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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
31f71e | nt_count_divisible_and_v1_124444284_4534 | Let $S$ be the set of all integers $n$ with $2\le n\le 61$ such that $n$ is prime, and let $A$ be the number of elements of $S$.
Let $P$ be the greatest possible value of $xy$, where $x$ and $y$ are positive integers satisfying $x+y=A$. Let $B$ be the least possible value of $x+y$, where $x$ and $y$ are positive integ... | 7,031 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(50024),
"upper": Const(15516),
"d1": Const(12),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositi... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/B1/B3"
] | a6f1f6 | nt_count_divisible_and_v1 | null | 8 | 0 | [
"B1",
"B3",
"COUNT_PRIMES"
] | 3 | 0.519 | 2026-02-08T06:04:33.867068Z | {
"verified": true,
"answer": 7031,
"timestamp": "2026-02-08T06:04:34.385574Z"
} | 34f7ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1778
},
"timestamp": "2026-02-12T19:05:33.375Z",
"answer": 7031
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
23b743 | nt_count_divisors_in_range_v1_784195855_424 | Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 9922500 $. Let $ T $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq \min\{x + y \mid (x, y) \in S\} $ and $ 5 $ divides the $ n $-th Fibonacci number. Let $ N $ be the number of elements in $ T $. Determine t... | 3,090 | graphs = [
Graph(
let={
"_n": Const(70836),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositi... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.011 | 2026-02-08T04:21:57.531532Z | {
"verified": true,
"answer": 3090,
"timestamp": "2026-02-08T04:21:57.542961Z"
} | 2373a6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 3354
},
"timestamp": "2026-02-10T16:14:52.004Z",
"answer": 3090
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
78e901_l | diophantine_fbi2_min_v1_151522320_719 | Let $m = 144$. Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $s_{\min}$ be the minimum value of $x + y$ over all $(x, y) \in A$. Let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s_{\min}$. Let $P$ be the maximum value of $xy$ over a... | 132 | NT | null | EXTREMUM | sympy | B3 | [
"B3/B1"
] | 6cdf3d | diophantine_fbi2_min_v1 | negation_mod | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.015 | 2026-02-08T03:28:23.900868Z | {
"verified": false,
"answer": 142,
"timestamp": "2026-02-08T03:28:23.915590Z"
} | 8af908 | 78e901 | 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": 287,
"completion_tokens": 954
},
"timestamp": "2026-02-10T14:33:54.219Z",
"answer": 142
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | |
a2d569 | comb_count_partitions_v1_1520064083_435 | Let $m = 40$. Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = m$. Let $M$ be the maximum value of $x \cdot y$ over all pairs $(x, y) \in P$. Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = M$. Let $p(n)$ denote ... | 52,657 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": Const(63099),
"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")), MaxOverSet(set=Ma... | COMB | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_count_partitions_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T03:21:29.635727Z | {
"verified": true,
"answer": 52657,
"timestamp": "2026-02-08T03:21:29.637924Z"
} | baf4a4 | 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": 1430
},
"timestamp": "2026-02-23T22:20:21.101Z",
"answer": 52657
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
c97358 | geo_visible_lattice_v1_601307018_1135 | Let $n = \sum_{k=1}^{11} k$. Find the number of lattice points $(x,y)$ with $1 \le x, y \le n$ and $\gcd(x,y) = 1$. Compute the remainder when $29528$ times this number is divided by $61679$. | 2,831 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(11), expr=Var("k")),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(29528),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(61679)),
},
goal=Ref... | GEOM | GEOM | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | geo_visible_lattice_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.132 | 2026-03-10T01:43:32.393798Z | {
"verified": true,
"answer": 2831,
"timestamp": "2026-03-10T01:43:32.525468Z"
} | eccce9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T01:18:27.372Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": 2.84,
"mid": 4.95,
"hi": 7.12
} | ||
b0dae5 | modular_mod_compute_v1_1742523217_1606 | Let $\mathcal{S}$ be the set of all real solutions $x$ to the equation $$x^2 - 961x + 83808 = 0.$$ Let $a$ be the sum of all elements of $\mathcal{S}$. Find the remainder when $a$ is divided by $16641$. | 961 | graphs = [
Graph(
let={
"_n": Const(2),
"a": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-961), Var("x")), Const(83808)), Const(0)))),
"m": Const(16641),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | modular_mod_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T04:04:29.054186Z | {
"verified": true,
"answer": 961,
"timestamp": "2026-02-08T04:04:29.055006Z"
} | c32ff8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 552
},
"timestamp": "2026-02-10T15:16:22.819Z",
"answer": 961
},
{
"id... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
9d4734 | antilemma_k3_v1_1470522791_1069 | Let $ n = 9626 $. Define $ a = \sum_{d \mid n} \phi(d) $, where $ \phi $ denotes Euler's totient function. Now define $ x = \sum_{d \mid a} \phi(d) $. Compute $ x $. | 9,626 | graphs = [
Graph(
let={
"_n": Const(9626),
