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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
e0314a | nt_count_divisible_and_v1_1248542787_433 | Let $n$ be a positive integer. Define $d_1 = 6$ and $d_2 = \sum_{k=1}^{4} k$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 144150$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Let $r$ be the number of elements in $S$. Compute the smallest positive integer $k$ such that the $k$-... | 360 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(144150),
"d1": Const(6),
"d2": Summation(var="k", start=EulerPhi(n=Const(1)), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Eu... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"ONE_PHI_1"
] | 342157 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"ONE_PHI_1",
"SUM_ARITHMETIC"
] | 2 | 5.004 | 2026-02-08T03:07:16.888009Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T03:07:21.891998Z"
} | a28017 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 3174
},
"timestamp": "2026-02-09T04:04:48.988Z",
"answer": 360
},
{
"id... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
1cd289 | comb_catalan_compute_v1_1125832087_1405 | Let $N$ be the number of integers $t$ in the interval $[5, 16]$ such that $t = 2a + 3b$ for some positive integers $a \in [1, 5]$ and $b \in [1, 2]$. Let $C_N$ denote the $N$-th Catalan number. Compute the remainder when $48625 \cdot C_N$ is divided by $74256$. | 38,012 | graphs = [
Graph(
let={
"_n": Const(74256),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:43:02.921634Z | {
"verified": true,
"answer": 38012,
"timestamp": "2026-02-08T03:43:02.924355Z"
} | b42820 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2738
},
"timestamp": "2026-02-23T22:43:54.798Z",
"answer": 38012
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
3e8ecd | modular_modexp_compute_v1_1520064083_1506 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 186$. Let $e = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $19^e$ is divided by $32768$. | 4,211 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(186)))), expr=Mul(Var("x"), Var("y")))),
"a": Const(19),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/K3"
] | 759f54 | modular_modexp_compute_v1 | null | 5 | 0 | [
"B1",
"K3"
] | 2 | 0.001 | 2026-02-08T04:03:16.510638Z | {
"verified": true,
"answer": 4211,
"timestamp": "2026-02-08T04:03:16.511916Z"
} | 3e3e66 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 6255
},
"timestamp": "2026-02-10T15:23:59.838Z",
"answer": 4211
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"le... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b2d947 | alg_qf_psd_orbit_v1_601307018_564 | Find the number of ordered triples $(a, b, c)$ of positive integers such that $1 \le a \le b \le c \le 55$ and $$
50a^2 + 50b^2 + 50c^2 - 34ab - 34ac - 34bc = 86330.
$$ | 6 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(55)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(55)), Geq(Var("c"), Const(1)), Leq(Var("c"), Const(55)), Leq(Var("a"),... | ALG | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | alg_qf_psd_orbit_v1 | null | 5 | null | [
"MOBIUS_COPRIME"
] | 1 | 1.231 | 2026-03-10T01:05:43.121640Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-03-10T01:05:44.352566Z"
} | b5bdcc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 18047
},
"timestamp": "2026-03-28T23:25:42.369Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
10f5ec | geo_count_lattice_rect_v1_124444284_6942 | Let $a = 169$ and $b = 260$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. | 44,370 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(260),
"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 | 2026-02-08T08:43:28.552685Z | {
"verified": true,
"answer": 44370,
"timestamp": "2026-02-08T08:43:28.553083Z"
} | c4b532 | 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": 286
},
"timestamp": "2026-02-24T09:58:26.271Z",
"answer": 44370
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
f160a9 | diophantine_fbi2_min_v1_1918700295_1558 | Let $k = 35$ and $n_0 = 5$. Let $S$ be the set of all ordered pairs $(k', j)$ with $k'$ and $j$ integers from 1 to 9, inclusive. Define $\text{sum} = \sum_{(k',j) \in S} k'$. Let $\text{upper} = \frac{2 \cdot \text{sum}}{18}$. Let $d_{\text{min}}$ be the smallest integer $d$ such that $d \geq 4$, $d \leq \text{upper}$,... | 9,381 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(35),
"upper": Div(Mul(Const(2), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=Inte... | NT | null | EXTREMUM | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.006 | 2026-02-08T05:53:01.147309Z | {
"verified": true,
"answer": 9381,
"timestamp": "2026-02-08T05:53:01.153316Z"
} | 05404e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 814
},
"timestamp": "2026-02-12T15:42:15.360Z",
"answer": 9381
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V1",
"st... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
50bce9 | comb_factorial_compute_v1_1353956133_570 | Let $n = 7$. Define $d_{\text{max}}$ to be the largest positive integer $d$ such that $d \leq n$ and $d$ divides 119. Let $f = d_{\text{max}}!$. Compute the remainder when $44735 \cdot f$ is divided by 84284. | 4,700 | graphs = [
Graph(
let={
"_n": Const(7),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(119))))),
"result": Factorial(Ref("n")),
"_c": Const(44735),
... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T11:31:36.335887Z | {
"verified": true,
"answer": 4700,
"timestamp": "2026-02-08T11:31:36.337488Z"
} | ca44cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 2582
},
"timestamp": "2026-02-14T17:47:28.111Z",
"answer": 4700
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bcbecb | sequence_fibonacci_compute_v1_1520064083_4623 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $38416 - F_n$ is divided by $86345$. | 78,393 | graphs = [
Graph(
let={
"_n": Const(86345),
"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(144)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T06:21:38.563704Z | {
"verified": true,
"answer": 78393,
"timestamp": "2026-02-08T06:21:38.564705Z"
} | a520b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 832
},
"timestamp": "2026-02-12T22:54:18.013Z",
"answer": 78393
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
706c52 | comb_factorial_compute_v1_153355830_2508 | Let $n$ be the smallest integer greater than or equal to $2$ that divides $3773$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(3773))))),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T07:11:42.847842Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T07:11:42.848557Z"
} | 53e455 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 816
},
"timestamp": "2026-02-13T08:24:28.175Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
3b4993 | comb_count_derangements_v1_1520064083_3263 | Let $T$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Let $n_1$ be the number of elements in $T$. Let $n_2$ be the largest prime number at most 9. Define $n$ to be the largest prime number such that $n_1 \leq n \leq n_2$. Compute th... | 1,854 | graphs = [
Graph(
let={
"_c": Const(9),
"_m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_c")), IsPrime(Var("n"))))),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Ex... | NT | COMB | COUNT | sympy | MAX_DIVISOR | [
"MAX_PRIME_BELOW/COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 4eefd3 | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 0.033 | 2026-02-08T05:33:06.784654Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T05:33:06.817642Z"
} | ce3a13 | 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": 1434
},
"timestamp": "2026-02-12T10:20:01.905Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
b93f0c | nt_sum_divisors_mod_v1_677425708_2544 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Let $n$ be the minimum value of $x + y$ over all such pairs.
Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Define
$$
\text{result} = \sigma(n) \bmod 11311,
$$
and
$$
Q = (44121 \cdot \text{result}) \bmod 55... | 47,726 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1131... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T05:07:00.087522Z | {
"verified": true,
"answer": 47726,
"timestamp": "2026-02-08T05:07:00.090727Z"
} | 5b35d8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2601
},
"timestamp": "2026-02-11T22:51:56.127Z",
"answer": 47726
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0ce4d2 | antilemma_k2_v1_397696148_1769 | Let $x = \sum_{k=1}^{140} \phi(k) \left\lfloor \frac{140}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q = 66049 - x$. Compute the value of $Q$. | 56,179 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(140), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(140), Var("k"))))),
"_c": Const(66049),
"Q": Sub(Ref("_c"), Ref("x")),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T12:46:02.206644Z | {
"verified": true,
"answer": 56179,
"timestamp": "2026-02-08T12:46:02.207518Z"
} | 19f6d9 | 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": 555
},
"timestamp": "2026-02-15T04:58:08.849Z",
"answer": 56179
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ae77fc | diophantine_fbi2_count_v1_349078426_1692 | Let $k = 1260$ and $m = 67320$. Let $S$ be the set of all positive integers $d$ such that $4 \leq d \leq 166$, $d$ divides $k$, $\frac{k}{d} \geq 3$, and $\frac{k}{d} \leq T$, where $T$ is the number of positive integers $k'$ not exceeding the number of positive integers $n \leq m$ for which $24$ divides $F_n$ (the $n$... | 22 | graphs = [
Graph(
let={
"_m": Const(67320),
"_n": Const(4),
"k": Const(1260),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(166)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/C2"
] | 65cf21 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"C2",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.014 | 2026-02-08T13:51:11.265589Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T13:51:11.280057Z"
} | d9edb4 | 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": 2478
},
"timestamp": "2026-02-15T20:52:53.784Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
524c05 | nt_min_crt_v1_2051736721_1721 | Let $m = 4$, $k = 5$, $a = 3$, $b = 3$, and $\text{upper} = 20$. Consider the set of all integers $n$ such that $1 \leq n \leq 20$, $n \equiv 3 \pmod{4}$, and $n \equiv 3 \pmod{5}$. Let $r$ be the minimum value of $n$ in this set. Compute $r$. | 3 | graphs = [
Graph(
let={
"m": Const(4),
"k": Const(5),
"a": Const(3),
"b": Const(3),
"upper": Const(20),
"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 | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"LIOUVILLE_ONE"
] | 16e91f | nt_min_crt_v1 | null | 3 | 0 | [
"LIOUVILLE_ONE",
"MOBIUS_COPRIME"
] | 2 | 0.11 | 2026-02-08T16:10:47.983890Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T16:10:48.093553Z"
} | 035689 | 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": 590
},
"timestamp": "2026-02-16T22:36:39.058Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b2eac6 | nt_num_divisors_compute_v1_124444284_9282 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 31$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 8$, $1 \leq b \leq 5$, and $t = 2a + 3b$. Let $r$ be the number of positive divisors of $n$. Let $m = r + 2$. The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F... | 5 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T12:21:15.707128Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T12:21:15.710100Z"
} | 3ebd21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2060
},
"timestamp": "2026-02-15T00:11:55.246Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
611ea5 | geo_count_lattice_triangle_v1_1419126231_1425 | Let $S = |100 \cdot 196 + 6 \cdot (-57)|$. Let $T = \gcd(100, 57) + \gcd\left(\left|6 - \left|\{ (a, b) : 1 \le a, b \le 35,\, 10a^2 - 18ab + 25b^2 \le \min\{x+y : x,y > 0,\, xy = 436921\}\}\right|\right|, |196 - 57|\right) + \gcd\left(6, \left|\max\{x_1 y_1 : x_1, y_1 > 0,\, x_1 + y_1 = 28\}\right|\right)$. Compute $\... | 9,628 | graphs = [
Graph(
let={
"_c": Const(6),
"_m": Const(100),
"_n": Const(6),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_m'), Const(value=196)), Mul(Const(value=6), Sub(left=Const(value=0), right=Const(value=57))))),
"boundary": Sum(GCD(a=Abs(arg=Const(valu... | GEOM | NT | COUNT | sympy | B3 | [
"B3/QF_PSD_COUNT_LEQ",
"B1"
] | 9c61a5 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B1",
"B3",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.018 | 2026-02-25T10:52:13.173430Z | {
"verified": true,
"answer": 9628,
"timestamp": "2026-02-25T10:52:13.191611Z"
} | b4fd34 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 4912
},
"timestamp": "2026-03-30T12:28:53.561Z",
"answer": 9628
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
3f3025 | nt_count_divisible_and_v1_1125832087_1649 | Let $d_1$ be the number of positive integers $k$ such that $1 \leq k \leq 108$ and $9$ divides $k$. Let $d_2 = 18$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 135900$, $n \equiv 0 \pmod{d_1}$, and $n \equiv 0 \pmod{d_2}$. Compute the smallest positive integer $Q$ such that the $Q$-th Fibona... | 2,516 | graphs = [
Graph(
let={
"upper": Const(135900),
"d1": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(108)), Divides(divisor=Const(9), dividend=Var("k"))), domain='positive_integers')),
"d2": Const(18),
"r... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_divisible_and_v1 | null | 6 | 0 | [
"C2"
] | 1 | 4.731 | 2026-02-08T03:51:15.983931Z | {
"verified": true,
"answer": 2516,
"timestamp": "2026-02-08T03:51:20.715422Z"
} | ff6b6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1667
},
"timestamp": "2026-02-11T19:44:38.855Z",
"answer": 2516
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
76f0b6 | antilemma_k3_v1_1520064083_1123 | Let $n = 51138$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 51,138 | graphs = [
Graph(
let={
"_n": Const(51138),
"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 | 2026-02-08T03:48:08.559252Z | {
"verified": true,
"answer": 51138,
"timestamp": "2026-02-08T03:48:08.559600Z"
} | 16c18b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 350
},
"timestamp": "2026-02-10T15:45:34.587Z",
"answer": 51138
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
fef26b | lte_diff_endings_v1_168721529_1843 | Let $ a = 7 $, $ b = 3 $, $ p = 2 $, $ K = 6 $, and $ N = 1005157 $. Let $ v_p(a-b) $ denote the highest power of $ p $ dividing $ a - b $. Let $ m = K - v_p(a-b) $, and let $ p^m $ be the $ m $-th power of $ p $. Compute the greatest integer less than or equal to $ \frac{N}{p^m} $. | 62,822 | graphs = [
Graph(
let={
"a_val": Const(7),
"b_val": Const(3),
"p_val": Const(2),
"K_val": Const(6),
"N_val": Const(1005157),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T13:57:09.046076Z | {
"verified": true,
"answer": 62822,
"timestamp": "2026-02-08T13:57:09.047361Z"
} | f161b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 675
},
"timestamp": "2026-02-09T22:20:31.005Z",
"answer": 62822
},
{
"i... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
cf6b75 | comb_count_permutations_fixed_v1_124444284_2337 | Let $n = \sum_{k=1}^{3} \phi(k) \cdot \left\lfloor \frac{3}{k} \right\rfloor$.
Compute the value of $\binom{n}{1} \cdot !(n - 1)$, where $!m$ denotes the number of derangements of $m$ elements. | 264 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'),... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T04:35:58.856865Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T04:35:58.858158Z"
} | d093e0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 831
},
"timestamp": "2026-02-10T17:15:58.613Z",
"answer": 264
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
e53085 | nt_count_gcd_equals_v1_865884756_614 | Let $k$ be the number of integers $t$ in the range $27 \leq t \leq 1062$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 135$, $1 \leq b \leq 12$, and $t = 6a + 21b$. Determine the number of positive integers $n \leq 38226$ such that $\gcd(n, k) = 340$. | 112 | graphs = [
Graph(
let={
"upper": Const(38226),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=135)), Geq(le... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 6.229 | 2026-02-08T15:31:53.231832Z | {
"verified": true,
"answer": 112,
"timestamp": "2026-02-08T15:31:59.460618Z"
} | 1182ac | 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": 3014
},
"timestamp": "2026-02-16T07:45:42.683Z",
"answer": 112
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0edb56 | antilemma_cartesian_v1_784195855_5103 | Let $A$ be the Cartesian product of the sets $\{1, 2, \dots, 13\}$ and $\{1, 2, \dots, 47\}$. Let $B$ be the Cartesian product of the sets $\{1, 2, \dots, 16\}$ and $\{1, 2, \dots, 32\}$.
Let $x$ be the number of elements in $A$, and let $y$ be the number of elements in $B$.
Compute the remainder when $y - x$ is divi... | 50,497 | graphs = [
Graph(
let={
"_n": Const(50596),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(47)))),
"Q": Mod(value=Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1),... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_CARTESIAN"
] | f9c395 | antilemma_cartesian_v1 | negation_mod | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T07:40:24.595039Z | {
"verified": true,
"answer": 50497,
"timestamp": "2026-02-08T07:40:24.596103Z"
} | e56340 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 273
},
"timestamp": "2026-02-24T08:19:47.527Z",
"answer": 50497
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
87fd78 | nt_gcd_compute_v1_124444284_1010 | Let $n_1$ be the number of positive integers $n \leq 6584$ such that the sum of the digits of $n$ is odd. Let $c$ be the remainder when the number of positive divisors of $n_1$ is divided by $2$. Let $w = \sum_{d \mid 1} \mu(d)$, where $\mu$ is the M\"obius function. Let $a = 247654$ and $b = (427766 + c) \cdot w$. Com... | 22,514 | graphs = [
Graph(
let={
"_n": Const(2),
"n1": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6584)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"c": Mod(value=NumDivisors(n=Ref("n1")), modulus=... | NT | null | COMPUTE | sympy | L3B | [
"L3B/DIVISOR_PARITY",
"MOBIUS_SUM"
] | a4569a | nt_gcd_compute_v1 | null | 4 | 2 | [
"DIVISOR_PARITY",
"L3B",
"MOBIUS_SUM"
] | 3 | 0.002 | 2026-02-08T03:38:55.681739Z | {
"verified": true,
"answer": 22514,
"timestamp": "2026-02-08T03:38:55.683334Z"
} | 11ca0e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2218
},
"timestamp": "2026-02-09T08:41:39.867Z",
"answer": 22514
},
{
... | 2 | [
{
"lemma": "DIVISOR_PARITY",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
f6eb53 | diophantine_fbi2_min_v1_784195855_8206 | Let $k = 125$. Consider the set of all integers $d$ such that $4 \leq d \leq 135$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Let $\text{result}$ be the smallest element of this set. Let $Q$ be the Bell number $B_r$, where $r$ is the remainder when $|\text{result}|$ is divided by $11$. Compute $Q$. | 52 | graphs = [
Graph(
let={
"k": Const(125),
"a": Const(3),
"b": Const(3),
"upper": Const(135),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | COMB | EXTREMUM | sympy | COMB1 | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"COMB1",
"K2",
"MAX_PRIME_BELOW"
] | 3 | 0.051 | 2026-02-08T15:56:10.637151Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T15:56:10.687896Z"
} | 1eefd3 | 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": 603
},
"timestamp": "2026-02-16T17:38:37.576Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f48325_l | diophantine_product_count_v1_1918700295_507 | Let $k = 60$, and let $u$ be the largest prime number satisfying $2 \leq u \leq 42$. Determine the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. | 11 | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_product_count_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 2 | 0.035 | 2026-02-08T03:17:43.459154Z | {
