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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
40b625 | geo_count_lattice_rect_v1_1915831931_956 | Compute the number of lattice points in the rectangle $[0, 377] \times [0, 140]$. | 53,298 | graphs = [
Graph(
let={
"a": Const(377),
"b": Const(140),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T15:46:11.642618Z | {
"verified": true,
"answer": 53298,
"timestamp": "2026-02-08T15:46:11.644562Z"
} | 522f2f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 282
},
"timestamp": "2026-02-24T18:27:47.984Z",
"answer": 53298
},
{
"... | 1 | [] | {
"lo": -5.09,
"mid": -2.97,
"hi": -0.71
} | ||||
627a1e | nt_count_gcd_equals_v1_1915831931_1408 | Let $p_{\text{max}}$ be the largest prime number $n$ such that $2 \le n \le 5859$. Let $k = 346$ and $d = 1$. Let $N$ be the number of positive integers $n_1$ such that $1 \le n_1 \le p_{\text{max}}$ and $\gcd(n_1, k) = d$. Compute the remainder when $39611 \cdot N$ is divided by $76348$. | 61,752 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(5859)), IsPrime(Var("n"))))),
"k": Const(346),
"d": Const(1),
"result": CountOverSet(set=Solution... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.52 | 2026-02-08T16:04:16.085199Z | {
"verified": true,
"answer": 61752,
"timestamp": "2026-02-08T16:04:16.604773Z"
} | 69a505 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1863
},
"timestamp": "2026-02-16T21:45:52.314Z",
"answer": 61752
},
... | 1 | [
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69250b | sequence_fibonacci_compute_v1_48377204_1902 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$, where $m$ is the number of integers $t$ in the range $27 \leq t \leq 210$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 10$, and $t = 15a + 12b$. Compute the $n$th Fibonacci number... | 75,025 | 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=6)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T16:29:03.291017Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T16:29:03.294971Z"
} | 927b0f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2209
},
"timestamp": "2026-02-17T04:37:46.106Z",
"answer": 75025
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b8687e_l | modular_count_residue_v1_151522320_1049 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $r = 1$ and let $\text{upper} = 64980$. Define $n$ to be a positive integer satisfying $1 \le n \le \text{upper}$ and $n \equiv r \pmod{m}$. Determine the value of the Bel... | 1 | NT | COMB | COUNT | sympy | LIN_FORM | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_count_residue_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 14.701 | 2026-02-08T03:43:38.223748Z | {
"verified": false,
"answer": 877,
"timestamp": "2026-02-08T03:43:52.924551Z"
} | ac2700 | b8687e | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 2172
},
"timestamp": "2026-02-10T15:33:53.694Z",
"answer": 877
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | |
62cd8b | nt_count_divisible_v1_784195855_430 | Let $n = 75428$ and let $U = 60516$. Let $T$ be the set of all positive integers $k$ such that $k$ is divisible by 15 and $1 \leq k \leq 75$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = \sum_{k \in T} k$. Define $d$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $P$. ... | 62,445 | graphs = [
Graph(
let={
"_n": Const(75428),
"upper": Const(60516),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), SumOv... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/B3"
] | 07ffbd | nt_count_divisible_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 4.3 | 2026-02-08T04:22:13.964659Z | {
"verified": true,
"answer": 62445,
"timestamp": "2026-02-08T04:22:18.264719Z"
} | aa10ef | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 1591
},
"timestamp": "2026-02-10T16:15:05.306Z",
"answer": 62445
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
c867be | nt_sum_divisors_mod_v1_865884756_6183 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 14288400$. Let $\sigma$ be the sum of all positive divisors of $n$. Let $M = 11257$ and let $r$ be the remainder when $\sigma$ is divided by $M$. Compute the remainder when $25707 \cdot r$ is divided by $92572$. ... | 56,062 | graphs = [
Graph(
let={
"_n": Const(92572),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400)))), expr=Sum(Var("x"), Var("y"... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T19:02:07.321258Z | {
"verified": true,
"answer": 56062,
"timestamp": "2026-02-08T19:02:07.324261Z"
} | 3cf58b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 2767
},
"timestamp": "2026-02-18T21:00:34.038Z",
"answer": 56062
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2d993f | nt_sum_divisors_compute_v1_1978505735_812 | Let $n = 52900$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2829124$. Define $c$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the remainder when $c - \sigma(n)$ is divided by $73382$. | 30,127 | graphs = [
Graph(
let={
"_n": Const(73382),
"n": Const(52900),
"result": SumDivisors(n=Ref("n")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_sum_divisors_compute_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T15:37:37.312667Z | {
"verified": true,
"answer": 30127,
"timestamp": "2026-02-08T15:37:37.316623Z"
} | 4f1b90 | 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": 1478
},
"timestamp": "2026-02-16T09:49:25.573Z",
"answer": 30127
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
27e550 | antilemma_k2_v1_784195855_4070 | Let $s = \sum_{d \mid 355} \phi(d)$, where $\phi$ is Euler's totient function. Define
$$
x = \sum_{k=1}^{s} \phi(k) \left\lfloor \frac{355}{k} \right\rfloor.
$$
Let $c = 27011$. Compute the remainder when $c \cdot x$ is divided by $78576$. | 75,794 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(89), Const(89)), end=SumOverDivisors(n=Const(value=355), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(355), Var("k"))))),
"_c": Const(27011),
"Q": Mod(value=Mul(Ref... | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K3/K2",
"K2"
] | 8236d1 | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_DIV_SELF",
"K2",
"K3"
] | 3 | 0.001 | 2026-02-08T06:47:52.610047Z | {
"verified": true,
"answer": 75794,
"timestamp": "2026-02-08T06:47:52.611156Z"
} | 391b50 | 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": 2471
},
"timestamp": "2026-02-13T04:57:04.634Z",
"answer": 75794
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0da7f4 | nt_min_crt_v1_153355830_74 | Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1296$. Find the smallest positive integer $n$ such that $n \le s$, $n \equiv 4 \pmod{8}$, and $n \equiv 5 \pmod{9}$. | 68 | graphs = [
Graph(
let={
"m": Const(8),
"k": Const(9),
"a": Const(4),
"b": Const(5),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"ONE_PHI_1",
"B3"
] | d3bb9b | nt_min_crt_v1 | null | 6 | 0 | [
"B3",
"ONE_PHI_1",
"ONE_PHI_2"
] | 3 | 0.069 | 2026-02-08T02:52:59.508570Z | {
"verified": true,
"answer": 68,
"timestamp": "2026-02-08T02:52:59.577230Z"
} | 31ebbf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 769
},
"timestamp": "2026-02-08T22:41:24.129Z",
"answer": 68
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "O... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
eadcc5 | antilemma_sum_equals_v1_1116507919_64 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 12$, $1 \leq j \leq 12$, and $i + j = 13$. Let $x$ be the number of elements in $S$. Compute $31329 - x$. | 31,317 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(13)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(12))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.04 | 2026-02-08T02:24:12.613020Z | {
"verified": true,
"answer": 31317,
"timestamp": "2026-02-08T02:24:12.652957Z"
} | 822395 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 503
},
"timestamp": "2026-02-08T18:58:30.047Z",
"answer": 31317
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -7.09,
"mid": -5.33,
"hi": -3.62
} | ||
1d0eda | antilemma_k3_v1_655260480_6063 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $71135$, where $\phi$ denotes Euler's totient function. | 71,135 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=71135), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T18:48:29.902592Z | {
"verified": true,
"answer": 71135,
"timestamp": "2026-02-08T18:48:29.903294Z"
} | e91c24 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 529
},
"timestamp": "2026-02-16T16:06:50.895Z",
"answer": 11085
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
eb96bd | algebra_quadratic_discriminant_v1_655260480_3089 | Let $A$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $B$ be the number of ordered pairs $(p_1, q)$ of positive integers such that $p_1q = 750$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Define
$$
D = (-18)^A - B \cdot (-2) \cdot (-28).