"x": SumOverDivisors(n=SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3",
"K3"
] | 79f53d | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:23:33.049414Z | {
"verified": true,
"answer": 9626,
"timestamp": "2026-02-08T13:23:33.050362Z"
} | 6ae468 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 4578
},
"timestamp": "2026-02-15T14:11:20.548Z",
"answer": 9626
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
fa3dcd | diophantine_product_count_v1_153355830_542 | Let $k = 480$. Let $U$ be the number of integers $t$ such that $15 \leq t \leq 573$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 19$, $1 \leq b \leq 51$, and $t = 6a + 9b$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq U$, $x$ divides $k$, and $k/x \leq U$. Compute the nu... | 20 | graphs = [
Graph(
let={
"k": Const(480),
"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=19)), Geq(left=... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 4 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME"
] | 2 | 0.079 | 2026-02-08T03:09:32.559755Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T03:09:32.638863Z"
} | 001184 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 5274
},
"timestamp": "2026-02-10T15:14:04.139Z",
"answer": 20
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
a8a120 | comb_binomial_compute_v1_784195855_9709 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 19$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 3a + 2b$. Compute the value of $\binom{n}{7}$. | 1,716 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:59:38.351558Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T16:59:38.354290Z"
} | 5e4d03 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1478
},
"timestamp": "2026-02-17T16:37:04.495Z",
"answer": 1716
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
539d10 | comb_count_partitions_v1_1978505735_4820 | Let $c = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $n_1 = \binom{7}{0} - 1$. Define $v = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}$. Let $n = 44 \cdot c$. Let $P(n)$ denote the number of integer partitions of $n$. Compute the remainder when $3691 \cdot P(n)$ is divided by $52813 \cdot v$. | 44,236 | graphs = [
Graph(
let={
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sub(Binom(n=Const(7), k=Const(0)), Const(1)),
"v": Summation(var="k1", start=Const(0), end... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.003 | 2026-02-08T18:35:12.703510Z | {
"verified": true,
"answer": 44236,
"timestamp": "2026-02-08T18:35:12.706340Z"
} | 3a3176 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 2381
},
"timestamp": "2026-02-18T17:58:26.915Z",
"answer": 44236
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
e8cb4a | diophantine_product_count_v1_48377204_1488 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 32400$. Let $u$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1,y_1)$ of positive integers such that $x_1 y_1 = 121$. Determine the value of the number of positive integers $x_2$ such that $1 \le... | 2 | graphs = [
Graph(
let={
"_n": Const(121),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.163 | 2026-02-08T16:08:01.365242Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:08:01.528586Z"
} | 20f1a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1440
},
"timestamp": "2026-02-16T21:11:51.678Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3eeaef | nt_count_gcd_equals_v1_971394319_151 | Let $S$ be the set of positive integers $n$ such that $1 \le n \le 10404$ and $\gcd(n, 240) = 5$. Let $k$ be the number of elements in $S$. Compute the sum of the number of positive divisors of each integer from 1 to $k$, inclusive. | 4,646 | graphs = [
Graph(
let={
"upper": Const(10404),
"k": Const(240),
"d": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 66e6c4 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 9.399 | 2026-02-08T12:51:21.051843Z | {
"verified": true,
"answer": 4646,
"timestamp": "2026-02-08T12:51:30.450832Z"
} | c6457f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 3060
},
"timestamp": "2026-02-15T06:54:12.042Z",
"answer": 4646
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
715f8f | comb_count_derangements_v1_1915831931_131 | Let $n$ be the largest prime number that is at most $10$. Compute the remainder when $44159 \cdot !n$ is divided by $63936$, where $!n$ denotes the number of derangements of $n$ objects. | 32,706 | graphs = [
Graph(
let={
"_n": Const(44159),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(10)), IsPrime(Var("n1"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T15:12:07.996137Z | {
"verified": true,
"answer": 32706,
"timestamp": "2026-02-08T15:12:07.997867Z"
} | 453f1b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 2320
},
"timestamp": "2026-02-16T01:57:28.597Z",
"answer": 32706
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
16bd6b | diophantine_fbi2_min_v1_655260480_3857 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Let $S$ be the set of all integers $d$ such that $5 \leq d \leq 20$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. Determine the value of the smallest element in $S$. | 5 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(20),
... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.159 | 2026-02-08T17:34:42.891574Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T17:34:43.050778Z"
} | ebf7ab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 528
},