"verified": false,
"answer": 10,
"timestamp": "2026-02-08T03:17:43.493935Z"
} | 5df067 | f48325 | 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": 181,
"completion_tokens": 908
},
"timestamp": "2026-02-10T13:45:23.524Z",
"answer": 10
},
{
"id":... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | |
03b87e | modular_modexp_compute_v1_1742523217_1713 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 4$. Let $e$ be the number of positive integers $p$ for which there exists an integer $q$ such that $p \cdot q = 21910816304837460$, $\gcd(p, q) = 1$, and $p < q$. Let $m = 73984$. Compute the value of $a^e \bmod m$, the remainder when $a^e$ is divided by ... | 52,225 | graphs = [
Graph(
let={
"_n": Const(4),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"e": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exis... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | modular_modexp_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T04:06:50.312711Z | {
"verified": true,
"answer": 52225,
"timestamp": "2026-02-08T04:06:50.314440Z"
} | 99b381 | 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": 3814
},
"timestamp": "2026-02-11T22:54:04.467Z",
"answer": 52225
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "o... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bef34b | alg_poly_preperiod_count_v1_601307018_7700 | Let $f(x) = 3x^4 + 2x^3 + 3x^2 + 5x + 2$. For each non-negative integer $a \leq 98824$, define $N = f(a) \bmod 67$, $M = f(N) \bmod 67$, $R = f(M) \bmod 67$, $S = f(R) \bmod 67$. Find the number of such $a$ for which $S = M$ and $R \neq M$. | 11,800 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(4))), Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(3), Pow(Var("a"), Const(2))), Mul(Const(5), Var("a")), Const(2)), modulus=Const(67)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(4))), Mul... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.06 | 2026-03-10T08:18:02.882960Z | {
"verified": true,
"answer": 11800,
"timestamp": "2026-03-10T08:18:02.943286Z"
} | 5444a5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 17982
},
"timestamp": "2026-04-19T07:19:11.888Z",
"answer": 11800
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
134460 | diophantine_fbi2_min_v1_784195855_5120 | Let $k = 55$ and $u = 65$. Determine the smallest integer $d$ such that $6 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Compute the value of $d$. | 11 | graphs = [
Graph(
let={
"k": Const(55),
"upper": Const(65),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4))))),
... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.005 | 2026-02-08T07:41:18.086617Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T07:41:18.091400Z"
} | 827ca7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 370
},
"timestamp": "2026-02-15T19:03:09.566Z",
"answer": 5
},
{
"id": 11,
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
978958 | comb_binomial_compute_v1_2051736721_1910 | Let $T$ be the set of all integers $t$ with $7 \leq t \leq 24$ that can be expressed as $t = 5a + 2b$ for positive integers $a, b$ with $1 \leq a \leq 2$ and $1 \leq b \leq 7$. Let $n$ be the number of elements in $T$. Let $k$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $pq... | 9,766 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | comb_binomial_compute_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T16:19:10.593027Z | {
"verified": true,
"answer": 9766,
"timestamp": "2026-02-08T16:19:10.597272Z"
} | bd0890 | 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": 1872
},
"timestamp": "2026-02-17T02:33:34.948Z",
"answer": 9766
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc1466 | lin_form_endings_v1_153355830_107 | Let $a = 9$, $b = 6$, $A = 31$, and $B = 6$. Compute $g = \gcd(a, b)$. Define
$$
n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.
$$
Let $k = 6093$ and $s = k \cdot n$. Find the remainder when $s$ is divided by $83013$. | 34,302 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(6),
"A_val": Const(31),
"B_val": Const(6),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), Ref(... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:53:16.843833Z | {
"verified": true,
"answer": 34302,
"timestamp": "2026-02-08T02:53:16.844372Z"
} | 91493d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 537
},
"timestamp": "2026-02-10T11:48:22.116Z",
"answer": 34302
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -3.88,
"mid": -1.29,
"hi": 0.9
} | ||
5f5943 | nt_count_phi_equals_v1_1820931509_521 | Let $n = 114$. Define $u$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Define $k$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 191844$. Let $r$ be the number of positive integers $m$ with $1 \leq m ... | 1,431 | graphs = [
Graph(
let={
"_n": Const(114),
"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")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | 655d51 | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.587 | 2026-02-08T11:40:51.203315Z | {
"verified": true,
"answer": 1431,
"timestamp": "2026-02-08T11:40:51.790349Z"
} | 624c9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 4798
},
"timestamp": "2026-02-14T18:01:34.768Z",
"answer": 1431
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1349ab_l | antilemma_sum_equals_v1_153355830_1037 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 8$, $1 \leq i \leq 7$, and $1 \leq j \leq 8$. Define $Q$ to be $11025$ plus the sum, over all digits of $|x|$, of the square of the position index (starting from 0 for the units digit) multiplied by the digit. Compute $Q$. | 11,025 | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.032 | 2026-02-08T04:22:08.304081Z | {
"verified": false,
"answer": 11032,
"timestamp": "2026-02-08T04:22:08.335805Z"
} | 9d61de | 1349ab | 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": 211,
"completion_tokens": 3701
},
"timestamp": "2026-02-11T08:55:17.759Z",
"answer": 11025
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |
47cd8d | comb_count_surjections_v1_1520064083_7609 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 28$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = |S|$. Compute $3! \cdot S(n, 3)$, where $S(n, 3)$ is the Stirling number of the second kind. | 1,806 | 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 | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T09:12:27.956863Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T09:12:27.960543Z"
} | c5890b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1487
},
"timestamp": "2026-02-24T10:45:59.749Z",
"answer": 1806
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
1cc463 | comb_count_permutations_fixed_v1_1218484723_3371 | Let $D_n$ denote the number of derangements of $n$ elements. Let $n$ be the number of non-negative integers $a$ with $0 \le a \le 72$ satisfying
$$
\left(\left(\left(a^{2} -31 \bmod 73\right)^{2} -31 \bmod 73\right)^{2} -31 \bmod 73\right)^{2} -31 \bmod 73 = a,
$$
$$
\left(a^{36} \bmod 73\right) + \left((a^{2} -31 \bmo... | 28 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(72)), Eq(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-31)), modulus=Const(73)), C... | COMB | NT | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE"
] | 7c2be8 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"POLY_ORBIT_LEGENDRE"
] | 1 | 0.006 | 2026-02-25T05:04:50.778776Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-25T05:04:50.784633Z"
} | c49adf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 474,
"completion_tokens": 26927
},
"timestamp": "2026-03-29T09:54:39.687Z",
"answer": 28
},
{
"id... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
d3456c | sequence_fibonacci_compute_v1_458359167_5455 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1 \le a \le 8$, $1 \le b \le 3$, $20 \le t \le 90$, and $t = 6a + 14b$. Let $n$ be the number of elements in $S$. Define $m = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes... | 46,368 | 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=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/K3"
] | c7df50 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T12:31:28.262701Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T12:31:28.264628Z"
} | a99030 | 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": 1214
},
"timestamp": "2026-02-15T02:01:48.536Z",
"answer": 46368
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b44076 | diophantine_product_count_v1_717093673_997 | Let $k = 60$. Define $$
$$
Let $r$ be the number of positive integers $x$ such that $1 \le x \le u$, $x$ divides $k$, and $\frac{k}{x} \le u$. Compute $$
Q = r + \phi(|r| + 1) + \tau(|r| + 1),
$$
where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. Find the va... | 22 | graphs = [
Graph(
let={
"k": Const(60),
"upper": Summation(var="k1", start=Const(1), end=Const(8), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(8), Var("k1"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"),... | NT | null | COUNT | sympy | K3 | [
"K2"
] | 6897ab | diophantine_product_count_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.393 | 2026-02-08T15:46:53.342534Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T15:46:53.735900Z"
} | 6a6601 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 3057
},
"timestamp": "2026-02-16T13:57:48.847Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
55104f | diophantine_sum_product_min_v1_784195855_6011 | Let $S = 51$. Let $P$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 29584$. Let $x_0$ be the smallest integer $x$ with $1 \leq x \leq 50$ such that $x(S - x) = P$. Let $c = 27415$. Compute the remainder when $c \cdot x_0$ is divided by $72424$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(50),
"S": Const(51),
"P": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(29584)))), expr... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T08:15:16.790239Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T08:15:16.795668Z"
} | 83bb45 | 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": 1047
},
"timestamp": "2026-02-13T16:55:49.493Z",
"answer": 2048
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2f5da0 | nt_count_gcd_equals_v1_784195855_10397 | Let $ k $ be the number of ordered pairs $ (a, b) $ such that $ 1 \leq a \leq 9 $ and $ 1 \leq b \leq 17 $. Let $ S $ be the set of all positive integers $ n \leq 31329 $ such that $ \gcd(n, k) = 1 $. Compute the remainder when $ 17937 \cdot |S| $ is divided by $ 71263 $. | 67,485 | graphs = [
Graph(
let={
"upper": Const(31329),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const(17)))),
"d": Const(1),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), con... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 2.455 | 2026-02-08T17:49:42.804835Z | {
"verified": true,
"answer": 67485,
"timestamp": "2026-02-08T17:49:45.259422Z"
} | 33a84d | 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": 1610
},
"timestamp": "2026-02-18T13:36:37.050Z",
"answer": 67485
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
679d2f | lin_form_endings_v1_48377204_2062 | Let $a = 16$, $b = 40$, $A = 8$, and $B = 5$. Let $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define $\text{size}_T = a'A + b'B - a'b'$ and $\text{total} = aA + bB - a - b + 1$. Let $r = 16221 \times (\text{total} - \text{size}_T)$. Compute the rem... | 21,612 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(40),
"A_val": Const(8),
"B_val": Const(5),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": Fl... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:35:39.000031Z | {
"verified": true,
"answer": 21612,
"timestamp": "2026-02-08T16:35:39.002431Z"
} | 356b31 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1197
},
"timestamp": "2026-02-17T07:20:09.290Z",
"answer": 21612
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
89ce37 | antilemma_k2_v1_809748730_1833 | Let $n = 117$ and define $$
S = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{117}{k} \right\rfloor.