$$
Let $\alpha = 1$... | 34,967 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(-18),
"c": Const(-28),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.007 | 2026-02-08T17:10:50.248403Z | {
"verified": true,
"answer": 34967,
"timestamp": "2026-02-08T17:10:50.255547Z"
} | d73490 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2025
},
"timestamp": "2026-02-17T21:04:58.792Z",
"answer": 34967
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f9d0e4 | antilemma_k2_v1_458359167_5397 | Let $x = \sum_{k=1}^{173} \phi(k) \left\lfloor \frac{173}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Find the remainder when $9444 \cdot x$ is divided by $75733$. | 66,536 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(173), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(173), Var("k"))))),
"Q": Mod(value=Mul(Const(9444), Ref("x")), modulus=Const(75733)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.003 | 2026-02-08T12:27:32.798174Z | {
"verified": true,
"answer": 66536,
"timestamp": "2026-02-08T12:27:32.801600Z"
} | 4692b7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 802
},
"timestamp": "2026-02-15T01:00:57.033Z",
"answer": 66536
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3bfcd2 | diophantine_fbi2_count_v1_1520064083_7297 | Compute the number of positive integers $d$ such that $6 \leq d \leq 55$, $d$ divides $60$, and $5 \leq \frac{60}{d} \leq 54$. | 3 | graphs = [
Graph(
let={
"k": Const(60),
"a": Const(5),
"b": Const(4),
"upper": Const(50),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(55)), Divides(divisor=Var("d"), dividend=Ref(... | NT | null | COUNT | sympy | LIN_FORM | [
"B1/C5",
"LIN_FORM"
] | 0dec89 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B1",
"C5",
"LIN_FORM"
] | 3 | 0.077 | 2026-02-08T08:53:28.613562Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T08:53:28.690272Z"
} | f2ed49 | 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": 938
},
"timestamp": "2026-02-13T22:52:03.153Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemm... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
45d781 | comb_catalan_compute_v1_971394319_139 | Let $a = 5$ and $b = 3$, and define $n_2 = a + b$. Let $v = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Define $n_1 = \binom{13}{0} - 1 + v$. Let $u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 11$, $j \leq 12$, and $i + j = 12$. Let $r =... | 56,392 | graphs = [
Graph(
let={
"_n": Const(12),
"a": Const(5),
"b": Const(3),
"n2": Sum(Ref("a"), Ref("b")),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ZERO_BINOM_0"
] | dd300a | comb_catalan_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ZERO_BINOM_0"
] | 3 | 0.016 | 2026-02-08T12:51:20.191810Z | {
"verified": true,
"answer": 56392,
"timestamp": "2026-02-08T12:51:20.207916Z"
} | 24a2fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 21813
},
"timestamp": "2026-02-24T16:37:28.894Z",
"answer": 56392
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
5c3945 | antilemma_sum_equals_v1_865884756_362 | Let $t$ be a positive integer such that $21 \le t \le 192$ and there exist positive integers $a$, $b$ with $1 \le a \le 10$, $1 \le b \le 7$, and $t = 15a + 6b$. Let $n$ be the number of such integers $t$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 54$, $1 \le j \le 54$,... | 53 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T15:19:38.173672Z | {
"verified": true,
"answer": 53,
"timestamp": "2026-02-08T15:19:38.180181Z"
} | 59eca4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T20:34:20.587Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
a465a2 | alg_poly_preperiod_count_v1_1419126231_1296 | Let $f(x) = 3x^5 - 5x^4 - 4x^3 + 3x^2 + 5x - 4$. For a non-negative integer $a$, define the sequence $N = f(a) \bmod 19$, $M = f(N) \bmod 19$, $R = f(M) \bmod 19$, $S = f(R) \bmod 19$, $T = f(S) \bmod 19$, $K = f(T) \bmod 19$. Find the number of integers $a$ with $0 \le a \le 20082$ such that $K = M$, $R \ne M$, $S \ne... | 6,342 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(5))), Mul(Const(-5), Pow(Var("a"), Const(4))), Mul(Const(-4), Pow(Var("a"), Const(3))), Mul(Const(3), Pow(Var("a"), Const(2))), Mul(Const(5), Var("a")), Const(-4)), modulus=Const(19)),
"p2": Mod(value=Sum(M... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 1.274 | 2026-02-25T10:44:15.696754Z | {
"verified": true,
"answer": 6342,
"timestamp": "2026-02-25T10:44:16.970819Z"
} | 1a0f53 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 22861
},
"timestamp": "2026-03-30T12:03:52.280Z",
"answer": 6342
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
98ec1f | algebra_poly_eval_v1_655260480_5396 | Let $n = 6$. Define $S$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4$. Let $T$ be the set of all values of $x + y$ as $(x, y)$ ranges over $S$. Let $m$ be the minimum value in $T$. Compute $7n^3 + 5n^2 + m n + 10$. | 1,726 | graphs = [
Graph(
let={
"_n": Const(10),
"n": Const(6),
"result": Sum(Mul(Const(7), Pow(Ref("n"), Const(3))), Mul(Const(5), Pow(Ref("n"), Const(2))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T18:27:31.683954Z | {
"verified": true,
"answer": 1726,
"timestamp": "2026-02-08T18:27:31.685752Z"
} | 8417d1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 451
},
"timestamp": "2026-02-16T12:21:57.738Z",
"answer": 1726
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
f7daab | nt_count_gcd_equals_v1_1520064083_1926 | Let $n$ be a positive integer such that $1 \leq n \leq 22222$ and $\gcd(n, 291) = 1$. Compute the number of such integers $n$. | 14,662 | graphs = [
Graph(
let={
"upper": Const(22222),
"k": Const(291),
"d": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
},
... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 3.789 | 2026-02-08T04:22:54.787030Z | {
"verified": true,
"answer": 14662,
"timestamp": "2026-02-08T04:22:58.576225Z"
} | a9010a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1021
},
"timestamp": "2026-02-10T16:21:44.422Z",
"answer": 14662
},
{
... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
d38c54 | modular_inverse_v1_151522320_2399 | Let $a$ be the number of integers $t$ such that $11 \leq t \leq 561$ and there exist integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 121$, and $t = 7a + 4b$.
Let $m$ be the largest prime number less than or equal to $557$.
Let $n = 77284$, and define $\text{upper}$ to be the minimum value of $x + y$ over... | 116 | graphs = [
Graph(
let={
"_n": Const(77284),
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=V... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM",
"B3"
] | f0dad2 | modular_inverse_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.055 | 2026-02-08T04:47:39.033950Z | {
"verified": true,
"answer": 116,
"timestamp": "2026-02-08T04:47:39.089434Z"
} | 32ac92 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 292,
"completion_tokens": 4818
},
"timestamp": "2026-02-11T21:56:17.355Z",
"answer": 116
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b965ff | comb_count_partitions_v1_784195855_3860 | Let $n = 38$. Let $A$ be the number of positive integers $j$ such that $1 \leq j \leq 2809$ and $j^3 \leq 22164361129$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $A - p(n)$ is divided by 86744. | 63,538 | graphs = [
Graph(
let={
"_n": Const(86744),
"n": Const(38),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2809)), Leq(Pow(Var("j"), Const(3)), C... | COMB | null | COUNT | sympy | C3 | [
"C3"
] | a45c54 | comb_count_partitions_v1 | negation_mod | 5 | 0 | [
"C3"
] | 1 | 0.002 | 2026-02-08T06:40:31.339255Z | {
"verified": true,
"answer": 63538,
"timestamp": "2026-02-08T06:40:31.341128Z"
} | 637b1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T06:48:34.000Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
e5912c | nt_num_divisors_compute_v1_458359167_4685 | Let $T$ be the set of all integers $t$ with $18 \leq t \leq 1722$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 69$, $1 \leq b \leq 189$, and $t = 14a + 4b$. Let $n$ be the smallest integer $d \geq 2$ that divides the number of elements in $T$. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=69)), Geq(left=Var(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.012 | 2026-02-08T11:59:20.913076Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T11:59:20.925551Z"
} | 3bac2d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2867
},
"timestamp": "2026-02-14T21:42:58.313Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5c538b | alg_sum_ap_v1_1218484723_6262 | Let $S$ be the set of integers $t$ such that $t = 4a + 3b$ for some integers $a, b$ with $1 \leq a \leq 118$, $1 \leq b \leq 708$, and $7 \leq t \leq 2596$. Let $T$ be the set of integers $t_1$ such that $t_1 = 3a + 2b$ for some integers $a, b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $5 \leq t_1 \leq 17$. Define... | 203 | graphs = [
Graph(
let={
"_n": Const(80),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(995), expr=Sum(Mul(Const(4), Var("k")), Ref("_n"))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), c... | COMB | COMB | COMPUTE | sympy | COUNT_CARTESIAN | [
"LIN_FORM"
] | 1ae498 | alg_sum_ap_v1 | bell_mod | 4 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.031 | 2026-02-25T07:49:44.452485Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-25T07:49:44.483199Z"
} | 713e7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 329,
"completion_tokens": 2218
},
"timestamp": "2026-03-30T00:57:36.351Z",
"answer": 15
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
d756d4 | diophantine_fbi2_min_v1_151522320_2532 | Let $n = 32400$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$.
Let $r$ be the smallest integer $d$ in the interval $[6, 370]$ such that $d$ divides $k$ and $\frac{k}{d} \geq 5$.
