | cd60e7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 500
},
"timestamp": "2026-02-14T22:30:14.617Z",
"answer": 44101
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0be4ec | nt_min_with_divisor_count_v1_1520064083_5370 | Let $n$ be a positive integer such that $n \leq 92416$ and the number of positive divisors of $n$ is exactly 4. Determine the value of the smallest such $n$. | 6 | graphs = [
Graph(
let={
"upper": Const(92416),
"div_count": Const(4),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("res... | NT | null | EXTREMUM | sympy | K2 | [
"MOBIUS_SQUAREFREE",
"MOBIUS_SUM"
] | 60a6e7 | nt_min_with_divisor_count_v1 | null | 3 | 0 | [
"K2",
"MOBIUS_SQUAREFREE",
"MOBIUS_SUM"
] | 3 | 29.535 | 2026-02-08T06:45:36.808767Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T06:46:06.344108Z"
} | 9eef0c | 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": 635
},
"timestamp": "2026-02-13T04:13:49.804Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
2a7d94 | nt_min_coprime_above_v1_124444284_4345 | Let $p$ be the largest prime number less than or equal to $158$. Let $T$ be the set of all integers $n$ such that $29929 < n \leq 30096$ and $\gcd(n, p) = 1$. Let $m$ be the smallest element of $T$. Compute the remainder when $32382 \cdot m$ is divided by $60427$. | 4,607 | graphs = [
Graph(
let={
"_n": Const(158),
"start": Const(29929),
"upper": Const(30096),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": MinOverSet... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.031 | 2026-02-08T05:56:27.920833Z | {
"verified": true,
"answer": 4607,
"timestamp": "2026-02-08T05:56:27.952276Z"
} | 005c65 | 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": 1261
},
"timestamp": "2026-02-12T16:40:43.804Z",
"answer": 4607
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f53b38 | comb_binomial_compute_v1_458359167_3591 | Let $n$ be the largest prime number such that $2 \leq n \leq 13$. Compute the binomial coefficient $\binom{n}{6}$. | 1,716 | graphs = [
Graph(
let={
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(13)), IsPrime(Var("n"))))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T08:27:17.106468Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T08:27:17.107376Z"
} | 89f580 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 792
},
"timestamp": "2026-02-15T20:14:27.050Z",
"answer": 1716
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma"... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
d7f366 | sequence_lucas_compute_v1_1915831931_4199 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 28$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 9$, and $t = 5a + 2b$. 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 $17155 \cdot... | 94,860 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T18:11:00.789912Z | {
"verified": true,
"answer": 94860,
"timestamp": "2026-02-08T18:11:00.792589Z"
} | d90ac6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2384
},
"timestamp": "2026-02-18T14:33:23.391Z",
"answer": 94860
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab5529 | nt_sum_divisors_range_v1_898971024_3009 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 104729$. Let $s$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute the sum of the number of positive divisors of each integer from $1$ to $s$. | 93,668 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(104729)), IsPrime(Var("n"))))),
"upper": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
... | NT | null | SUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/K3"
] | 682f29 | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"K3"
] | 2 | 0.462 | 2026-02-08T17:07:02.671764Z | {
"verified": true,
"answer": 93668,
"timestamp": "2026-02-08T17:07:03.133569Z"
} | 5ec727 | 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": 3539
},
"timestamp": "2026-02-17T19:20:00.868Z",
"answer": 93668
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
04700c | alg_poly_preperiod_count_v1_292587783_6 | Define the function $f(x) = (2x^3 - x^2 - 3x - 1) \bmod 41$. For each non-negative integer $a$ with $0 \le a \le 7174$, let $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$, $K = f(T)$. Let $Q$ be the number of such $a$ for which $K = M$, but $R \ne M$, $S \ne M$, and $T \ne M$. Find $Q$. | 2,450 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-1), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(-1)), modulus=Const(41)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-1), Pow(Ref("p1"), Const(2)))... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.147 | 2026-02-25T01:35:11.271680Z | {
"verified": true,
"answer": 2450,
"timestamp": "2026-02-25T01:35:11.418630Z"
} | e8b56a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 20724
},
"timestamp": "2026-03-10T07:53:00.138Z",
"answer": 2450
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
e01b57 | geo_count_lattice_rect_v1_1874849503_141 | Let $a = 37$ and $b = 35$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $Q$ be the remainder when $91685 \times \text{result}$ is divided by $92317$. Compute $Q$. | 58,594 | graphs = [
Graph(
let={
"a": Const(37),
"b": Const(35),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(91685), Ref("result")), modulus=Const(92317)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T12:49:55.195281Z | {
"verified": true,
"answer": 58594,
"timestamp": "2026-02-08T12:49:55.198252Z"
} | 8062d5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1154
},
"timestamp": "2026-02-09T14:07:02.997Z",
"answer": 58594
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
27e3bd | sequence_fibonacci_compute_v1_1978505735_3036 | Let $m = 22$. Define $n$ to be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1$ equals the maximum value of $xy$ over all pairs of positive integers $(x, y)$ with $x + y = m$. Let $F_n$ denote the $n$-th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_... | 11,055 | graphs = [
Graph(
let={
"_m": Const(22),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | K2 | [
"B1/B3"
] | 80b49d | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B1",
"B3",
"K2"
] | 3 | 0.014 | 2026-02-08T17:18:30.747141Z | {
"verified": true,
"answer": 11055,
"timestamp": "2026-02-08T17:18:30.761239Z"
} | 3e6717 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1541
},
"timestamp": "2026-02-18T00:31:18.226Z",
"answer": 11055
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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