$$ Let $D$ be the sum of $d_i \cdot (i+1)^2$ over all digits $d_i$ of $|S|$, where $d_i$ is the $i$-th digit from the right, starting at $i=0$. Compute $D + 3136$. | 3,316 | graphs = [
Graph(
let={
"_n": Const(117),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(117), Var("k"))))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T12:43:27.310294Z | {
"verified": true,
"answer": 3316,
"timestamp": "2026-02-08T12:43:27.311021Z"
} | 74bfc5 | 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": 764
},
"timestamp": "2026-02-15T04:19:18.809Z",
"answer": 3316
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b86216 | modular_count_residue_v1_48377204_258 | Let $S_2$ be the set of all ordered pairs $(x_2, y_2)$ of positive integers such that $x_2 y_2 = 26244$. Let $s_2 = \min\{x_2 + y_2 \mid (x_2, y_2) \in S_2\}$. Let $S_1$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = s_2$. Let $s_1 = \min\{x_1 + y_1 \mid (x_1, y_1) \in S_1\}$. Le... | 4,166 | graphs = [
Graph(
let={
"upper": Const(62500),
"m": Const(15),
"r": 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")), MinOverSet(set=... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | modular_count_residue_v1 | null | 7 | 0 | [
"B3"
] | 1 | 2.063 | 2026-02-08T15:19:41.946169Z | {
"verified": true,
"answer": 4166,
"timestamp": "2026-02-08T15:19:44.009085Z"
} | 40e651 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 1309
},
"timestamp": "2026-02-16T03:06:35.474Z",
"answer": 4166
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d9f741 | nt_count_divisors_in_range_v1_168721529_1514 | Let $n = 720$ and $a = 1$. Let $b$ be the smallest positive integer such that $5^{180}$ divides $b!$. Find the number of positive divisors of $n$ that are at least $a$ and at most $b$. | 30 | graphs = [
Graph(
let={
"_n": Const(180),
"n": Const(720),
"a": Const(1),
"b": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(5)), Ref("_n")), domain='Z_{>0}')),
"result": CountOverSet(set... | NT | null | COUNT | sympy | V5 | [
"V5"
] | 79df37 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"V5"
] | 1 | 0.02 | 2026-02-08T13:44:40.888297Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T13:44:40.908729Z"
} | df2c9c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 840
},
"timestamp": "2026-02-09T18:24:35.325Z",
"answer": 30
},
{
"id":... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
b4acfe | nt_num_divisors_compute_v1_1520064083_7313 | Find the number of positive divisors of $2022$. | 8 | graphs = [
Graph(
let={
"n": Const(2022),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | L3C | [
"L3C/MOBIUS_COPRIME",
"MOBIUS_SUM",
"ONE_PHI_1"
] | 1a5e7d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"L3C",
"MOBIUS_COPRIME",
"MOBIUS_SUM",
"ONE_PHI_1"
] | 4 | 0.018 | 2026-02-08T08:54:13.190155Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T08:54:13.207976Z"
} | a5787e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 68,
"completion_tokens": 303
},
"timestamp": "2026-02-15T20:27:44.632Z",
"answer": 8
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"l... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
628e9c | alg_telescope_v1_1218484723_5241 | Compute the remainder when
$$
\sum_{k=0}^{\sum_{j=1}^{19} j} (4k^3 + 6k^2 + 4k + 1)
$$
is divided by $1637$. | 368 | graphs = [
Graph(
let={
"_n": Const(4),
"result": Mod(value=Summation(var="k", start=Const(0), end=Summation(var="k1", start=Const(1), end=Const(19), expr=Var("k1")), expr=Sum(Mul(Ref("_n"), Pow(Var("k"), Const(3))), Mul(Const(6), Pow(Var("k"), Const(2))), Mul(Const(4), Var("k")), Co... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | alg_telescope_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.024 | 2026-02-25T06:53:49.446588Z | {
"verified": true,
"answer": 368,
"timestamp": "2026-02-25T06:53:49.470634Z"
} | 24052f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1772
},
"timestamp": "2026-03-29T20:09:35.247Z",
"answer": 368
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
1e8cc4 | geo_count_lattice_triangle_v1_458359167_293 | Let $A = |121 \cdot 128 + 4 \cdot (-31)|$. Let $B = \gcd(121, 31) + \gcd(|121 - 4|, |31 - c|) + \gcd(4, d)$, where $c$ is the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 751021292521500$ and $\gcd(p, q) = 1$, and $d$ is the number of positive integers $p$ for which ... | 7,680 | graphs = [
Graph(
let={
"_n": Const(31),
"area_2x": Abs(arg=Sum(Mul(Const(value=121), Const(value=128)), Mul(Const(value=4), Sub(left=Const(value=0), right=Ref(name='_n'))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=121)), b=Abs(arg=Const(value=31))), GCD(a=Abs(arg=Sub(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.013 | 2026-02-08T03:10:56.879956Z | {
"verified": true,
"answer": 7680,
"timestamp": "2026-02-08T03:10:56.892684Z"
} | 26925e | 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": 10647
},
"timestamp": "2026-02-23T17:05:31.081Z",
"answer": 7680
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
049228 | comb_factorial_compute_v1_1419126231_463 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 40$ such that $2a^2 + 2b^2 - 4ab = 2178$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(40),
"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(40)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(2), Pow(... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_factorial_compute_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.001 | 2026-02-25T09:59:17.088607Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T09:59:17.089842Z"
} | 83edda | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 871
},
"timestamp": "2026-03-30T08:36:48.359Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V8_SUM",... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
ab9ba7 | nt_sum_over_divisible_v1_1874849503_644 | Let $n$ be a positive integer. Define $d$ to be the number of positive integers $n$ such that $1 \leq n \leq 338$ and $\gcd(n, 21) = 1$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 20160$ and $n$ is divisible by $d$. Compute the sum of all elements in $S$, multiply this sum by $44121$, and ... | 15,195 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(20160),
"divisor": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(338)), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"result": SumOverSet(set=... | NT | null | SUM | sympy | C4 | [
"C4"
] | 08d162 | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.827 | 2026-02-08T13:14:16.189577Z | {
"verified": true,
"answer": 15195,
"timestamp": "2026-02-08T13:14:17.017027Z"
} | 65e213 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 2850
},
"timestamp": "2026-02-09T19:19:48.761Z",
"answer": 15195
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
fd7d11 | alg_poly4_min_v1_1218484723_2824 | Let $S$ be the set of integers $v$ such that $16 \leq v \leq 10489$ and $v = 20a^2 + b^2 - 4ab$ for some integers $a, b$ with $1 \leq a, b \leq 23$. Let $A = |S|$. Minimize the expression
\[
168592a^4 - 666496a^3b + 1023360a^2b^2 - 650752ab^3 + 178432b^4
\]
over all positive integers $a, b$ with $1 \leq a \leq A$ and $... | 53,136 | graphs = [
Graph(
let={
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(16)), Leq(Var("v")... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly4_min_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.851 | 2026-02-25T04:33:03.364134Z | {
"verified": true,
"answer": 53136,
"timestamp": "2026-02-25T04:33:04.215446Z"
} | d74a2f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T06:52:18.841Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
4c2814 | diophantine_fbi2_min_v1_238844314_961 | Let $d$ be a positive integer. Let $k = 240$ and let $n = 4$. Define $\mathcal{D}$ to be the set of all positive divisors of 62750 that are at most 250. Let $U$ be the maximum element of $\mathcal{D}$. Define $\mathcal{S}$ to be the set of all integers $d$ such that $n \leq d \leq U$, $d$ divides $k$, and $\frac{k}{d} ... | 4 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(240),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(250)), Divides(divisor=Var("d"), dividend=Const(62750))))),
"result": MinOverSet(set=Solution... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"MAX_DIVISOR",
"SUM_DIVISIBLE"
] | 2 | 0.06 | 2026-02-08T13:50:05.935068Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T13:50:05.995384Z"
} | 49f7ca | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 727
},
"timestamp": "2026-02-16T05:07:27.725Z",
"answer": 4
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
788df2 | diophantine_product_count_v1_655260480_3562 | Let $k = 1260$. Define $u$ to be the number of integers $t$ such that $24 \leq t \leq 759$ and there exist integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 44$, and $t = 9a + 15b$. Let $S$ be the set of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Let $r$ be ... | 61,518 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(1260),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), righ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.027 | 2026-02-08T17:26:46.619842Z | {
"verified": true,
"answer": 61518,
"timestamp": "2026-02-08T17:26:46.646905Z"
} | 53710d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 4181
},
"timestamp": "2026-02-18T01:45:27.214Z",
"answer": 61518
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b9df8f | comb_count_partitions_v1_717093673_4008 | Let $c = 11948$. Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq = 108, \quad \gcd(p,q)=1, \quad p<q.$$
Let $S$ be the set of all integers $x$ satisfying
$$x^{m} - 441x + c = 0,$$
and let $n_0$ be the sum of all elements of $S$.