"timestamp": "2026-02-18T04:15:17.742Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bbe74f | alg_poly3_sum_v1_1218484723_2706 | Find the remainder when $$\sum_{\substack{1 \leq a \leq 278 \\ 1 \leq b \leq 278}} \left|\left\{ v : \begin{array}{c} 0 \leq v \leq \left|\left\{ (a_1, b_1) : \begin{array}{c} 1 \leq a_1 \leq 35, \, 1 \leq b_1 \leq 35 \\ 41a_1^2 - 12a_1b_1 + 20b_1^2 \leq 28649 \end{array} \right\}\right| \\ \text{and } \exists\, 1 \leq... | 75,857 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(135),
"_n": Const(278),
"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"), Const(278)), Geq(Var("b"),... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_DISTINCT"
] | 0cf842 | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 2 | 0.524 | 2026-02-25T04:26:34.264099Z | {
"verified": true,
"answer": 75857,
"timestamp": "2026-02-25T04:26:34.788112Z"
} | d0d0ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 449,
"completion_tokens": 31672
},
"timestamp": "2026-03-29T06:09:06.814Z",
"answer": 75857
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
89b69d | comb_catalan_compute_v1_1742523217_1379 | Let $a = 1$ and $b = 4$. Define $n_2 = a + b$. Let $c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Define $n_1 = \left( \sum_{k=0}^{9} (-1)^k \binom{9}{k} \right) + c$. Let $s = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $N$ be the number of integers $t$ such that $5 \le t \le 17$ and there exist positive integers $a$ ... | 58,786 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(4),
"n2": Sum(Ref("a"), Ref("b")),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(Summation(var="k", start=Cons... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_catalan_compute_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T03:41:58.935831Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T03:41:58.941385Z"
} | 0a9bc6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 329,
"completion_tokens": 1425
},
"timestamp": "2026-02-10T16:25:35.655Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
f10f31 | alg_poly_orbit_hensel_v1_1218484723_495 | For each integer $a$ with $0 \le a \le 301077$, define $$N = 2a^5 + 4a^4 - a^3 - 5a^2 + 5a - 1 \bmod 841,$$ and let $M$ be the result of applying the same polynomial to $N$ modulo 841. Let $Q$ be the number of such $a$ for which $M = a$ and $N \neq a$. Find $Q$. | 716 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(5))), Mul(Const(4), Pow(Var("a"), Const(4))), Mul(Const(-1), Pow(Var("a"), Const(3))), Mul(Const(-5), Pow(Var("a"), Const(2))), Mul(Const(5), Var("a")), Const(-1)), modulus=Const(841)),
"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 | 0.107 | 2026-02-25T02:10:42.304435Z | {
"verified": true,
"answer": 716,
"timestamp": "2026-02-25T02:10:42.411188Z"
} | 51786e | 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": 15510
},
"timestamp": "2026-03-28T22:49:05.127Z",
"answer": 716
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.74,
"mid": 4.78,
"hi": 6.68
} | ||
68a389 | diophantine_fbi2_count_v1_458359167_1417 | Let $k = 120$. Consider the set of all integers $d$ such that $6 \leq d \leq 93$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 89$. Let $r$ be the number of elements in this set. Compute the value of $11^{|r|} \mod 99991$, and then add $20736$ to the result. Find the final sum. | 79,910 | graphs = [
Graph(
let={
"_n": Const(20736),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(93)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Di... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T04:36:17.091996Z | {
"verified": true,
"answer": 79910,
"timestamp": "2026-02-08T04:36:17.100659Z"
} | 0ddace | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1565
},
"timestamp": "2026-02-10T17:20:21.396Z",
"answer": 79910
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7d1c59_n | comb_count_surjections_v1_601307018_882 | A school is organizing a relay race with 14 students divided into exactly 3 non-empty teams, where the order of students within a team doesn't matter, but the teams are unlabeled. Before grouping, the students line up in two odd-numbered groups: one of size $x_1$ and one of size $x_2$, with $x_1 + x_2 = 14$, both odd. ... | 51,526 | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | null | [
"COMB1"
] | 1 | 0.003 | 2026-03-10T01:30:09.207300Z | null | 46b7e9 | 7d1c59 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 4351
},
"timestamp": "2026-03-29T14:40:39.200Z",
"answer": 51526
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
10c925 | diophantine_fbi2_min_v1_655260480_2903 | Let $k = 32$ and $u = 42$. Define $S$ as the set of all integers $d$ such that $6 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Let $r$ be the minimum element of $S$. Let $T$ be the set of all integers $t$ with $5 \leq t \leq 17$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 4$, $1 \... | 4,140 | graphs = [
Graph(
let={
"k": Const(32),
"upper": Const(42),
"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 | COMB | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | diophantine_fbi2_min_v1 | bell_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T17:03:30.929954Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T17:03:30.936568Z"
} | ae682c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1119
},
"timestamp": "2026-02-17T18:15:34.278Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
837819 | modular_sum_quadratic_residues_v1_784195855_3380 | Let $m = 42436$. Define $n$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$.