Let $Q = \sum_{i=1}^{r} \phi(i)$, where $\phi$ denotes Euler's totient fu... | 12 | graphs = [
Graph(
let={
"_n": Const(32400),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.05 | 2026-02-08T04:52:19.098135Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T04:52:19.147909Z"
} | 1001cf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 854
},
"timestamp": "2026-02-11T22:21:14.479Z",
"answer": 12
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
24de51 | nt_count_with_divisor_count_v1_153355830_2080 | Let $n$ be a positive integer such that $1 \leq n \leq 44551$. A nonnegative integer $j$ is called *odd-binomial* if $0 \leq j \leq 65560$ and $\binom{65560}{j}$ is odd. Let $d$ be the number of odd-binomial integers, increased by 3. Compute the number of positive integers $n \leq 44551$ that have exactly $d$ positive ... | 1 | graphs = [
Graph(
let={
"upper": Const(44551),
"div_count": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65560)), Eq(Mod(value=Binom(n=Const(65560), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers'... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_with_divisor_count_v1 | null | 7 | 0 | [
"V8"
] | 1 | 1.837 | 2026-02-08T06:53:20.952229Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T06:53:22.789456Z"
} | 0ba44a | 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": 1293
},
"timestamp": "2026-02-13T05:37:33.319Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
783294 | diophantine_fbi2_min_v1_2051736721_1741 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 144$. Let $S$ be the set of all integers $d$ such that $6 \leq d \leq 34$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Determine the value of $44121$ multiplied by the smallest element of $S$, modulo $66427$. Com... | 65,445 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(144)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(34),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T16:12:12.626138Z | {
"verified": true,
"answer": 65445,
"timestamp": "2026-02-08T16:12:12.631633Z"
} | 181123 | 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": 656
},
"timestamp": "2026-02-16T22:40:09.569Z",
"answer": 65445
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b810d3 | modular_mod_compute_v1_655260480_4591 | Let $d = 5$. Let $m$ be the largest prime number less than or equal to $d$. Let $T$ be the set of all nonnegative integers $j$ such that $0 \le j \le 48463$ and $\binom{48463}{j}$ is odd. Define $n$ to be the number of elements in $T$. Let $a = -1369$. Let $S$ be the set of all positive integers $j_1$ such that $1 \le ... | 55,017 | graphs = [
Graph(
let={
"_d": Const(5),
"_m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_d")), IsPrime(Var("n"))))),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/V8/C3"
] | 87ba48 | modular_mod_compute_v1 | null | 7 | 0 | [
"C3",
"MAX_PRIME_BELOW",
"V8"
] | 3 | 0.007 | 2026-02-08T18:00:27.682631Z | {
"verified": true,
"answer": 55017,
"timestamp": "2026-02-08T18:00:27.689730Z"
} | 1f88b5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 1868
},
"timestamp": "2026-02-18T11:45:35.446Z",
"answer": 55017
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
127d38 | comb_count_derangements_v1_1218484723_3489 | Let $n = \sum_{k=0}^{2} 2^k$ and let $D_n$ denote the number of derangements of $n$ elements. Compute $D_n$. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Ref("_n"), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 2 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T05:09:44.388600Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-25T05:09:44.389450Z"
} | f3df8a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1227
},
"timestamp": "2026-03-29T10:33:18.651Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
5f2c87 | diophantine_fbi2_count_v1_1978505735_1079 | Let $m=1764$, $n_0=4$, and $k=240$.
Let $A$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le4$, $1\le b\le21$, $21\le t\le116$, and
$$t=5a+4b+12.$$
Let $B$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=72, \quad \gcd(p... | 9 | graphs = [
Graph(
let={
"_m": Const(1764),
"_n": Const(4),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3/MAX_PRIME_BELOW",
"LIN_FORM"
] | 04da8e | diophantine_fbi2_count_v1 | null | 8 | 0 | [
"B3",
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 4 | 0.025 | 2026-02-08T15:48:56.647435Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T15:48:56.672856Z"
} | 518af8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 342,
"completion_tokens": 4343
},
"timestamp": "2026-02-16T14:45:43.492Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
45c966 | comb_bell_compute_v1_2051736721_2694 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 4231249$. Let $T$ be the set of all values $x+y$ where $(x,y) \in S$. Let $m$ be the minimum value in $T$. For each nonnegative integer $j$ with $0 \leq j \leq 4114$, compute $\binom{m}{j} \bmod 2$. Let $n$ be the number of values of $... | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4114)), Eq(Mod(value=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositi... | COMB | null | COMPUTE | sympy | B3 | [
"B3/V8"
] | 4fad5b | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.005 | 2026-02-08T16:50:59.929987Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:50:59.935029Z"
} | b30f64 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1375
},
"timestamp": "2026-02-17T13:13:45.481Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
387d02 | nt_count_divisible_v1_168721529_465 | Let $n$ be a positive integer. Define $d$ to be the number of positive integers $t$ such that $1 \leq t \leq 51$ and $\gcd(t, 10) = 1$. Let $k$ be the number of ordered pairs $(a, b)$ of positive integers such that $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $7 \leq 5a + 2b \leq 25$. Define $m = \sum_{d \mid \gcd(8, k)} ... | 3,048 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": Const(64009),
"divisor": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(51)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_COPRIME",
"C4"
] | 5f36ae | nt_count_divisible_v1 | null | 7 | 0 | [
"C4",
"LIN_FORM",
"MOBIUS_COPRIME"
] | 3 | 3.145 | 2026-02-08T13:03:52.775271Z | {
"verified": true,
"answer": 3048,
"timestamp": "2026-02-08T13:03:55.920403Z"
} | a033e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 300,
"completion_tokens": 2271
},
"timestamp": "2026-02-09T05:20:34.542Z",
"answer": 3048
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
1cdf8f | comb_count_surjections_v1_458359167_3129 | Let $S$ be the set of all integers $t$ such that $21 \leq t \leq 47$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 10a + 4b + 7$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = |S|$. Compute the value of $2! \cdot S(n, 2)$, ... | 30 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T06:59:19.107051Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T06:59:19.109458Z"
} | 47fe57 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1178
},
"timestamp": "2026-02-24T07:28:18.735Z",
"answer": 30
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
ae35a0 | comb_factorial_compute_v1_784195855_10215 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 40961$ such that $\binom{40961}{j}$ is odd. Let $r = n!$. Compute the remainder when $10478r$ is divided by $69851$. | 14,112 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(40961)), Eq(Mod(value=Binom(n=Const(40961), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T17:30:36.901028Z | {
"verified": true,
"answer": 14112,
"timestamp": "2026-02-08T17:30:36.902607Z"
} | c2b1fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 2321
},
"timestamp": "2026-02-18T03:18:09.695Z",
"answer": 14112
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
ed6890 | geo_visible_lattice_v1_677425708_2651 | Let $n = 144$. Define $\text{result}$ to be the number of visible lattice points $(x,y)$ with $1 \leq x, y \leq n$, where a point $(x,y)$ is visible if $\gcd(x,y) = 1$. Let $Q$ be the remainder when $2020 - \text{result}$ is divided by $57830$. Compute $Q$. | 47,191 | graphs = [
Graph(
let={
"n": Const(144),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(2020),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(57830)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 2.762 | 2026-02-08T05:10:18.667617Z | {
"verified": true,
"answer": 47191,
"timestamp": "2026-02-08T05:10:21.429526Z"
} | c3a2c5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 7327
},
"timestamp": "2026-02-24T02:47:09.469Z",
"answer": 47167
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
3fe79b | sequence_lucas_compute_v1_601307018_10360 | Let $R$ be the number of integers $j$ with $0 \le j \le 1404$ such that $\binom{1404}{j} \equiv 1 \pmod{2}$. Let $S$ be the largest positive divisor $d$ of $149376$ such that $d^{2} \le 149376$. Let $E$ be the set
\[E = \{p : p > 0,\ \text{there exists an integer } q \text{ with } pq = 12,\ \gcd(p, q) = 1,\ p < q\},\]
... | 9,349 | graphs = [
Graph(
let={
"_d": Const(40),
"_c": Const(3),
"_m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1404)), Eq(Mod(value=Binom(n=Const(1404), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_... | NT | null | COMPUTE | sympy | V8 | [
"V8/B3_CLOSEST/POLY3_COUNT",
"COPRIME_PAIRS/POLY3_COUNT",
"B3/POLY3_COUNT"
] | 311601 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"B3",
"B3_CLOSEST",
"COPRIME_PAIRS",
"POLY3_COUNT",
"V8"
] | 5 | 0.023 | 2026-03-10T10:50:36.039643Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-03-10T10:50:36.062660Z"
} | 9c1f7c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 414,
"completion_tokens": 2174
},
"timestamp": "2026-04-19T13:37:52.497Z",
"answer": 9349
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
57e7c9 | comb_count_partitions_v1_2051736721_3951 | Let $ m = 26741 $. Define $ n_0 $ to be the smallest divisor of $ m $ that is at least $ 2 $. Let $ T $ be the set of all integers $ t $ such that $ 24 \leq t \leq 171 $ and there exist integers $ a $ and $ b $ with $ 1 \leq a \leq 3 $, $ 1 \leq b \leq 14 $, and $ t = 15a + 9b $. Let $ n $ be the number of elements in ... | 1 | graphs = [
Graph(
let={
"_m": Const(26741),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condit... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/LIN_FORM"
] | b86314 | comb_count_partitions_v1 | bell_mod | 7 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.029 | 2026-02-08T17:38:10.393007Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:38:10.422440Z"
} | dd7bd5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1422
},
"timestamp": "2026-02-18T05:05:15.235Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ddfa74 | antilemma_v1_legendre_1742523217_751 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1361889$. Let $s$ be the minimum value of $x + y$ over all such pairs. Determine the largest integer $k$ such that $3^k$ divides $s!$. | 1,164 | graphs = [
Graph(
let={
"_n": Const(3),
"x": MaxKDivides(target=Factorial(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(1361889)))), ex... | NT | null | COMPUTE | sympy | B3 | [
"B3/V1",
"V1"
] | 25e8f3 | antilemma_v1_legendre | null | 5 | 0 | [
"B3",
"V1"
] | 2 | 0.002 | 2026-02-08T03:12:12.150029Z | {
"verified": true,
"answer": 1164,
"timestamp": "2026-02-08T03:12:12.152039Z"
} | 205c54 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2135
},
"timestamp": "2026-02-09T22:12:54.797Z",
"answer": 1164
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
04a73c | modular_inverse_v1_1520064083_4547 | Let $a = 322$ and $m = 691$. Let $U = \sum_{d \mid 690} \phi(d)$, where $\phi$ is Euler's totient function. Determine the value of the smallest positive integer $x$ such that $1 \le x \le U$ and
$$
322x \equiv 1 \pmod{691}.
$$ | 294 | graphs = [
Graph(
let={
"a": Const(322),
"m": Const(691),
"upper": SumOverDivisors(n=Const(value=690), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper... | NT | null | EXTREMUM | sympy | K3 | [
"K3"
] | 54c41e | modular_inverse_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.066 | 2026-02-08T06:19:05.894237Z | {
"verified": true,
"answer": 294,
"timestamp": "2026-02-08T06:19:05.960285Z"
} | 783b99 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1264
},
"timestamp": "2026-02-15T17:22:23.915Z",
"answer": 578
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e1f22e | alg_telescope_v1_1218484723_2026 | Let
\[
R \equiv \sum_{k=0}^{451} \bigl(4k^{3} + C\,k^{2} + 4k + 1\bigr) \pmod{9167},
\]
where
\[
C = \min\{x + y : (x, y),\ x > 0,\ y > 0,\ x y = D\}
\]
and
\[
D = \min\{-46ab + 26b^{2} + 29a^{2} : (a, b),\ a \ge 1,\ a \le 23,\ b \ge 1,\ b \le 23\}.