Let $n$ be the minimum value ... | 53,174 | graphs = [
Graph(
let={
"_c": Const(11948),
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/VIETA_SUM/B3"
] | dddd7f | comb_count_partitions_v1 | null | 8 | 0 | [
"B3",
"COPRIME_PAIRS",
"VIETA_SUM"
] | 3 | 0.005 | 2026-02-08T17:59:43.678100Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T17:59:43.682694Z"
} | 2de23a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1685
},
"timestamp": "2026-02-18T11:01:30.702Z",
"answer": 53174
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d9cd8 | comb_catalan_compute_v1_1874849503_1647 | Let $c$ be the number of ordered pairs $(i, j)$ where $i \in \{1, 2, 3, 4\}$ and $j \in \{1, 2, \dots, 8\}$. Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 14$, $1 \leq j \leq 14$, and $i + j = m... | 58,786 | graphs = [
Graph(
let={
"_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(8)))),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS"
] | a0469e | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.024 | 2026-02-08T14:00:46.908198Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T14:00:46.932593Z"
} | d7dc12 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 308,
"completion_tokens": 1259
},
"timestamp": "2026-02-10T06:06:33.205Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
456b56 | modular_min_linear_v1_677425708_128 | Let $a = 22914$, $b = 46956$, and $m = 60576$. Define $s = \sum_{d\mid \gcd(3,5)} \mu(d)$, where $\mu$ is the M\"obius function. Let $r$ be the smallest integer $x$ such that $x \geq s$, $x \leq m$, and $ax \equiv b \pmod{m}$. Compute $31329 - r$. | 27,803 | graphs = [
Graph(
let={
"a": Const(22914),
"b": Const(46956),
"m": Const(60576),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=Const(value=3), b=Const(value=5)), var='d', expr=MoebiusMu(n=Var(name='d'))... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_min_linear_v1 | null | 6 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 4.86 | 2026-02-08T03:06:01.629627Z | {
"verified": true,
"answer": 27803,
"timestamp": "2026-02-08T03:06:06.489893Z"
} | d4fb5e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 2476
},
"timestamp": "2026-02-08T20:20:02.001Z",
"answer": 27803
},
{
"... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
fb1288 | comb_count_surjections_v1_784195855_3036 | Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 8$ such that $i + j = 8$. Let $k$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 3$ and $1 \leq j \leq 3$ such that $i + j = 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ... | 126 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.021 | 2026-02-08T06:11:48.765948Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T06:11:48.786542Z"
} | 8b1467 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 751
},
"timestamp": "2026-02-24T05:35:20.092Z",
"answer": 126
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
944a30 | alg_poly3_sum_v1_601307018_5459 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 25$ such that $25b_1^2 + 10a_1^2 - 18a_1b_1 \le 1954$. Let $A = |S|$. Compute the remainder when $$\sum_{\substack{a \ge 1,\, a \le A \\ b \ge 1,\, b \le 152}} \left( -63b^3 - 45a^2b - 93ab^2 - 7a^3 \right)$$ is divided by $8... | 67,502 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=An... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.808 | 2026-03-10T06:04:51.261765Z | {
"verified": true,
"answer": 67502,
"timestamp": "2026-03-10T06:04:52.069367Z"
} | 712585 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 7732
},
"timestamp": "2026-04-19T02:09:04.663Z",
"answer": 67502
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
4a5272 | diophantine_fbi2_count_v1_1742523217_3713 | Let $k = 240$. Determine the number of positive integers $d$ such that $2 \leq d \leq 170$, $d$ divides $k$, and the quotient $k/d$ satisfies $2 \leq k/d \leq 170$. Let $r$ be this count. Find the smallest positive integer $t$ such that the $t$-th Fibonacci number is divisible by $r + 2$. | 30 | graphs = [
Graph(
let={
"_n": Const(170),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(170)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"L3C"
] | 73f8b0 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID",
"L3C"
] | 2 | 0.048 | 2026-02-08T06:03:32.124184Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T06:03:32.172285Z"
} | 026640 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1833
},
"timestamp": "2026-02-12T18:41:38.339Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
df2be8 | nt_min_coprime_above_v1_1440796553_624 | Let $S$ be the set of all ordered pairs of positive integers $(p, q)$ such that $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of such pairs. Compute $\phi(c)$, where $\phi$ is Euler's totient function. Find the smallest integer $n$ such that $53824 < n \leq 53849$ and $\gcd(n, 15) = \phi(c)$. D... | 53,827 | graphs = [
Graph(
let={
"start": Const(53824),
"upper": Const(53849),
"modulus": Const(15),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), EulerPh... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2"
] | 761f00 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2"
] | 2 | 0.015 | 2026-02-08T11:54:11.236788Z | {
"verified": true,
"answer": 53827,
"timestamp": "2026-02-08T11:54:11.251439Z"
} | 1f2ab4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 374
},
"timestamp": "2026-02-22T03:14:58.152Z",
"answer": 53827
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
}... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
0a37ef | lin_form_endings_v1_260342960_18 | Let $a = 45$ and $b = 27$. Define $g = \gcd(45, 27)$, and let $a' = \left\lfloor \frac{45}{g} \right\rfloor$ and $b' = \left\lfloor \frac{27}{g} \right\rfloor$. Let $A = 45$ and $B = 34$.
Define $S_T$ to be the sum $a'A + b'B - a'b'$, and define $S_{\text{total}}$ to be $45 \cdot 45 + 27 \cdot 34 - 45 - 27 + 1$.
Comp... | 2,560 | graphs = [
Graph(
let={
"a_coeff": Const(45),
"b_coeff": Const(27),
"A_val": Const(45),
"B_val": Const(34),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:11:10.927896Z | {
"verified": true,
"answer": 2560,
"timestamp": "2026-02-08T11:11:10.928947Z"
} | dfa388 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 698
},
"timestamp": "2026-02-08T20:27:35.397Z",
"answer": 2560
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.81,
"mid": -1.12,
"hi": 1.3
} | ||
90920e | comb_count_surjections_v1_124444284_6775 | Let $n$ be the number of integers $t$ with $26 \leq t \leq 40$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 2$, and $t = 4a + 6b + 16$. Let $s$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10$. Let $k$ be the number of ordered trip... | 53,284 | graphs = [
Graph(
let={
"_n": Const(53824),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/COMB1",
"LIN_FORM"
] | eea36a | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.036 | 2026-02-08T08:37:46.901848Z | {
"verified": true,
"answer": 53284,
"timestamp": "2026-02-08T08:37:46.937714Z"
} | da03dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 1176
},
"timestamp": "2026-02-24T09:47:48.976Z",
"answer": 53284
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
394d3b | nt_count_divisible_and_v1_865884756_4483 | Let $n = 67816$. Define $\text{upper} = 105528$, $d_1 = 8$, and $d_2$ to be the number of positive integers $k$ such that $1 \leq k \leq 768$ and $64$ divides $k$. Let $\text{result}$ be the number of positive integers $m$ such that $1 \leq m \leq \text{upper}$, $m \equiv 0 \pmod{d_1}$, and $m \equiv 0 \pmod{d_2}$. Let... | 33,527 | graphs = [
Graph(
let={
"_n": Const(67816),
"upper": Const(105528),
"d1": Const(8),
"d2": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(768)), Divides(divisor=Const(64), dividend=Var("k"))), domain='posi... | ALG | NT | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_divisible_and_v1 | null | 4 | 0 | [
"C2"
] | 1 | 3.489 | 2026-02-08T17:57:33.801699Z | {
"verified": true,
"answer": 33527,
"timestamp": "2026-02-08T17:57:37.291040Z"
} | eb56a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1274
},
"timestamp": "2026-02-18T10:31:45.117Z",
"answer": 33527
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e3ebf8 | geo_visible_lattice_v1_971394319_1415 | Let $n = 121$. Define $L$ as the number of visible lattice points $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $44121 \cdot L$ is divided by $80126$.
Find the value of $Q$. | 68,211 | graphs = [
Graph(
let={
"n": Const(121),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(80126)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.324 | 2026-02-08T13:40:44.204478Z | {
"verified": true,
"answer": 68211,
"timestamp": "2026-02-08T13:40:44.528128Z"
} | 73dae1 | 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": 7730
},
"timestamp": "2026-02-24T18:55:27.732Z",
"answer": 68211
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
760b9b | sequence_count_fib_divisible_v1_784195855_9146 | Let $\phi(n)$ denote Euler's totient function. Define
$$
\text{upper} = \sum_{k=1}^{36} \phi(k) \left\lfloor \frac{36}{k} \right\rfloor.
$$
Let $d = 4$. Compute the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $d$ divides the $n$th Fibonacci number $F_n$.