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $s_{\min}$ be the minimum value of $x + y$ over all such ... | 41,718 | graphs = [
Graph(
let={
"_m": Const(42436),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3/MAX_PRIME_BELOW"
] | d45f76 | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.006 | 2026-02-08T06:22:51.703970Z | {
"verified": true,
"answer": 41718,
"timestamp": "2026-02-08T06:22:51.710189Z"
} | 47d22b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2576
},
"timestamp": "2026-02-12T23:29:33.803Z",
"answer": 41718
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
55aaaa | v1_endings_v1_1248542787_925 | Let $n = 15260$, $k = 4329$, and $p = 3$. Define $v_p(m)$ to be the largest integer $e$ such that $p^e$ divides $m!$. Let $v_n = v_p(n)$, $v_k = v_p(k)$, and $v_{n-k} = v_p(n-k)$ where $n-k = 10931$. Compute the remainder when $5432 \cdot (v_n - (v_k + v_{n-k}))$ is divided by $68140$. | 32,592 | graphs = [
Graph(
let={
"n_val": Const(15260),
"k_val": Const(4329),
"p_val": Const(3),
"nk_val": Const(10931),
"n_fact": Factorial(Ref("n_val")),
"k_fact": Factorial(Ref("k_val")),
"nk_fact": Factorial(Ref("nk_val")),
... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 6 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T03:29:37.278588Z | {
"verified": true,
"answer": 32592,
"timestamp": "2026-02-08T03:29:37.279142Z"
} | c7baf3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 3689
},
"timestamp": "2026-02-09T10:06:53.730Z",
"answer": 38024
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
218e42 | antilemma_cartesian_v1_784195855_8486 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 7$ and $1 \leq b \leq 10$.
Let $s$ be the number of ordered pairs $(u, v)$ of positive odd integers such that $u + v = 192$.
Let $t$ be the number of ordered pairs $(u, v)$ of positive odd integers such that $u + v = s$.
Compute $x^2 + t \cdot ... | 8,263 | graphs = [
Graph(
let={
"_n": Const(192),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(10)))),
"_c": Const(3),
"Q": Sum(Pow(Ref("x"), Const(2)), Mul(CountOverSet(set=Soluti... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COMB1",
"COUNT_CARTESIAN"
] | 08716d | antilemma_cartesian_v1 | quadratic_mod | 3 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.003 | 2026-02-08T16:06:47.093681Z | {
"verified": true,
"answer": 8263,
"timestamp": "2026-02-08T16:06:47.096266Z"
} | 85fa5d | 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": 759
},
"timestamp": "2026-02-24T19:52:19.818Z",
"answer": 8263
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
c561dc | antilemma_k2_v1_1978505735_4007 | Compute $$\sum_{k=1}^{74} \phi(k) \left\lfloor \frac{74}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. Find the value of this sum. | 2,775 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(36), Const(36)), end=Const(74), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(74), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 4 | 0 | [
"IDENTITY_DIV_SELF",
"K2"
] | 2 | 0.001 | 2026-02-08T17:58:46.033289Z | {
"verified": true,
"answer": 2775,
"timestamp": "2026-02-08T17:58:46.034339Z"
} | 7a7e93 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 557
},
"timestamp": "2026-02-16T11:48:47.738Z",
"answer": 225
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
54974a | antilemma_k2_v1_1915831931_1864 | Let $ n = 218 $. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{218}{k} \right\rfloor,
$$
where $ \phi(k) $ denotes Euler's totient function. Let $ Q $ be the remainder when $ 44121x $ is divided by $ 91933 $. Compute $ Q $. | 27,943 | graphs = [
Graph(
let={
"_n": Const(218),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(218), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(91933)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K13",
"K2"
] | 2 | 0.004 | 2026-02-08T16:29:19.865624Z | {
"verified": true,
"answer": 27943,
"timestamp": "2026-02-08T16:29:19.869529Z"
} | e54107 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1269
},
"timestamp": "2026-02-17T04:50:09.511Z",
"answer": 27943
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
faa310 | algebra_poly_eval_v1_1218484723_7598 | Let $m = 6$. Compute
$$
4m^4 + 4m^3 + 4m^2 + \left|\left\{ v \in [0, 1274] : \exists\, a,b \in \{1,2,\dots,8\} \text{ such that } 26b^2 - 52ab + 26a^2 = v \right\}\right| \cdot m - 4.