\]
Compute $66564 - R$. | 61,582 | graphs = [
Graph(
let={
"_m": Const(23),
"_n": Const(66564),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(451), expr=Sum(Mul(Const(4), Pow(Var("k"), Const(3))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN/B3"
] | c7baf3 | alg_telescope_v1 | null | 7 | 0 | [
"B3",
"QF_PSD_MIN"
] | 2 | 0.041 | 2026-02-25T03:43:42.207350Z | {
"verified": true,
"answer": 61582,
"timestamp": "2026-02-25T03:43:42.248010Z"
} | 93d109 | 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": 3364
},
"timestamp": "2026-03-29T02:35:25.050Z",
"answer": 61582
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
43f2de | nt_count_divisible_v1_784195855_5007 | Let $A$ be the number of positive integers $n$ such that $n \leq 60000$ and $n$ is divisible by 19. Let $B$ be the largest positive divisor of 1147 that is at most 31. Compute the remainder when $A^2 + 3A + B$ is divided by 56548. | 23,703 | graphs = [
Graph(
let={
"_n": Const(31),
"upper": Const(60000),
"divisor": Const(19),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Cons... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | d27307 | nt_count_divisible_v1 | quadratic_mod | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 1.933 | 2026-02-08T07:32:54.557170Z | {
"verified": true,
"answer": 23703,
"timestamp": "2026-02-08T07:32:56.489935Z"
} | f10bbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1289
},
"timestamp": "2026-02-13T11:14:56.774Z",
"answer": 23703
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8ee4e6 | modular_modexp_compute_v1_151522320_852 | Let $a = 17$. Let $e$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 5$ and $1 \leq j \leq 96$ such that $\gcd(i, j) = 1$. Compute the remainder when $a^e$ is divided by $32768$. | 25,297 | graphs = [
Graph(
let={
"a": Const(17),
"e": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Co... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | modular_modexp_compute_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T03:35:20.689614Z | {
"verified": true,
"answer": 25297,
"timestamp": "2026-02-08T03:35:20.691545Z"
} | 76715e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 2902
},
"timestamp": "2026-02-10T13:53:36.434Z",
"answer": 25297
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
121861 | antilemma_sum_equals_v1_1456120455_55 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 5$, $1 \leq j \leq 6$, and $i + j = 6$. Compute $x + \phi(|x| + 1) + \tau(|x| + \binom{14}{14})$, where $\phi$ is Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. | 11 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(6))))),
"Q": Sum... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | eb8b36 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | 3 | 0.031 | 2026-02-08T02:51:48.925554Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T02:51:48.956314Z"
} | 2f541a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 694
},
"timestamp": "2026-02-08T19:55:18.560Z",
"answer": 11
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.98
} | ||
465444 | nt_min_crt_v1_124444284_3156 | Compute the smallest positive integer $n$ such that $n \le 15$, $n \equiv 0 \pmod{3}$, and $n \equiv 1 \pmod{5}$. | 6 | graphs = [
Graph(
let={
"m": Const(3),
"k": Const(5),
"a": Const(0),
"b": Const(1),
"upper": Const(15),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/OMEGA_ZERO",
"BIG_OMEGA_ZERO"
] | 1c3ded | nt_min_crt_v1 | null | 3 | 0 | [
"BIG_OMEGA_ZERO",
"MIN_PRIME_FACTOR",
"OMEGA_ZERO"
] | 3 | 0.079 | 2026-02-08T05:16:26.000581Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T05:16:26.079669Z"
} | b013d7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 580
},
"timestamp": "2026-02-11T22:23:30.911Z",
"answer": 6
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "OMEGA_ZERO",
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
9d33d0 | sequence_fibonacci_compute_v1_601307018_8058 | Let $F_n$ denote the $n$-th Fibonacci number. Determine the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $16b^2 = 1600$, and let $n$ be this count. Compute $F_n$. | 75,025 | graphs = [
Graph(
let={
"_n": Const(25),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Mul(Const(16), Pow(Var("b"), Const(2))), Const(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.003 | 2026-03-10T08:34:54.337492Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-03-10T08:34:54.340366Z"
} | 60da26 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 820
},
"timestamp": "2026-04-19T08:10:54.211Z",
"answer": 75025
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
36813c | lin_form_endings_v1_1915831931_941 | Let $a = 56$ and $b = 16$. Compute $\text{lcm}(a, b)$. Multiply this least common multiple by $9058$, and let $M = 59035$. Find the remainder when the product is divided by $M$. | 10,901 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(16),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(9058),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(59035),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:46:02.864988Z | {
"verified": true,
"answer": 10901,
"timestamp": "2026-02-08T15:46:02.866150Z"
} | cb084d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 551
},
"timestamp": "2026-02-16T12:27:14.209Z",
"answer": 10901
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
32dbad | algebra_poly_eval_v1_784195855_5735 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 15$, $3$ divides $n$, and $\gcd(n, 14) = 1$. Let $m_1$ be the number of elements in $A$.
Let $B$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 7$, $16 \leq t \leq 43$, an... | 1,534 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(15)), Divides(divisor=Const(3), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_m")), Const(1))))),
"m": CountOverSet(set=S... | NT | null | COMPUTE | sympy | C5 | [
"C5/LIN_FORM"
] | d740a6 | algebra_poly_eval_v1 | null | 5 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T08:05:17.829917Z | {
"verified": true,
"answer": 1534,
"timestamp": "2026-02-08T08:05:17.833087Z"
} | e84569 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1706
},
"timestamp": "2026-02-13T14:29:31.876Z",
"answer": 1534
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e40ffd | nt_count_intersection_v1_1439011603_1894 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $a = 7$ and $b = 12$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 12) = 1$. Compute the remainder when $44121 \cdot |T|$ is divided by... | 41,078 | 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(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(7),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.355 | 2026-02-08T16:20:52.862762Z | {
"verified": true,
"answer": 41078,
"timestamp": "2026-02-08T16:20:53.218065Z"
} | db5d6d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1504
},
"timestamp": "2026-02-17T01:42:27.199Z",
"answer": 41078
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7da6ae | antilemma_sum_primes_v1_53965629_105 | Let $m=3$ and let $n_0$ be the smallest positive integer $n$ such that the highest power of $2$ dividing $n!$ is at least $m$.