Find the value of this count. | 111 | graphs = [
Graph(
let={
"upper": Summation(var="k", start=Const(1), end=Const(36), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(36), Var("k"))))),
"d": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), R... | NT | null | COUNT | sympy | B3 | [
"K2"
] | 6897ab | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"K2"
] | 2 | 0.092 | 2026-02-08T16:33:38.211457Z | {
"verified": true,
"answer": 111,
"timestamp": "2026-02-08T16:33:38.303524Z"
} | 3088d3 | 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": 979
},
"timestamp": "2026-02-17T07:27:21.321Z",
"answer": 111
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cd10ac | modular_inverse_v1_1248542787_64 | Let $a = 198$ and let $m$ be the largest prime number not exceeding $715$. Let $u = 708$. Determine the smallest positive integer $x \leq u$ such that $198x \equiv 1 \pmod{m}$. Compute the remainder when $21773 \cdot x$ is divided by $83768$. | 36,214 | graphs = [
Graph(
let={
"_n": Const(83768),
"a": Const(198),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(715)), IsPrime(Var("n"))))),
"upper": Const(708),
"result": MinOverSet(set=Soluti... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.033 | 2026-02-08T02:56:14.524187Z | {
"verified": true,
"answer": 36214,
"timestamp": "2026-02-08T02:56:14.557114Z"
} | 03fbe4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1530
},
"timestamp": "2026-02-08T23:58:44.673Z",
"answer": 36214
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -1,
"mid": 0.95,
"hi": 2.6
} | ||
974932_n | alg_poly3_min_v1_1218484723_5729 | A robotics team designs a power function for their motor controller: $P(a,b) = 658b^3 + C a b^2 + 31584a^2b + 42112a^3$, where $C$ is the minimal perimeter (sum of length and width) of a rectangular enclosure with area $15586704$. The parameter $b$ must be a positive integer no greater than the number of distinct volta... | 82,250 | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT",
"B3"
] | a6e1c7 | alg_poly3_min_v1 | null | 6 | null | [
"B3",
"QF_PSD_DISTINCT"
] | 2 | 0.028 | 2026-02-25T07:18:04.805695Z | null | d377d1 | 974932 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 12323
},
"timestamp": "2026-03-31T00:04:21.143Z",
"answer": 82250
},
{
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
e6a4ee | diophantine_fbi2_min_v1_655260480_448 | Let $k = \sum_{k_1=1}^{6} k_1$. Let $u$ be the largest prime number $n$ such that $2 \le n \le 34$. Determine the value of $\min\{ d \mid 3 \le d \le u,\ d \text{ divides } k,\ k/d \ge 7 \}$. | 3 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Summation(var="k1", start=Const(1), end=Const(6), expr=Var("k1")),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(34)), IsPrime(Var("n"))))),
"result":... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 15f63b | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.007 | 2026-02-08T15:23:40.530673Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T15:23:40.538066Z"
} | 25e3c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 523
},
"timestamp": "2026-02-16T05:24:46.582Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
13882f | comb_sum_binomial_row_v1_1520064083_9067 | Let $n = 12$. Compute $2^n$. Let $D$ be the set of all positive integers $d$ such that $1 \le d \le 9801$ and $d$ divides $96079203$. Let $M$ be the maximum element of $D$.
Find the value of $M - 2^n$. | 5,705 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"result": Pow(Ref("_n"), Ref("n")),
"Q": Sub(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(9801)), Divides(divisor=Var("d"), dividend=Const(96079203)... | NT | null | SUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | ad1a9b | comb_sum_binomial_row_v1 | negation_mod | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T10:32:00.450000Z | {
"verified": true,
"answer": 5705,
"timestamp": "2026-02-08T10:32:00.451317Z"
} | e3815c | 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": 4965
},
"timestamp": "2026-02-14T07:40:13.126Z",
"answer": 5705
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ac9f67 | algebra_poly_eval_v1_784195855_5813 | Compute the value of
$$
\left( \sum_{k=1}^{4} k \right) \cdot 23^2 + (-6) \cdot 23 + 6.
$$
Multiply this result by $96933$, then compute the final value modulo $94450$. Give your answer as an integer between $0$ and $94449$. | 56,564 | graphs = [
Graph(
let={
"k": Const(23),
"result": Sum(Mul(Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")), Pow(Ref("k"), Const(2))), Mul(Const(-6), Ref("k")), Const(6)),
"_c": Const(96933),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T08:07:23.339120Z | {
"verified": true,
"answer": 56564,
"timestamp": "2026-02-08T08:07:23.340212Z"
} | 7fcb44 | 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": 1095
},
"timestamp": "2026-02-13T15:16:05.083Z",
"answer": 56564
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
678639 | nt_gcd_compute_v1_1116507919_215 | Let $a = 170625$ and $b = 398125$. Let $d = \gcd(a, b)$. Let $s = \sum_{k=1}^{5} k$. Compute the value of $$d + \left(2^{d \bmod s} \bmod 91299\right).$$ | 57,899 | graphs = [
Graph(
let={
"_n": Const(91299),
"a": Const(170625),
"b": Const(398125),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Sum(Ref("result"), Mod(value=Pow(Const(2), Mod(value=Ref("result"), modulus=Summation(var="k", start=EulerPhi(n=Const(1)... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"ONE_PHI_1"
] | 712f3e | nt_gcd_compute_v1 | mod_exp | 5 | 0 | [
"ONE_PHI_1",
"SUM_ARITHMETIC"
] | 2 | 0.001 | 2026-02-08T02:28:55.777750Z | {
"verified": true,
"answer": 57899,
"timestamp": "2026-02-08T02:28:55.779007Z"
} | 699f8e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 374
},
"timestamp": "2026-02-08T19:15:15.841Z",
"answer": 57899
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "SUM_ARI... | {
"lo": -4.6,
"mid": 0.15,
"hi": 4.61
} | ||
93bc2a | nt_num_divisors_compute_v1_48377204_2270 | Let $ n = 22500 $. Compute the number of positive divisors of $ n $. | 45 | graphs = [
Graph(
let={
"n": Const(22500),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | C3 | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.075 | 2026-02-08T16:42:06.661613Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T16:42:06.736631Z"
} | 7f9c60 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 374
},
"timestamp": "2026-02-16T07:43:51.383Z",
"answer": 45
},
{
"id": 11,
"... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d7db4a | modular_count_residue_v1_397696148_1227 | Let $m$ be the number of positive integers $k \leq 990$ that are divisible by $99$. Let $r = 4$. Compute the number of positive integers $n \leq 72361$ such that $n \equiv r \pmod{m}$. | 7,236 | graphs = [
Graph(
let={
"_n": Const(990),
"upper": Const(72361),
"m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(99), dividend=Var("k"))), domain='positive_integers')),
"r"... | ALG | NT | COUNT | sympy | C2 | [
"C2"
] | 9685eb | modular_count_residue_v1 | null | 3 | 0 | [
"C2"
] | 1 | 6.918 | 2026-02-08T12:25:25.168643Z | {
"verified": true,
"answer": 7236,
"timestamp": "2026-02-08T12:25:32.086460Z"
} | 4bf228 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 247
},
"timestamp": "2026-02-16T03:46:52.569Z",
"answer": 7236
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
837707 | diophantine_product_count_v1_1520064083_7890 | Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq 149$, $x$ divides $1260$, and $\frac{1260}{x} \leq 149$. Let $c$ be the largest positive divisor of $49098013$ that is at most $7001$. Compute the remainder when $r \bmod 317 + c \cdot (r \bmod 313)$ is divided by $70168$. | 13,708 | graphs = [
Graph(
let={
"_n": Const(317),
"k": Const(1260),
"upper": Const(149),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 9dada8 | diophantine_product_count_v1 | two_moduli | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.008 | 2026-02-08T09:21:33.375481Z | {
"verified": true,
"answer": 13708,
"timestamp": "2026-02-08T09:21:33.383546Z"
} | 9b1fa8 | 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": 2874
},
"timestamp": "2026-02-14T03:53:45.074Z",
"answer": 13708
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c320c7 | alg_poly4_min_v1_1218484723_5721 | Find the minimum value of $27175824a^2b^2 - 16259040a^3b + 3755064a^4 + 6271344b^4 - 20904480ab^3$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a \le 188$ and $1 \le b \le N$, where $N$ is the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 15$ and $41a_1^2 - 12a_1... | 38,712 | graphs = [
Graph(
let={
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(188)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elem... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_min_v1 | null | 5 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.692 | 2026-02-25T07:17:56.984428Z | {
"verified": true,
"answer": 38712,
"timestamp": "2026-02-25T07:17:57.676709Z"
} | 517670 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T22:31:25.146Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
3a14fa | comb_sum_binomial_row_v1_1978505735_3277 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 82208$ and $\binom{82208}{j}$ is odd. Define $r = 2^n$. Compute the remainder when $55696 - r$ is divided by $80047$. Find the value of this remainder. | 70,207 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(82208)), Eq(Mod(value=Binom(n=Const(82208), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"result": Pow(Const(2), Ref("n"... | ALG | COMB | SUM | sympy | V8 | [
"V8"
] | 86348e | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T17:32:27.865395Z | {
"verified": true,
"answer": 70207,
"timestamp": "2026-02-08T17:32:27.867517Z"
} | fedf48 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1196
},
"timestamp": "2026-02-18T03:45:57.085Z",
"answer": 70207
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b35526 | comb_factorial_compute_v1_1520064083_2554 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 567$ and $81$ divides $k$. Let $r = 44121$. Compute the remainder when $r$ times $n!$ is divided by $64810$. | 6,730 | graphs = [
Graph(
let={
"_n": Const(81),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(567)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": Factorial(Ref("n")),
... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | comb_factorial_compute_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T04:51:43.985574Z | {
"verified": true,
"answer": 6730,
"timestamp": "2026-02-08T04:51:43.987225Z"
} | 1672df | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1715