$$ | 6,236 | graphs = [
Graph(
let={
"_n": Const(4),
"m": Const(6),
"result": Sum(Mul(Const(4), Pow(Ref("m"), Ref("_n"))), Mul(Const(4), Pow(Ref("m"), Const(3))), Mul(Const(4), Pow(Ref("m"), Const(2))), Mul(CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | algebra_poly_eval_v1 | null | 4 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.003 | 2026-02-25T09:02:00.102199Z | {
"verified": true,
"answer": 6236,
"timestamp": "2026-02-25T09:02:00.105233Z"
} | a4d6fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1059
},
"timestamp": "2026-03-30T05:26:00.540Z",
"answer": 6236
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
bdb332 | sequence_lucas_compute_v1_784195855_9504 | Let $n = \sum_{k=1}^{6} k$. Let $L_n$ be the $n$-th Lucas number. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|L_n| + 2$. | 36,714 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T16:52:08.838534Z | {
"verified": true,
"answer": 36714,
"timestamp": "2026-02-08T16:52:08.840800Z"
} | 328d97 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 2557
},
"timestamp": "2026-02-17T13:54:01.576Z",
"answer": 36714
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
81195d | alg_qf_psd_orbit_v1_1218484723_2235 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 236$ such that $4a^2 + 4b^2 = 224900$. | 6 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(236)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(236)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(4), Pow(Var("b"), Const(2))), ... | ALG | null | COUNT | sympy | QUADRATIC_INEQ | [
"QUADRATIC_INEQ"
] | 241de8 | alg_qf_psd_orbit_v1 | null | 3 | null | [
"QUADRATIC_INEQ"
] | 1 | 0.897 | 2026-02-25T04:00:26.359053Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T04:00:27.256115Z"
} | 5e6f15 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 4611
},
"timestamp": "2026-03-29T03:41:11.312Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QUADRATIC_INEQ",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
b9621b | comb_count_surjections_v1_898971024_2634 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 9$, $1 \le i \le 7$, and $1 \le j \le 7$. Let $k = 5$. Define $S = k! \cdot S(n,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Compute $S$. | 1,800 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(9)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(7))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.071 | 2026-02-08T16:53:24.213843Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T16:53:24.284724Z"
} | 863a5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1081
},
"timestamp": "2026-02-17T14:12:43.280Z",
"answer": 1800
},
{... | 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",
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
ea92f8 | nt_count_coprime_and_v1_971394319_1083 | Let $k_1 = 5$ and let $k_2$ be the sum of all (not necessarily distinct) real solutions $x$ to the equation $x^2 - 7x - 4680 = 0$. Let $u = 16782$. Determine the number of positive integers $n$ such that $1 \leq n \leq u$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Find the remainder when the absolute value of this nu... | 11,508 | graphs = [
Graph(
let={
"upper": Const(16782),
"k1": Const(5),
"k2": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-7), Var("x")), Const(-4680)), Const(0)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_coprime_and_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 1.815 | 2026-02-08T13:29:34.435926Z | {
"verified": true,
"answer": 11508,
"timestamp": "2026-02-08T13:29:36.250541Z"
} | facc0a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1382
},
"timestamp": "2026-02-15T16:32:01.129Z",
"answer": 11508
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f6207c | alg_linear_system_2x2_v1_1218484723_4326 | Let $T$ be the number of integer pairs $(a, b)$ with $1 \le a, b \le 25$ satisfying
$$
384a^2b + 128a^3 + 384ab^2 + mb^3 = 432000,
$$
where $m = \min\{x + y : x > 0, y > 0, xy = 4096\}$. Let $\det = -17T + 40$, $R = -1589101 \cdot 14 + 744190 \cdot 5$, and $S = -17 \cdot (-744190) + 8 \cdot (-1589101)$. Compute $\frac{... | 93,879 | graphs = [
Graph(
let={
"_m": Const(384),
"_n": Const(128),
"num_x": Sub(Mul(Const(-1589101), Const(14)), Mul(Const(-744190), Const(5))),
"num_y": Sub(Mul(Const(-17), Const(-744190)), Mul(Const(-8), Const(-1589101))),
"det": Sub(Mul(Const(-17), Cou... | ALG | null | COMPUTE | sympy | B3 | [
"B3/POLY3_COUNT"
] | f5b896 | alg_linear_system_2x2_v1 | null | 5 | 0 | [
"B3",
"POLY3_COUNT"
] | 2 | 0.009 | 2026-02-25T05:57:32.158855Z | {
"verified": true,
"answer": 93879,
"timestamp": "2026-02-25T05:57:32.167375Z"
} | df61ef | 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": 1961
},
"timestamp": "2026-03-29T15:01:13.078Z",
"answer": 93879
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
234c64 | diophantine_fbi2_count_v1_1520064083_2433 | Let $k$ be the number of integers $t$ such that $7 \leq t \leq 850$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 215$, $1 \leq b \leq 84$, and $t = 2a + 5b$. Let $\text{result}$ be the number of positive integers $d$ such that $4 \leq d \leq 183$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 183$.... | 84 | graphs = [
Graph(
let={
"_n": Const(183),
"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=215)), Geq(left=Va... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.195 | 2026-02-08T04:44:09.222096Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T04:44:09.417003Z"
} | 80cd2e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 5500
},
"timestamp": "2026-02-11T21:50:40.984Z",
"answer": 84
},
{
"id... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ff9bf0 | sequence_fibonacci_compute_v1_153355830_2403 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 28$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 4$, and $t = 2a + 3b$. Compute the $n$-th Fibonacci number.