Let $A$ be the set of all ordered pairs $(p,q)$ of positive integers such that $pq=24$, $\gcd(p,q)=1$, and $p<q$. Let $k$ be the number of positive integers $p$ for which there exists a positi... | 52 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"x": SumOverSet(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(... | NT | COMB | COMPUTE | sympy | SUM_PRIMES | [
"MIN_PRIME_FACTOR",
"COPRIME_PAIRS/SUM_PRIMES",
"V5/SUM_PRIMES",
"SUM_PRIMES"
] | a70149 | antilemma_sum_primes_v1 | bell_mod | 8 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"SUM_PRIMES",
"V5"
] | 4 | 0.201 | 2026-02-08T11:16:57.186676Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T11:16:57.387709Z"
} | b54ddf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 369,
"completion_tokens": 4301
},
"timestamp": "2026-02-09T12:28:43.130Z",
"answer": 52
},
{
"id"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"... | {
"lo": -6.51,
"mid": -0.38,
"hi": 5.12
} | ||
ccfedb | comb_count_permutations_fixed_v1_1918700295_4444 | Let $S$ be the set of all positive integers $n$ such that the sum of the digits of $n$ is divisible by $2$, and $n$ is at most the number of prime numbers between $2$ and $d$, inclusive, where $d$ is the smallest divisor of $219539$ that is at least $2$. Let $n$ be the number of elements in $S$. Define $k = 0$ and let ... | 30,973 | graphs = [
Graph(
let={
"_m": Const(54822),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(se... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_PRIMES/L3B"
] | a8ddb6 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"COUNT_PRIMES",
"L3B",
"MIN_PRIME_FACTOR"
] | 3 | 0.004 | 2026-02-08T09:23:28.140836Z | {
"verified": true,
"answer": 30973,
"timestamp": "2026-02-08T09:23:28.144559Z"
} | b3c6fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 3000
},
"timestamp": "2026-02-14T03:24:01.592Z",
"answer": 30973
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
243db1 | nt_count_gcd_equals_v1_784195855_7849 | Let $k$ be the number of nonnegative integers $j$ such that $0 \le j \le 33508$ and $\binom{33508}{j}$ is odd. Let $d$ be the number of positive integers $n$ such that $1 \le n \le 15120$ and $\gcd(n, k) = 1$. Compute the smallest positive integer $m$ such that the $m$th Fibonacci number is divisible by $|d| + 2$. | 198 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(15120),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(33508)), Eq(Mod(value=Binom(n=Const(33508), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonn... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"V8"
] | 1 | 2.319 | 2026-02-08T09:33:35.545935Z | {
"verified": true,
"answer": 198,
"timestamp": "2026-02-08T09:33:37.864468Z"
} | 68e0ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 2583
},
"timestamp": "2026-02-14T05:05:02.063Z",
"answer": 198
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5371c6 | modular_min_modexp_v1_1915831931_1552 | Let $n = 15$, $a = 3$, and $b = 103$. Define $m$ to be the number of positive integers $k$ such that $1 \leq k \leq 11415$ and $n$ divides $k$. Let $\text{upper} = 152$. Consider the set of all positive integers $x$ such that $1 \leq x \leq \text{upper}$ and $a^x \equiv b \pmod{m}$. Let $r$ be the smallest such $x$. Co... | 28 | graphs = [
Graph(
let={
"_n": Const(15),
"a": Const(3),
"b": Const(103),
"m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(11415)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integ... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"C2"
] | 9685eb | modular_min_modexp_v1 | null | 7 | 0 | [
"C2",
"MIN_PRIME_FACTOR"
] | 2 | 0.077 | 2026-02-08T16:14:37.880454Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T16:14:37.957731Z"
} | b3eae1 | 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": 2643
},
"timestamp": "2026-02-17T00:30:23.729Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ce1ce9 | geo_count_lattice_rect_v1_168721529_773 | Let $a = 256$ and $b = 110$. Define the rectangle $R$ as the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $N$ be the number of lattice points in $R$. Compute the remainder when $61021 \cdot N$ is divided by $55838$. | 52,255 | graphs = [
Graph(
let={
"a": Const(256),
"b": Const(110),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(61021), Ref("result")), modulus=Const(55838)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T13:17:22.367103Z | {
"verified": true,
"answer": 52255,
"timestamp": "2026-02-08T13:17:22.369207Z"
} | 7286e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2279
},
"timestamp": "2026-02-09T08:59:05.948Z",
"answer": 52255
},
{
"... | 1 | [] | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||||
4567f4 | nt_min_coprime_above_v1_48377204_2175 | Let $m$ be the number of positive integers $j$ such that $1 \leq j \leq 275$ and $j^2 \leq 75625$. Let $R$ be the set of all integers $n$ such that $44444 < n \leq 44729$ and $\gcd(n, m) = 1$. Let $r$ be the smallest element of $R$. Compute $54323 \cdot r$ and find the remainder when this product is divided by $60792$.... | 24,986 | graphs = [
Graph(
let={
"_n": Const(2),
"start": Const(44444),
"upper": Const(44729),
"modulus": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(275)), Leq(Pow(Var("j"), Ref("_n")), Const(75625))), domain=... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | 8a214c | nt_min_coprime_above_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.12 | 2026-02-08T16:37:41.162329Z | {
"verified": true,
"answer": 24986,
"timestamp": "2026-02-08T16:37:41.281897Z"
} | 1f8944 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1588
},
"timestamp": "2026-02-17T09:10:52.034Z",
"answer": 24986
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c86b9 | diophantine_product_count_v1_1125832087_618 | Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 447$, $3$ divides $n$, and $$\gcd\left(n, \sum_{\substack{m=1 \\ 10 \mid m}}^{10} m\right) = 1.$$ Let the upper bound be $46$. Define $r$ as the number of positive integers $x$ such that $1 \leq x \leq 46$, $x$ divides $k$, and $\frac{k}{x} \leq 46... | 24,850 | graphs = [
Graph(
let={
"_n": Const(93323),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(447)), Divides(divisor=Const(3), dividend=Var("n")), Eq(GCD(a=Var("n"), b=SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Ge... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/C5"
] | 8ed5a5 | diophantine_product_count_v1 | null | 5 | 0 | [
"C5",
"SUM_DIVISIBLE"
] | 2 | 0.011 | 2026-02-08T03:10:13.911637Z | {
"verified": true,
"answer": 24850,
"timestamp": "2026-02-08T03:10:13.922759Z"
} | b7dd32 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 1652
},
"timestamp": "2026-02-10T12:56:15.563Z",
"answer": 24850
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f71929 | antilemma_k3_v1_898971024_2199 | Let $n = 99433$ and define $x = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$ and $\phi$ is Euler's totient function. Let $Q$ be the Bell number $B_r$, where $r$ is the remainder when $|x|$ is divided by $11$. Find the value of $Q$. | 15 | graphs = [
Graph(
let={
"_n": Const(99433),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:36:02.635209Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T16:36:02.635786Z"
} | 34aac7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1284
},
"timestamp": "2026-02-16T07:33:04.301Z",
"answer": 15
},
{
"id": 11,
... | 2 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
26bb3d | nt_num_divisors_compute_v1_1520064083_599 | Let $n = 50400$. Define $d(n)$ to be the number of positive divisors of $n$. Compute $d(n)$. | 108 | graphs = [
Graph(
let={
"n": Const(50400),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-08T03:29:15.227067Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T03:29:15.237903Z"
} | 387c8f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 501
},
"timestamp": "2026-02-10T14:37:30.513Z",
"answer": 108
},
{
"id"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
7b0967 | nt_min_coprime_above_v1_865884756_3996 | Let $n$ be a positive integer. Define $\mathcal{S}$ as the set of all positive integers $n \leq 2709$ such that $7$ divides $n$ and $\gcd(n, 10) = 1$. Let $m$ be the number of elements in $\mathcal{S}$. Define $\mathcal{T}$ as the set of all integers $n_1$ satisfying $62001 < n_1 \leq 62166$ and $\gcd(n_1, m) = 1$. Let... | 18,034 | graphs = [
Graph(
let={
"_n": Const(2709),
"start": Const(62001),
"upper": Const(62166),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(7), dividend=Var("n")), Eq(GC... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.041 | 2026-02-08T17:41:16.510386Z | {
"verified": true,
"answer": 18034,
"timestamp": "2026-02-08T17:41:16.551594Z"
} | 1b55bb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1992
},
"timestamp": "2026-02-18T06:39:02.379Z",
"answer": 18034
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9c9c88 | nt_count_coprime_v1_655260480_3191 | Let $k=17$, and let $R$ be the number of positive integers $n$ with $1\le n\le 10753$ such that $\gcd(n,k)=1$.
Let
\[
Q \equiv \bigl((R\bmod 317) + 1009\,(R\bmod 313)\bigr) \pmod{53326}, \quad 0\le Q<53326.