},
"timestamp": "2026-02-11T22:14:32.207Z",
"answer": 6730
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6c4c3d | comb_catalan_compute_v1_1431428450_601 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by $58747$. | 21,658 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), m... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T13:33:15.951887Z | {
"verified": true,
"answer": 21658,
"timestamp": "2026-02-08T13:33:15.954501Z"
} | 989b6b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 10072
},
"timestamp": "2026-02-24T18:43:08.682Z",
"answer": 9128
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
3e01d0 | alg_telescope_v1_1218484723_3861 | Let $M$ be the value of $\sum_{k=0}^{1478} \left((k+1)^2 - k^2\right)$ modulo the number of integers $t$ in the interval $[7, 9928]$ that can be expressed as $t = 3a + 4b$ for some integers $a, b$ with $1 \leq a \leq 500$, $1 \leq b \leq 2107$. Compute $|M|.$ | 5,921 | graphs = [
Graph(
let={
"_n": Const(1478),
"result": Mod(value=Summation(var="k", start=Const(0), end=Ref("_n"), expr=Sub(Pow(Sum(Var("k"), Const(1)), Const(2)), Pow(Var("k"), Const(2)))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), conditi... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.081 | 2026-02-25T05:30:23.480997Z | {
"verified": true,
"answer": 5921,
"timestamp": "2026-02-25T05:30:23.561695Z"
} | 45e531 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 19016
},
"timestamp": "2026-03-29T12:38:07.747Z",
"answer": 5921
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
933cca | nt_count_coprime_v1_1915831931_3117 | Let $k$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 40$, $1 \leq i \leq 39$, and $1 \leq j \leq 40$. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq 42436$ and $\gcd(n, k) = 1$. Compute the remainder when $44121 \cdot r$ is divided by $77267$. | 14,411 | graphs = [
Graph(
let={
"_n": Const(40),
"upper": Const(42436),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(39)), right=I... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_count_coprime_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 6.285 | 2026-02-08T17:22:12.688281Z | {
"verified": true,
"answer": 14411,
"timestamp": "2026-02-08T17:22:18.973637Z"
} | e1bba9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1653
},
"timestamp": "2026-02-18T01:10:42.031Z",
"answer": 14411
},
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f9264d | antilemma_sum_equals_v1_168721529_1440 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 88$ and $1 \leq i \leq 87$, $1 \leq j \leq 87$. Compute the remainder when $33 - x$ is divided by $87410$. | 87,356 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(88)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(87)), right=IntegerRange(start=Const(1), end=Const(87))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.005 | 2026-02-08T13:42:03.287279Z | {
"verified": true,
"answer": 87356,
"timestamp": "2026-02-08T13:42:03.292087Z"
} | bed420 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 512
},
"timestamp": "2026-02-09T17:08:34.632Z",
"answer": 87356
},
{
"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": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
231fc1 | alg_poly_orbit_hensel_v1_601307018_1615 | Let $N = (2a^5 + 5a^4 - 3a^3 + 4a^2 + 5a - 4) \bmod 2209$ and $M = (2N^5 + 5N^4 - 3N^3 + 4N^2 + 5N - 4) \bmod 2209$. Find the number of non-negative integers $a$ with $0 \le a \le 755477$ such that $M = a$ and $N \ne a$. | 684 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(5))), Mul(Const(5), Pow(Var("a"), Const(4))), Mul(Const(-3), Pow(Var("a"), Const(3))), Mul(Const(4), Pow(Var("a"), Const(2))), Mul(Const(5), Var("a")), Const(-4)), modulus=Const(2209)),
"p2": Mod(value=Sum(... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.088 | 2026-03-10T02:20:47.334246Z | {
"verified": true,
"answer": 684,
"timestamp": "2026-03-10T02:20:47.421768Z"
} | 4baf3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T02:55:22.394Z",
"answer": 684
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.78,
"mid": 4.94,
"hi": 7.11
} | ||
93df65 | nt_count_phi_equals_v1_798873815_297 | Let $F_n$ denote the $n$th Fibonacci number, defined by $F_1=1$, $F_2=1$, and $F_{n+2}=F_{n+1}+F_n$ for $n\ge 1$. Let $u$ be the number of integers $t$ for which there exist integers $a$ and $b$ such that
$$1\le a\le 711,\quad 1\le b\le 1181,\quad 11\le t\le 4501,\quad t=3a+2b+6.$$
Consider all ordered pairs $(x,y)$ o... | 308 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=711)), Geq(left=... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 6dd607 | nt_count_phi_equals_v1 | null | 8 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 0.284 | 2026-02-08T02:33:01.346015Z | {
"verified": true,
"answer": 308,
"timestamp": "2026-02-08T02:33:01.630325Z"
} | c42a74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 402,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T14:31:15.984Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"le... | {
"lo": 4.97,
"mid": 6.81,
"hi": 9.77
} | ||
7ed89b | geo_count_lattice_rect_v1_458359167_217 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 99$ and $0 \leq y \leq 39$. | 4,000 | graphs = [
Graph(
let={
"a": Const(99),
"b": Const(39),
"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 | 2026-02-08T03:04:46.881039Z | {
"verified": true,
"answer": 4000,
"timestamp": "2026-02-08T03:04:46.881454Z"
} | 741c49 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 92
},
"timestamp": "2026-02-10T13:17:28.902Z",
"answer": 4000
},
{
"id"... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
79b185 | nt_num_divisors_compute_v1_1080341949_276 | Let $n$ be the largest integer $k$ such that $3^k \leq 15$. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_n": Const(15),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(3), Var("k")), Ref("_n")))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"MAX_VAL"
] | 1da621 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"MAX_VAL"
] | 2 | 0.026 | 2026-02-08T13:22:04.664951Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:22:04.691114Z"
} | 67c4ee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 239
},
"timestamp": "2026-02-15T14:45:10.562Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "V1",
"st... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
169ed3 | comb_bell_compute_v1_784195855_7839 | Let $n = 8$ and define $r = B_n$, where $B_n$ denotes the $n$th Bell number. Let $d_k$ denote the $k$th decimal digit of $|r|$, with $d_0$ being the units digit. Define $s = \sum_{i=0}^{t} d_i (i+1)^2$, where $t$ is the number of digits in $|r|$ minus one. Let $e = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Compute $s + 5664... | 56,733 | graphs = [
Graph(
let={
"n2": Summation(var="k", start=Const(0), end=Const(7), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(7), k=Var("k")))),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T09:33:18.086165Z | {
"verified": true,
"answer": 56733,
"timestamp": "2026-02-08T09:33:18.088190Z"
} | 4881ef | 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": 428
},
"timestamp": "2026-02-24T11:30:23.673Z",
"answer": 56733
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
ead76a | modular_inverse_v1_1918700295_1164 | Let $a = 261$. Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 347$. Define $\text{upper} = 346$. Let $S$ be the set of all integers $x$ such that $1 \leq x \leq \text{upper}$ and $$261x \equiv 1 \pmod{m}.$$ Compute the smallest element of $S$. | 117 | graphs = [
Graph(
let={
"a": Const(261),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(347)), IsPrime(Var("n"))))),
"upper": Const(346),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=A... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_inverse_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.017 | 2026-02-08T05:36:38.397212Z | {
"verified": true,
"answer": 117,
"timestamp": "2026-02-08T05:36:38.414264Z"
} | d3adb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 780
},
"timestamp": "2026-02-12T11:04:04.388Z",
"answer": 117
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
ba2ac6 | antilemma_k3_v1_1742523217_1712 | Let $n = 72452$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute $x$. | 72,452 | graphs = [
Graph(
let={
"_n": Const(72452),
"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 | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:06:50.310959Z | {
"verified": true,
"answer": 72452,
"timestamp": "2026-02-08T04:06:50.311297Z"
} | 6fc637 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 305
},
"timestamp": "2026-02-10T15:50:12.957Z",
"answer": 72452
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
627d56 | nt_sum_divisors_mod_v1_153355830_1045 | Let $n = \sum_{d \mid 1680} \phi(d)$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$, and let $M = 11593$. Compute the remainder when $25091 \cdot (\sigma(n) \bmod M)$ is divided by $98634$. | 9,756 | graphs = [
Graph(
let={
"_n": Const(1680),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"M": Const(11593),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"_c": ... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.003 | 2026-02-08T04:22:08.848855Z | {
"verified": true,
"answer": 9756,
"timestamp": "2026-02-08T04:22:08.852325Z"
} | 8b52a1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1076
},
"timestamp": "2026-02-10T16:12:30.896Z",
"answer": 9756
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
21942c | antilemma_sum_equals_v1_124444284_6737 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \le i \le 7$ and $1 \le j \le 9$. Determine the number of ordered pairs $(i, j)$ of positive integers satisfying $1 \le i \le 61$, $1 \le j \le 62$, and $i + j = n.$ | 61 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(9)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.037 | 2026-02-08T08:36:19.283941Z | {
"verified": true,
"answer": 61,
"timestamp": "2026-02-08T08:36:19.321345Z"
} | 34e8f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1259
},
"timestamp": "2026-02-24T09:43:25.685Z",
"answer": 61
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
625a96 | comb_catalan_compute_v1_1978505735_3786 | Let $S$ be the set of all integers $t$ with $28 \leq t \leq 67$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 15a + 6b + 7$. Let $n$ be the number of elements in $S$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:50:47.642628Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T17:50:47.644649Z"