The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$.
F... | 17,711 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T07:06:52.611978Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T07:06:52.613916Z"
} | 3d2d91 | 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": 1774
},
"timestamp": "2026-02-13T07:49:51.944Z",
"answer": 17711
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1147af | modular_modexp_compute_v1_124444284_4215 | Let $a = 41$, $e = 200$, and $m = 22201$. Define $r = a^e \mod m$. Let $c$ be the sum of all real solutions $x$ to the equation $x^2 - 3001x + 53694 = 0$. Compute the value of $r \mod 293 + c \cdot (r \mod 337)$. | 33,081 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(41),
"e": Const(200),
"m": Const(22201),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
"_c": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref(... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 805c31 | modular_modexp_compute_v1 | two_moduli | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T05:51:17.795069Z | {
"verified": true,
"answer": 33081,
"timestamp": "2026-02-08T05:51:17.796335Z"
} | c4c427 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 3688
},
"timestamp": "2026-02-12T15:32:51.703Z",
"answer": 33081
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c25627_l | comb_count_permutations_fixed_v1_1125832087_193 | Let $n = 6$ and let $\_n = 2$. Define $k$ to be the number of nonnegative integers $j$ such that $0 \le j \le 1088$ and $\binom{1088}{j} \equiv 1 \pmod{2}$. Let $\_c = 40849$ and define
$$
Q = \_c \cdot \binom{n}{k} \cdot !(n - k) \pmod{86626},
$$
where $!m$ denotes the subfactorial of $m$. Compute $Q$. | 0 | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T02:55:50.809592Z | {
"verified": false,
"answer": 6353,
"timestamp": "2026-02-08T02:55:50.812212Z"
} | 021176 | c25627 | 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": 241,
"completion_tokens": 1003
},
"timestamp": "2026-02-10T12:49:24.473Z",
"answer": 6653
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": 1.09,
"mid": 2.49,
"hi": 3.8
} | |
378ab2 | diophantine_product_count_v1_151522320_1387 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1587600$. Let $m$ be the minimum value of $x + y$ over all such pairs. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Define $\text{upper} = 47$. Let $r$ be the number of positi... | 12 | graphs = [
Graph(
let={
"k": 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")), MinOverSet(set=MapOverSet(set=S... | NT | null | COUNT | sympy | B3 | [
"B3/COMB1"
] | e26f7e | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"COMB1"
] | 2 | 0.007 | 2026-02-08T03:58:21.793882Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T03:58:21.800634Z"
} | f4eeed | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 3350
},
"timestamp": "2026-02-10T14:51:42.479Z",
"answer": 12
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e1c6a6 | algebra_vieta_sum_v1_458359167_4174 | Let $m = 3$. Let $b$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 164$ and $\binom{164}{j}$ is odd. Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 54$. Consider the cubic equation $2x^3 + b x^c - 78x - 252... | 126 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(164)), Eq(Mod(value=Binom(n=Const(164), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"resul... | NT | null | COMPUTE | sympy | B3 | [
"V8/COPRIME_PAIRS"
] | cea98a | algebra_vieta_sum_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"V8"
] | 3 | 0.157 | 2026-02-08T11:36:00.823698Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T11:36:00.980949Z"
} | d4bdfd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 871
},
"timestamp": "2026-02-16T03:03:00.652Z",
"answer": 72
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
9121ef | algebra_poly_eval_v1_1820931509_254 | Let $n = 17$. Compute the value of
\[
\frac{40n^4 + 182n^3 - 110n^2 - 84n + 80}{\sum_{k=1}^{88} k}.