\]
Find the value of $Q$. | 52,913 | graphs = [
Graph(
let={
"upper": Const(10753),
"k": Const(17),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
"_c": Const(1009),
... | NT | null | COUNT | sympy | C3 | [
"C3/MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | db88c5 | nt_count_coprime_v1 | two_moduli | 3 | 0 | [
"C3",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 5.991 | 2026-02-08T17:14:41.782477Z | {
"verified": true,
"answer": 52913,
"timestamp": "2026-02-08T17:14:47.773429Z"
} | f96ae0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 694
},
"timestamp": "2026-02-17T22:41:05.341Z",
"answer": 52913
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fa4f7b | comb_count_surjections_v1_677425708_4194 | Define $a = 5$ and $b = 4$. Let $n_2 = a + b$. Compute
$$
v = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 0$ and compute
$$
m = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 5 + v$ and $k = 4m$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 240 | graphs = [
Graph(
let={
"a": Const(5),
"b": Const(4),
"n2": Sum(Ref("a"), Ref("b")),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"m": Summat... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.02 | 2026-02-08T06:29:19.383876Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T06:29:19.403714Z"
} | 869784 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 610
},
"timestamp": "2026-02-24T06:17:10.895Z",
"answer": 240
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
38b378 | comb_count_surjections_v1_865884756_4240 | Let $n = 5$ and $k = 5$. Define $x = k! \cdot S(n, k)$, where $S(n, k)$ is the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. Let $r = x \bmod 11$. Compute the remainder when the Bell number $B_r$ is divided by $71586$. | 44,389 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), modulus=Const(71586)),
},
goa... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1"
] | 0f4e92 | comb_count_surjections_v1 | bell_mod | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.079 | 2026-02-08T17:49:30.607945Z | {
"verified": true,
"answer": 44389,
"timestamp": "2026-02-08T17:49:30.686487Z"
} | 92564f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 4154
},
"timestamp": "2026-02-18T08:23:58.126Z",
"answer": 44389
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
9cd02c | modular_mod_compute_v1_865884756_1756 | Let $m = 160$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $P$ be the set of all products $xy$ for such pairs. Let $n$ be the maximum value in $P$. Define $a = 23871$. Let $\varphi(d)$ denote Euler's totient function, and let $m' = \sum_{d \mid n} \varphi(d)$. Compute ... | 4,671 | graphs = [
Graph(
let={
"_m": Const(160),
"_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 | B1 | [
"B1/K3"
] | 759f54 | modular_mod_compute_v1 | null | 4 | 0 | [
"B1",
"K3"
] | 2 | 0.002 | 2026-02-08T16:17:09.361602Z | {
"verified": true,
"answer": 4671,
"timestamp": "2026-02-08T16:17:09.363856Z"
} | c9cb42 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 550
},
"timestamp": "2026-02-17T00:24:25.714Z",
"answer": 4671
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"l... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ecf92 | comb_binomial_compute_v1_1742523217_292 | Let $S$ be the set of all positive integers $t$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 2$, $5 \leq t \leq 22$, and $t = 2a + 3b$. Let $n$ be the number of elements in $S$. Let $k$ be the smallest divisor $d$ of $847$ such that $d \geq 2$. Define $\binom{n}{k}$ to be the binomi... | 1,500 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T02:57:52.575148Z | {
"verified": true,
"answer": 1500,
"timestamp": "2026-02-08T02:57:52.577190Z"
} | 38c6fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 3023
},
"timestamp": "2026-02-09T16:00:09.569Z",
"answer": 25874
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": 2.08,
"mid": 3.62,
"hi": 5.18
} | ||
2f1441 | modular_mod_compute_v1_1978505735_4865 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 12321$. Let $m$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = 6350400$. Define $\text{result} = a \bmod m$. Let $\_c = 76952$ and $\_n = 92641$. Compute $Q = (... | 37,400 | graphs = [
Graph(
let={
"_n": Const(92641),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(12321)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T18:36:16.928068Z | {
"verified": true,
"answer": 37400,
"timestamp": "2026-02-08T18:36:16.930854Z"
} | f2f27b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1868
},
"timestamp": "2026-02-18T18:01:33.641Z",
"answer": 37400
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
715d7c | diophantine_product_count_v1_2051736721_1205 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 57600$. For each such pair, compute $x + y$. Let $T$ be the set of all such sums $x + y$. Let $m$ be the minimum value in $T$. Compute $\phi(d)$ for each positive divisor $d$ of $m$, and let $k$ be the sum of these values. Let $N$ be t... | 35,181 | graphs = [
Graph(
let={
"k": 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=57600)))), expr=S... | NT | null | COUNT | sympy | B3 | [
"B3/K3"
] | 4a4ef2 | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"K3"
] | 2 | 0.023 | 2026-02-08T15:53:47.077396Z | {
"verified": true,
"answer": 35181,
"timestamp": "2026-02-08T15:53:47.100319Z"
} | af01eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1387
},
"timestamp": "2026-02-16T15:58:13.980Z",
"answer": 35181
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
58a55a_l | modular_modexp_compute_v1_548369836_236 | Let $a = 5$. Define $e$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $6561$, where $\phi$ denotes Euler's totient function. Let $m = 32768$. Compute the remainder when $a^e$ is divided by $m$, and denote this value as $r$. Let $Q$ be the remainder when $3333 - r$ is divided by $86214$. Find the value of... | 3,332 | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | modular_modexp_compute_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.148 | 2026-02-08T02:49:25.577818Z | {
"verified": false,
"answer": 60998,
"timestamp": "2026-02-08T02:49:25.725696Z"
} | afc49c | 58a55a | 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": 213,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T16:33:18.016Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.45,
"mid": 3.01,
"hi": 4.55
} | |
3aa940 | diophantine_fbi2_min_v1_151522320_801 | Let $k = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8$ and let $U$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, \dots, 23\}$. Let $m$ be the smallest integer $d$ such that $4 \leq d \leq U$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Let $c$ be the number of positive integers $n \leq 53016$ s... | 8,832 | graphs = [
Graph(
let={
"_n": Const(8),
"k": Summation(var="k", start=Const(1), end=Const(8), expr=Var("k")),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(23)))),
"resu... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"COUNT_CARTESIAN",
"SUM_ARITHMETIC"
] | f7612d | diophantine_fbi2_min_v1 | negation_mod | 6 | 0 | [
"COUNT_CARTESIAN",
"COUNT_FIB_DIVISIBLE",
"SUM_ARITHMETIC"
] | 3 | 0.007 | 2026-02-08T03:32:28.659312Z | {
"verified": true,
"answer": 8832,
"timestamp": "2026-02-08T03:32:28.666542Z"
} | e855ec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 1687
},
"timestamp": "2026-02-10T15:02:14.814Z",
"answer": 8832
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
052296_l | comb_count_permutations_fixed_v1_1520064083_536 | Let $s = \sum_{k=0}^{9} (-1)^k \binom{9}{k}$ and let $t = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $n$ be the number of integers $t$ in the range $29 \leq t \leq 68$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, such that $t = 6a + 15b + 8$. Let $k$ be the number of ordered pairs... | 0 | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"LIN_FORM"
] | f7c074 | comb_count_permutations_fixed_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.006 | 2026-02-08T03:28:00.269257Z | {
"verified": false,
"answer": 11615,
"timestamp": "2026-02-08T03:28:00.275289Z"
} | 015fee | 052296 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 366,
"completion_tokens": 1895
},
"timestamp": "2026-02-10T14:35:13.730Z",
"answer": 11615
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"stat... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
20c8fb | antilemma_k2_v1_458359167_1049 | Compute $$\sum_{k=1}^{371} \phi(k) \left\lfloor \frac{371}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 69,006 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(371), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(371), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T04:14:48.390021Z | {
"verified": true,
"answer": 69006,
"timestamp": "2026-02-08T04:14:48.390618Z"
} | 71a6d8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 639
},
"timestamp": "2026-02-10T15:54:03.483Z",
"answer": 69006
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
cd57e9 | modular_mod_compute_v1_1918700295_1087 | Consider all ordered pairs $(x,y)$ of positive integers such that $xy=640000$, and let $N$ be the smallest possible value of $x+y$ over all such pairs.
Next, consider all ordered pairs $(x,y)$ of positive integers such that $xy=N$, and let $S$ be the smallest possible value of $x+y$ over all such pairs. Among all orde... | 1,600 | 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(640000)))), expr=Sum(Var("x"), Var("y")))),
"a": MaxOverSet... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3/B1"
] | 528bec | modular_mod_compute_v1 | null | 8 | 0 | [
"B1",
"B3"
] | 2 | 0.006 | 2026-02-08T05:33:25.891105Z | {
"verified": true,
"answer": 1600,
"timestamp": "2026-02-08T05:33:25.897503Z"
} | 6dd508 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1022
},
"timestamp": "2026-02-12T10:58:36.712Z",
"answer": 1600
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lem... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
32a715 | nt_gcd_compute_v1_1248542787_438 | Let $a = 419175$ and $b = 922185$. Let $r = \gcd(a, b)$. Let $c$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 14641$. Compute the remainder when $c \cdot r$ is divided by $55783$. | 38,841 | graphs = [
Graph(
let={
"_n": Const(55783),
"a": Const(419175),
"b": Const(922185),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | e0298c | nt_gcd_compute_v1 | affine_mod | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:07:43.382666Z | {
"verified": true,
"answer": 38841,
"timestamp": "2026-02-08T03:07:43.385053Z"
} | 56324f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 2559
},
"timestamp": "2026-02-09T04:09:02.420Z",
"answer": 38841
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
87fe2a | antilemma_k2_v1_153355830_1043 | Let $n = 260$. Compute the remainder when $47 - \sum_{k=1}^{260} \phi(k) \left\lfloor \frac{260}{k} \right\rfloor$ is divided by $52029$. | 18,146 | graphs = [
Graph(
let={
"_n": Const(260),
"x": Summation(var="k", start=Const(1), end=Const(260), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(value=Sub(Const(47), Ref("x")), modulus=Const(52029)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T04:22:08.427084Z | {
"verified": true,
"answer": 18146,
"timestamp": "2026-02-08T04:22:08.427530Z"
} | cc127a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 756
},
"timestamp": "2026-02-10T16:12:30.225Z",
"answer": 18146
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
164172 | antilemma_k3_v1_1915831931_191 | Let $n = 25133$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 25,133 | graphs = [
Graph(
let={
"_n": Const(25133),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:13:34.118775Z | {
"verified": true,
"answer": 25133,
"timestamp": "2026-02-08T15:13:34.119467Z"
} | e71cbf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 975
},
"timestamp": "2026-02-16T01:58:52.541Z",
"answer": 25133
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
81ce78 | comb_factorial_compute_v1_784195855_6767 | Let $n=7$ and let $R=n!$. Consider the set of all ordered pairs $(p,q)$ of positive integers such that $pq=12$, $\gcd(p,q)=1$, and $p<q$. Let $A$ be the number of such ordered pairs.