} | 66c486 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 671
},
"timestamp": "2026-02-18T09:14:41.394Z",
"answer": 16796
},
{... | 1 | [
{
"lemma": "C2",
"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",
"status": "no"
... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
f1b312_l | comb_count_partitions_v1_458359167_821 | Let $n_2 = 0$ and define
$$
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = \binom{18}{18} - 1$ and define
$$
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 38 \cdot t \cdot f$. Compute the value of $p(n)$, the number of integer partitions of $n$. | 1 | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | comb_count_partitions_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 0.001 | 2026-02-08T03:33:50.225377Z | {
"verified": false,
"answer": 26015,
"timestamp": "2026-02-08T03:33:50.226777Z"
} | 520556 | f1b312 | 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": 238,
"completion_tokens": 665
},
"timestamp": "2026-02-10T14:49:07.892Z",
"answer": 26015
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | |
42cc10 | antilemma_cartesian_v1_2051736721_814 | Let $n = 19$. Define $x$ to be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 30$ and $1 \leq j \leq 37$. Let $y$ be the number of ordered pairs $(i, j)$ of positive integers satisfying $i + j = n$ with $1 \leq i \leq 17$ and $1 \leq j \leq 17$. Compute $x + \left(2^{x \bmod y} \bmod 75313\right)$. | 1,174 | graphs = [
Graph(
let={
"_n": Const(19),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Const(37)))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=CountOverSet(set=S... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | 0c839d | antilemma_cartesian_v1 | mod_exp | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.016 | 2026-02-08T15:41:23.220291Z | {
"verified": true,
"answer": 1174,
"timestamp": "2026-02-08T15:41:23.235902Z"
} | 6159b2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 631
},
"timestamp": "2026-02-24T18:19:31.301Z",
"answer": 1174
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
a508de | nt_sum_gcd_range_mod_v1_655260480_4313 | Let $N = 7750$ and let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 1254$, $6$ divides $n$, and $\gcd(n, 35) = 1$. Let $s = \sum_{n_1=1}^{N} \gcd(n_1, k)$. Compute the remainder when $s$ is divided by $11173$. | 9,469 | graphs = [
Graph(
let={
"N": Const(7750),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1254)), Divides(divisor=Const(6), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"M": Const(11173),
... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.372 | 2026-02-08T17:52:45.686684Z | {
"verified": true,
"answer": 9469,
"timestamp": "2026-02-08T17:52:46.058265Z"
} | 79b4da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 2873
},
"timestamp": "2026-02-18T09:31:07.875Z",
"answer": 9469
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3f6df2_l | comb_count_surjections_v1_784195855_46 | Let $n = 7$ and $k = 5$. Define $S$ to be the set of all ordered pairs $(x_1, x_2)$ of positive integers such that $x_1$ is odd, $x_2$ is odd, and $x_1 + x_2 = 68 \times 76$. Let $A$ be the number of elements in $S$. Let $B = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be ... | 2,681 | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1"
] | af38b8 | comb_count_surjections_v1 | digits_weighted_mod | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.006 | 2026-02-08T02:55:23.673631Z | {
"verified": false,
"answer": 2777,
"timestamp": "2026-02-08T02:55:23.679397Z"
} | 3a438e | 3f6df2 | 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": 302,
"completion_tokens": 1836
},
"timestamp": "2026-02-10T11:54:12.550Z",
"answer": 2681
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": 4.05,
"mid": 5.31,
"hi": 6.62
} | |
8b9563 | comb_factorial_compute_v1_48377204_804 | Let $n_2 = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$ and $c = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}$. Let $n_1 = 0$ and $w = \sum_{k_2=0}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}$. Define $n = 8w$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n2": Summation(var="k", start=Const(0), end=Const(4), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(4), k=Var("k")))),
"c": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_factorial_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T15:42:43.661457Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T15:42:43.662901Z"
} | afa25a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 549
},
"timestamp": "2026-02-24T18:22:07.448Z",
"answer": 40320
},
{
"... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"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": "... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
6aa6e4 | comb_factorial_compute_v1_1116507919_113 | Let $m = 2$ and $n = 2$. Let $S$ be the set of prime numbers $p$ such that $m \leq p \leq 17$. Define $N$ to be the largest prime number $p$ satisfying $n \leq p \leq |S|$. Compute $N!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(17)), IsPri... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MAX_PRIME_BELOW"
] | d51604 | comb_factorial_compute_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T02:26:19.027188Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T02:26:19.028693Z"
} | 5cd663 | 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": 460
},
"timestamp": "2026-02-08T19:04:44.685Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"... | {
"lo": -10,
"mid": -7.08,
"hi": -5.18
} | ||
f4319a | alg_poly3_count_v1_601307018_8964 | Let $A = \left|\left\{ v \in [41, 8036] \mid \exists\, a,b \in \{1,2,\ldots,14\} \text{ such that } 16a^2 + 8ab + 17b^2 = v \right\}\right|$. Find the number of positive integers $a, b$ with $1 \leq a \leq A$ and $1 \leq b \leq 188$ such that $8b^3 = 24897088$. | 188 | graphs = [
Graph(
let={
"_n": Const(8036),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(41)), Leq(Var("v"), Ref("_n"... | ALG | null | COUNT | sympy | POLY4_MIN | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly3_count_v1 | null | 5 | 0 | [
"POLY4_MIN",
"QF_PSD_DISTINCT"
] | 2 | 5.891 | 2026-03-10T09:23:53.626068Z | {
"verified": true,
"answer": 188,
"timestamp": "2026-03-10T09:23:59.517298Z"
} | fa3091 | 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": 10275
},
"timestamp": "2026-04-19T10:15:32.973Z",
"answer": 188
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
99ff3b | algebra_quadratic_discriminant_v1_397696148_57 | Let $a = 2$, $b = 4$, and $c = 2$. Let $N$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Compute $b^N - 4ac$. Find the value of this expression. | 0 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(4),
"c": Const(2),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T11:16:49.942484Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T11:16:49.944176Z"
} | cad2f3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 329
},
"timestamp": "2026-02-15T21:10:32.012Z",
"answer": 48
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
612707 | nt_count_phi_equals_v1_865884756_6793 | Let $u$ be the number of prime numbers $n$ such that $2 \leq n \leq 15877$. Let $k = 130$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq u$ and $\phi(n_1) = k$. | 2 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(15877)), IsPrime(Var("n"))))),
"k": Const(130),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Cons... | NT | null | COUNT | sympy | K14 | [
"COUNT_PRIMES"
] | 07c874 | nt_count_phi_equals_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"K14"
] | 2 | 2.321 | 2026-02-08T19:23:26.266087Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T19:23:28.587478Z"
} | f557d8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 4650
},
"timestamp": "2026-02-18T22:15:18.548Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5aed50 | modular_product_range_v1_601307018_4822 | Let $M = \prod_{i=\sum_{k=1}^{3} \varphi(k) \cdot \lfloor \frac{3}{k} \rfloor}^{117} i$. Find the remainder when $M$ is divided by $11369€. | 2,950 | graphs = [
Graph(
let={
"_n": Const(117),
"prod": MathProduct(expr=Var("i"), var="i", start=Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))), end=Ref("_n")),
"result": Mod(value=Ref("prod"), modulus=Const(113... | NT | null | COMPUTE | sympy | SUM_AP | [
"K2"
] | 6897ab | modular_product_range_v1 | null | 5 | 0 | [
"K2",
"SUM_AP"
] | 2 | 0.1 | 2026-03-10T05:31:13.707760Z | {
"verified": true,
"answer": 2950,
"timestamp": "2026-03-10T05:31:13.808175Z"
} | 547faa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T13:32:12.498Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
9bae88 | diophantine_fbi2_min_v1_1978505735_2311 | Let $k$ be the number of positive integers between $1$ and $18432$ inclusive that are divisible by $256$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 9$. Define $s_{\text{min}}$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $d$ be a positive integer satisf... | 115 | graphs = [
Graph(
let={
"_n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k1"), Const(1)), Leq(Var("k1"), Const(18432)), Divides(divisor=Const(256), dividend=Var("k1"))), domain='positive_integers')),
"upper": Const(82),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"C2"
] | 83578c | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3",
"C2"
] | 2 | 0.016 | 2026-02-08T16:49:32.175790Z | {
"verified": true,
"answer": 115,
"timestamp": "2026-02-08T16:49:32.192246Z"
} | 4caf62 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 359
},
"timestamp": "2026-02-16T07:53:58.146Z",
"answer": 113
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": ... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
157863 | alg_qf_psd_count_v1_1218484723_2227 | Let $A$ be the number of positive integers $n \leq 737$ such that $\gcd(n, 12) = 1$, and let $B$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ with $xy = 15129$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le A$ and $1 \le b \le B$ such that $16b^2 + 5a^2... | 10 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"B3",
"C4"
] | 8d18b3 | alg_qf_psd_count_v1 | null | 5 | 0 | [
"B3",
"C4",
"ONE_PHI_1"
] | 3 | 1.016 | 2026-02-25T04:00:23.393228Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-25T04:00:24.408784Z"
} | e04713 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 10534
},
"timestamp": "2026-03-29T03:40:10.945Z",
"answer": 10
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lem... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} |
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