\] | 1,073 | graphs = [
Graph(
let={
"_n": Const(88),
"n": Const(17),
"result": Div(Sum(Mul(Const(40), Pow(Ref("n"), Const(4))), Mul(Const(182), Pow(Ref("n"), Const(3))), Mul(Const(-110), Pow(Ref("n"), Const(2))), Mul(Const(-84), Ref("n")), Const(80)), Summation(var="k", start=Const(1... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T11:27:45.923689Z | {
"verified": true,
"answer": 1073,
"timestamp": "2026-02-08T11:27:45.925820Z"
} | d1d7be | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 982
},
"timestamp": "2026-02-14T14:35:19.680Z",
"answer": 1073
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bb91a6 | alg_qf_psd_sum_v1_1218484723_3763 | Find the remainder when $$\sum_{a=1}^{5} \sum_{b=1}^{5} \sum_{c=1}^{5} \sum_{d=1}^{5} \left( 126bd + 24ac + 48cd + 63d^2 + 21c^2 + 66b^2 + 54ad + \min\{ x + y : x > 0, y > 0, xy = 625 \} \cdot bc + 45a^2 + 36ab \right)$$ is divided by $50769$. | 43,428 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(5)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(5)), Geq(V... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_qf_psd_sum_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.49 | 2026-02-25T05:24:48.794030Z | {
"verified": true,
"answer": 43428,
"timestamp": "2026-02-25T05:24:49.284114Z"
} | 11a0f2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2622
},
"timestamp": "2026-03-29T12:06:29.108Z",
"answer": 43428
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
62779f | antilemma_k3_v1_865884756_2637 | Let $n = 66196$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 66,196 | graphs = [
Graph(
let={
"_n": Const(66196),
"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 | 2026-02-08T16:51:45.165035Z | {
"verified": true,
"answer": 66196,
"timestamp": "2026-02-08T16:51:45.165480Z"
} | f562c4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1198
},
"timestamp": "2026-02-16T07:54:41.123Z",
"answer": 6048
},
{
"id": 11,... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
d554f9 | antilemma_k2_v1_1978505735_7530 | Let
$$
x = \sum_{k=1}^{266} \phi(k) \left\lfloor \frac{266}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Find the remainder when $86647x$ is divided by $94922$. | 24,987 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(266), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(266), Var("k"))))),
"Q": Mod(value=Mul(Const(86647), Ref("x")), modulus=Const(94922)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K13",
"K2"
] | 2 | 0.004 | 2026-02-08T20:18:15.880351Z | {
"verified": true,
"answer": 24987,
"timestamp": "2026-02-08T20:18:15.884140Z"
} | ed21a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 2182
},
"timestamp": "2026-02-19T00:20:55.043Z",
"answer": 24987
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ec293 | geo_count_lattice_rect_v1_1742523217_3329 | Let $a = 99$ and $b = 333$. Define $L$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute the value of $Q = (12321 - L) \bmod 76846$. | 55,767 | graphs = [
Graph(
let={
"a": Const(99),
"b": Const(333),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Sub(Const(12321), Ref("result")), modulus=Const(76846)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T05:46:50.850485Z | {
"verified": true,
"answer": 55767,
"timestamp": "2026-02-08T05:46:50.852938Z"
} | c5459b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 443
},
"timestamp": "2026-02-24T04:35:51.985Z",
"answer": 55767
},
{
"i... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
23a1a8 | antilemma_sum_factor_cartesian_v1_124444284_188 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 5$ and $1 \leq j \leq 16$ such that $$\sum_{d\mid \gcd(15,22)} \mu(d) > 0.$$ Let $x$ be the sum of $i \cdot j$ over all pairs $(i, j)$ in $S$. Find the value of $x$. | 2,040 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=15), b=Const(value=22)), var='d', expr=MoebiusMu(n=Var(name='d'))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME"
] | 1428b5 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T03:03:36.018476Z | {
"verified": true,
"answer": 2040,
"timestamp": "2026-02-08T03:03:36.019091Z"
} | f6a39a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1578
},
"timestamp": "2026-02-09T14:31:09.387Z",
"answer": 1323
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma":... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
bb6adf | comb_count_derangements_v1_677425708_3371 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 26460$, $\gcd(p, q) = 1$, and $p < q$. Let $r = !n$ denote the number of derangements of $n$ elements. Compute the remainder when $55891 \cdot r$ is divided by $59440$. | 21,523 | graphs = [
Graph(
let={
"_n": Const(55891),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=26460)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:40:37.228024Z | {
"verified": true,
"answer": 21523,
"timestamp": "2026-02-08T05:40:37.229087Z"
} | 551c52 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 3370
},