Consider the set of all integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le6$, $1\le b\le2$, $21\le t\le66$, a... | 2 | graphs = [
Graph(
let={
"n": Const(7),
"result": Factorial(Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Va... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | 1ad86c | comb_factorial_compute_v1 | bell_mod | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.005 | 2026-02-08T08:51:27.770751Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T08:51:27.775674Z"
} | a27a13 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 1246
},
"timestamp": "2026-02-13T22:13:29.521Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d85646 | nt_sum_gcd_range_mod_v1_865884756_4552 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 705600$. Let $N$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $k = 504$. Compute the sum $\sum_{n=1}^{N} \gcd(n, k)$. Let $M = 11311$. Find the remainder when this sum is divided by $M$. Multiply this remainder by ... | 81,255 | 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(705600)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(504),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.219 | 2026-02-08T17:59:04.614042Z | {
"verified": true,
"answer": 81255,
"timestamp": "2026-02-08T17:59:04.832726Z"
} | a5c103 | 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": 4768
},
"timestamp": "2026-02-18T11:48:43.307Z",
"answer": 81255
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5e0ae2 | nt_sum_totient_over_divisors_v1_1978505735_976 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 278784$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, and then find the remainder when $64203$ times this sum is divided by $50003$. | 44,303 | graphs = [
Graph(
let={
"_n": Const(64203),
"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(278784)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.19 | 2026-02-08T15:43:30.121528Z | {
"verified": true,
"answer": 44303,
"timestamp": "2026-02-08T15:43:30.311900Z"
} | 71062c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1396
},
"timestamp": "2026-02-16T12:57:34.386Z",
"answer": 44303
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4fd5fe | alg_telescope_v1_1218484723_6865 | Compute the remainder when $\sum_{k=0}^{78} \left((k+1)^2 - k^2\right)$ is divided by the number of integers $t$ such that $t = 3a + 7b + 18$ for integers $a,b$ with $1 \le a \le 1213$, $1 \le b \le 550$, and $28 \le t \le 7507$. | 6,241 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(78), expr=Sub(Pow(Sum(Var("k"), Const(1)), Ref("_n")), Pow(Var("k"), Const(2)))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-25T08:19:24.427696Z | {
"verified": true,
"answer": 6241,
"timestamp": "2026-02-25T08:19:24.434319Z"
} | 654b12 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 27659
},
"timestamp": "2026-03-30T02:55:53.906Z",
"answer": 6241
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
d6af84 | modular_min_linear_v1_1742523217_744 | Let $a = 19683$, $b = 14166$, and $m = 35980$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ such that $d$ divides $1037153$. Let $g = \gcd(d_{\text{min}}, 17)$. Define $S$ as the set of all integers $x$ such that $x \geq \sum_{d \mid g} \mu(d)$, $x \leq m$, and $ax \equiv b \pmod{m}$. Compute the minimum val... | 34,862 | graphs = [
Graph(
let={
"a": Const(19683),
"b": Const(14166),
"m": Const(35980),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=MinOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(left=Var(n... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME"
] | 60ba20 | modular_min_linear_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 1.8 | 2026-02-08T03:11:52.035781Z | {
"verified": true,
"answer": 34862,
"timestamp": "2026-02-08T03:11:53.835397Z"
} | d190a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 4051
},
"timestamp": "2026-02-09T22:05:15.302Z",
"answer": 34862
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
7f90d1 | alg_telescope_v1_601307018_10068 | Let $M = \sum_{k=0}^{1575} \left( (k+1)^2 - k^2 \right) \bmod 4519$. Find the remainder when $20915 \cdot M$ is divided by $88242$. | 28,067 | graphs = [
Graph(
let={
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(1575), expr=Sub(Pow(Sum(Var("k"), Const(1)), Const(2)), Pow(Var("k"), Const(2)))), modulus=Const(4519)),
"_c": Const(20915),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Cons... | ALG | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/STARS_BARS"
] | 031d5d | alg_telescope_v1 | null | 2 | 0 | [
"B3_CLOSEST",
"STARS_BARS"
] | 2 | 0.451 | 2026-03-10T10:34:31.478569Z | {
"verified": true,
"answer": 28067,
"timestamp": "2026-03-10T10:34:31.929663Z"
} | 1ff074 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1423
},
"timestamp": "2026-04-19T12:54:39.127Z",
"answer": 28067
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "STARS_BARS",
"status": "ok_later"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
043b51 | geo_count_lattice_rect_v1_1470522791_596 | Let $a = 89$ and $b = 355$. Consider the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of lattice points (points with integer coordinates) that lie inside or on the boundary of this rectangle.
Find the value of this quantity. | 32,040 | graphs = [
Graph(
let={
"a": Const(89),
"b": Const(355),
"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 | 2026-02-08T13:08:04.965493Z | {
"verified": true,
"answer": 32040,
"timestamp": "2026-02-08T13:08:04.965881Z"
} | 1293bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 385
},
"timestamp": "2026-02-24T17:16:32.382Z",
"answer": 32040
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
f0041d | nt_count_coprime_and_v1_898971024_1458 | Let $n = 15$. Let $k_1$ be the smallest divisor of $n$ that is at least 2. Let $k_2 = 7$. Let $c = 27720$. Define $r$ as the number of positive integers $n$ such that $1 \leq n \leq 23303$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Compute $c - r$. | 14,404 | graphs = [
Graph(
let={
"_n": Const(15),
"upper": Const(23303),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"k2": Const(7),
"result": CountOverSet(set=Solu... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.375 | 2026-02-08T16:08:54.236670Z | {
"verified": true,
"answer": 14404,
"timestamp": "2026-02-08T16:08:57.611976Z"
} | 627c4b | 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": 1025
},
"timestamp": "2026-02-16T21:53:08.918Z",
"answer": 14404
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c32339 | nt_count_intersection_v1_1978505735_5148 | Let $b = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi(n)$ denotes Euler's totient function. Let $N = 50000$. Compute the number of positive integers $n \leq N$ such that $9$ divides $n$ and $\gcd(n, b) = 1$. | 2,222 | graphs = [
Graph(
let={
"_n": Const(4),
"N": Const(50000),
"a": Const(9),
"b": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), ... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_intersection_v1 | null | 5 | 0 | [
"K2"
] | 1 | 1.641 | 2026-02-08T18:48:10.070650Z | {
"verified": true,
"answer": 2222,
"timestamp": "2026-02-08T18:48:11.711252Z"
} | 090dcf | 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": 1661
},
"timestamp": "2026-02-18T19:49:39.849Z",
"answer": 2222
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c8158 | nt_count_with_divisor_count_v1_168721529_1051 | Let $A = \sum_{d \mid \gcd(13,17)} \mu(d)$, where $\mu$ is the Möbius function. Let $N$ be the number of integers $n$ such that $n \geq A$, $n \leq 86436$, and $n$ has exactly 7 positive divisors. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Define $c$ to be the minimum... | 5,037 | graphs = [
Graph(
let={
"upper": Const(86436),
"div_count": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=13), b=Const(value=17)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), R... | NT | null | COUNT | sympy | B3 | [
"B3",
"MOBIUS_COPRIME"
] | 8608fe | nt_count_with_divisor_count_v1 | negation_mod | 5 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 3.723 | 2026-02-08T13:26:17.190720Z | {
"verified": true,
"answer": 5037,
"timestamp": "2026-02-08T13:26:20.913410Z"
} | 128c24 | 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": 1692
},
"timestamp": "2026-02-09T13:30:16.407Z",
"answer": 5037
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"le... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
0e2edb | diophantine_fbi2_min_v1_655260480_4310 | Let $k = 120$ and $u = 130$. Compute the smallest integer $d$ such that $7 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. | 8 | graphs = [
Graph(
let={
"k": Const(120),
"upper": Const(130),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(7)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3))))),
... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 6897ab | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.026 | 2026-02-08T17:52:45.632918Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T17:52:45.658722Z"
} | 3f0f27 | 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": 520
},
"timestamp": "2026-02-18T09:29:20.813Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1fefa6 | modular_modexp_compute_v1_601307018_7000 | Let $e$ be the number of positive integers $j$ with $1 \le j \le 2775$ such that $j^5 \le 164556460458984375$. Let $R = 2^e \bmod 80000$. Compute the remainder when $$353702 \cdot (|R| \bmod 97) + 329703 \cdot (|R|^2 + 1 \bmod 101) + 215534 \cdot (|R| + 8 \bmod 103)$$ is divided by $1009091$, and then find the remainde... | 29,196 | graphs = [
Graph(
let={
"_n": Const(99729),
"a": Const(2),
"e": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2775)), Leq(Pow(Var("j"), Const(5)), Const(164556460458984375))), domain='positive_integers')),
... | NT | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"C3"
] | 8a214c | modular_modexp_compute_v1 | null | 5 | 0 | [
"C3",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.12 | 2026-03-10T07:38:28.582951Z | {
"verified": true,
"answer": 29196,
"timestamp": "2026-03-10T07:38:28.702921Z"
} | 6fe37d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 3966
},
"timestamp": "2026-04-19T05:46:39.694Z",
"answer": 29196
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f74dc7 | algebra_vieta_sum_v1_1439011603_2625 | Let $S$ be the set of all real numbers $x$ satisfying the equation $x^4 - 15x^3 + 53x^2 + 15x - 54 = 0$. Compute the sum of all elements in $S$. | 15 | graphs = [
Graph(
let={
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(4)), Mul(Const(-15), Pow(Var("x"), Const(3))), Mul(Const(53), Pow(Var("x"), Const(2))), Mul(Const(15), Var("x")), Const(-54)), Const(0)))),
},
goal=Ref("result"),
... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_vieta_sum_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"COPRIME_PAIRS"
] | 2 | 0.075 | 2026-02-08T16:53:20.793600Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T16:53:20.868783Z"
} | 6335c6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 257
},
"timestamp": "2026-02-16T07:56:56.190Z",
"answer": 15
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_S... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
05a4af | nt_count_gcd_equals_v1_784195855_10025 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 200$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $M$ be the maximum value in $P$. Determine the number of positive integers $n$ such that $1 \leq n \leq M$ and $\gcd(n, 436) = 109$. | 46 | graphs = [
Graph(
let={
"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(200)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(436)... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.753 | 2026-02-08T17:22:35.752877Z | {
"verified": true,
"answer": 46,
"timestamp": "2026-02-08T17:22:36.505680Z"
} | 532073 | 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": 891
},
"timestamp": "2026-02-18T00:46:01.290Z",
"answer": 46
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5746b1 | antilemma_k3_v1_655260480_5159 | Compute the value of $\sum_{d \mid 86156} \phi(d)$, where $\phi(d)$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $86156$. | 86,156 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=86156), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T18:18:18.718027Z | {
"verified": true,
"answer": 86156,
"timestamp": "2026-02-08T18:18:18.718503Z"
} | 3629d0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 718
},
"timestamp": "2026-02-16T12:18:10.176Z",
"answer": 24960000
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ed0f4c | nt_count_coprime_and_v1_1874849503_658 | Let $k_1 = 11$ and let $k_2$ be the largest prime number $n$ such that $2 \leq n \leq 16$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 12597$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 10,571 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(12597),
"k1": Const(11),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(16)), IsPrime(Var("n"))))),
"result": CountOverSet(set=Solut... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.486 | 2026-02-08T13:14:37.327858Z | {
"verified": true,
"answer": 10571,
"timestamp": "2026-02-08T13:14:38.813632Z"
} | 6dacff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 944
},
"timestamp": "2026-02-09T19:29:21.147Z",
"answer": 10572
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
02372c_l | antilemma_sum_equals_v1_1520064083_139 | Compute the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 22$ and $1 \le j \le 22$ such that $i + j = 24$. | 22 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.06 | 2026-02-08T03:06:24.481709Z | {
"verified": false,
"answer": 21,
"timestamp": "2026-02-08T03:06:24.542131Z"
} | 02fa80 | 02372c | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 253
},
"timestamp": "2026-02-10T12:58:04.179Z",
"answer": 21
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | |
48fa27 | diophantine_fbi2_count_v1_2051736721_4294 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 900$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Let $k$ be the minimum element of $T$. Let $D$ be the set of all integers $d$ such that $4 \le d \le 58$, $d$ divides $k$, and $2 \le \frac{k}{d} \le 56$. Let $r$ be t... | 37,844 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(900)))), expr=Sum(Var("x"), Var("y")))),
"result": CountOver... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T17:53:23.619952Z | {
"verified": true,
"answer": 37844,
"timestamp": "2026-02-08T17:53:23.633018Z"
} | 0a30a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 945
},
"timestamp": "2026-02-18T10:01:04.481Z",
"answer": 37844
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5e6e0a | comb_binomial_compute_v1_865884756_3922 | Let $n = 13$. Let $k$ be the smallest integer $d \geq 2$ that divides $175$. Compute $\binom{n}{k}$. Find the value of this binomial coefficient. | 1,287 | graphs = [
Graph(
let={
"n": Const(13),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(175))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T17:39:53.298615Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T17:39:53.299966Z"
} | 479012 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 383
},
"timestamp": "2026-02-16T11:30:47.511Z",
"answer": 1
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
94dc59 | antilemma_cartesian_v1_1978505735_6427 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 15, inclusive, and $b$ is an integer from 1 to 23, inclusive. Compute the remainder when $44121 \cdot x$ is divided by 63391. | 7,905 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Const(23)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(63391)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T19:35:44.780971Z | {
"verified": true,
"answer": 7905,
"timestamp": "2026-02-08T19:35:44.781598Z"
} | b5833f | 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": 837
},
"timestamp": "2026-02-18T22:56:22.220Z",
"answer": 7905
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
0b4779 | algebra_quadratic_discriminant_v1_1440796553_1418 | Let $a = 2$, $b = 12$, and $c = 18$. Let $D = b^2 - 4ac$.
Compute $2 \cdot [D > 0] + [D = 0]$, where $[P]$ denotes the Iverson bracket, equal to $1$ if $P$ is true and $0$ otherwise. | 1 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(12),
"c": Const(18),
"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"), Cons... | NT | null | COMPUTE | sympy | B3 | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B1",
"B3"
] | 2 | 0.044 | 2026-02-08T13:59:02.153462Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T13:59:02.197148Z"
} | b5a634 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 404
},
"timestamp": "2026-02-16T05:11:49.693Z",
"answer": 1
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
62dfd5 | nt_count_divisible_v1_124444284_6297 | Let $A$ be the set of ordered pairs $(i, j)$ with $1 \leq i \leq 4$ and $1 \leq j \leq 9$ such that $\gcd(i, j) = 1$. Let $d$ be the number of elements in $A$. Find the number of positive integers $n \leq 46368$ such that $n$ is divisible by $d$. | 1,854 | graphs = [
Graph(
let={
"upper": Const(46368),
"divisor": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Con... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 4.856 | 2026-02-08T08:16:42.256426Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T08:16:47.112740Z"
} | 7f0cc1 | 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": 774
},
"timestamp": "2026-02-13T16:31:42.369Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
03647c | comb_factorial_compute_v1_1470522791_914 | Let $N$ be the number of nonnegative integers $j$ such that $0 \leq j \leq T$ and $\binom{8456}{j}$ is odd, where $T$ is the number of integers $t$ with $22 \leq t \leq 16968$ for which there exist positive integers $a \leq 508$ and $b \leq 1232$ such that $t = 14a + 8b$. Compute $N!$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(8456),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V8"
] | 654a7e | comb_factorial_compute_v1 | null | 7 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.003 | 2026-02-08T13:18:41.724108Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T13:18:41.727266Z"
} | 90ac7e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T17:52:58.975Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
91996f | comb_count_partitions_v1_1218484723_5754 | Let $n$ be the number of non-negative integers $a$ with $0 \le a \le 1368$ such that
$$
\left( (a^3 + 2a^2 - 3a + 4) \bmod 1369 \right)^3 + 2\left( (a^3 + 2a^2 - 3a + 4) \bmod 1369 \right)^2 - 3\left( (a^3 + 2a^2 - 3a + 4) \bmod 1369 \right) + 4 \equiv a \pmod{1369}
$$
and
$$
(a^3 + 2a^2 - 3a + 4) \bmod 1369 \ne a.
$... | 26,015 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(1368)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(2), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Re... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_partitions_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.002 | 2026-02-25T07:19:16.329198Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-25T07:19:16.330920Z"
} | 795746 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 25401
},
"timestamp": "2026-03-29T22:37:03.702Z",
"answer": 26015
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V8",... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
bd745e | comb_count_derangements_v1_1125832087_44 | Let $n$ be the largest prime number less than or equal to $9$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(9),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Ref("result"),
},
goal... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T02:50:48.248231Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T02:50:48.249186Z"
} | 59b998 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 915
},
"timestamp": "2026-02-10T11:40:54.931Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -7.05,
"mid": -4.76,
"hi": -2.5
} | ||
8f5571 | nt_sum_divisors_compute_v1_458359167_2377 | Let $n = 21499$. Let $S$ be the set of all positive integers $p$ such that there exists an integer $q$ with $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $2 \leq n \leq 11$. Let $A$ be the set of all prime numbers $n$ satisfying $|S| \leq n \leq \max(T)$. Let $r ... | 203 | graphs = [
Graph(
let={
"n": Const(21499),
"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"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositiv... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | fa2047 | nt_sum_divisors_compute_v1 | bell_mod | 7 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T05:21:02.296600Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T05:21:02.301201Z"
} | 7cbf28 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2146
},
"timestamp": "2026-02-12T08:00:57.983Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fe624f | antilemma_sum_equals_v1_124444284_4139 | Let $m = 50$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 48$ and $1 \le j \le 49$ such that $i + j = m$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 47$ and $1 \le j \le 48$ such that $i + j = n$. Compute the remainder when $33289 \cdot x$ is divided by $87160$. | 82,863 | graphs = [
Graph(
let={
"_m": Const(50),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(48)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.017 | 2026-02-08T05:48:37.104065Z | {
"verified": true,
"answer": 82863,
"timestamp": "2026-02-08T05:48:37.120565Z"
} | ea45e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1206
},
"timestamp": "2026-02-24T04:32:18.864Z",
"answer": 82863
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
d4516a | nt_count_divisible_and_v1_48377204_836 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 4500$, $\gcd(p, q) = 1$, and $p < q$. Let $n = |A|$. Let $d_1 = 6$ and let $d_2 = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$. Compute the number of positive integers $n \le 85200$ that are d... | 2,840 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=4500)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2"
] | 846647 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 3.039 | 2026-02-08T15:42:53.398696Z | {
"verified": true,
"answer": 2840,
"timestamp": "2026-02-08T15:42:56.437882Z"
} | bbd98a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1573
},
"timestamp": "2026-02-16T11:22:32.318Z",
"answer": 2840
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.