"timestamp": "2026-02-12T12:22:17.019Z",
"answer": 21523
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c713cb | nt_max_prime_below_v1_898971024_2054 | Let $n_0$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number $n'$ satisfying $n' \geq n_0$ and $n' \leq 82944$. Let $c = 81135$ and $m = 85778$. Compute the remainder when $c \cdot n$ is divided by $m$. | 57,443 | graphs = [
Graph(
let={
"_n": Const(85778),
"upper": Const(82944),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.96 | 2026-02-08T16:30:35.877108Z | {
"verified": true,
"answer": 57443,
"timestamp": "2026-02-08T16:30:38.837404Z"
} | b4d466 | 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": 3039
},
"timestamp": "2026-02-17T06:40:49.306Z",
"answer": 57443
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69b66d | nt_min_coprime_above_v1_168721529_538 | Let $d_0$ be the smallest positive divisor of $11776575876041$ that is at least the number of positive integers $n \leq 8$ such that $3$ divides the $n$-th Fibonacci number. Let $n_0$ be the smallest integer greater than $56953$ and at most $57364$ that is relatively prime to $d_0$. Determine the value of $n_0$. | 56,954 | graphs = [
Graph(
let={
"_n": Const(3),
"start": Const(56953),
"upper": Const(57364),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MIN_PRIME_FACTOR"
] | 0c6279 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 0.061 | 2026-02-08T13:05:57.152697Z | {
"verified": true,
"answer": 56954,
"timestamp": "2026-02-08T13:05:57.213381Z"
} | 853aad | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 449
},
"timestamp": "2026-02-09T18:22:33.812Z",
"answer": 56954
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status"... | {
"lo": -5.65,
"mid": -2.14,
"hi": 1.97
} | ||
e37128 | antilemma_sum_equals_v1_1470522791_1078 | Let $n = 24$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = n$, where $1 \leq i \leq 23$ and $1 \leq j \leq 24$. Let $x$ be the number of such ordered pairs. Compute the remainder when $44121 \cdot x$ is divided by $66884$. | 11,523 | graphs = [
Graph(
let={
"_n": Const(24),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T13:23:42.806520Z | {
"verified": true,
"answer": 11523,
"timestamp": "2026-02-08T13:23:42.817851Z"
} | 3cbe75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1961
},
"timestamp": "2026-02-24T18:19:07.189Z",
"answer": 11523
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
adde5c | comb_catalan_compute_v1_1470522791_1683 | Let $m = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$ and $n_1 = 9 + m$. Let $w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Define $n$ to be the sum of $w$ and 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 $19321 - C_n$. | 2,525 | graphs = [
Graph(
let={
"n2": Const(4),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(Const(9), Ref("m")),
"w": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(P... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING"
] | d0de27 | comb_catalan_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | 2 | 0.004 | 2026-02-08T13:50:04.220076Z | {
"verified": true,
"answer": 2525,
"timestamp": "2026-02-08T13:50:04.223826Z"
} | 142e55 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 548
},
"timestamp": "2026-02-24T19:12:42.661Z",
"answer": 2525
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma"... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
2a6342 | nt_count_intersection_v1_153355830_1465 | Let $a$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $N = 50000$. Let $R$ be the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, 10) = 1$. Let $s$ be the number of unordered pairs of positive integers $(p, q)$ such that $... | 48,901 | graphs = [
Graph(
let={
"_n": Const(6),
"N": Const(50000),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=... | NT | null | COUNT | sympy | C3 | [
"COPRIME_PAIRS",
"B1"
] | 387897 | nt_count_intersection_v1 | digits_weighted_mod | 6 | 0 | [
"B1",
"C3",
"COPRIME_PAIRS"
] | 3 | 1.979 | 2026-02-08T06:25:47.185257Z | {
"verified": true,
"answer": 48901,
"timestamp": "2026-02-08T06:25:49.164251Z"
} | 33bb40 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1257
},
"timestamp": "2026-02-13T00:13:16.996Z",
"answer": 48901
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
ba779a | geo_count_lattice_rect_v1_1915831931_815 | Let $a = 64$ and $b = 30$. Define $L$ to be the number of lattice points $(x, y)$ in the rectangle $0 \le x \le a$, $0 \le y \le b$, including the boundary. Let $k$ be the smallest positive integer such that the $k$-th Fibonacci number is divisible by $|L| + 2$. Compute $k$. Determine the value of $k$. | 1,009 | graphs = [
Graph(
let={
"a": Const(64),
"b": Const(30),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T15:41:08.968788Z | {
"verified": true,
"answer": 1009,
"timestamp": "2026-02-08T15:41:08.970062Z"
} | a336a0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 4023
},
"timestamp": "2026-02-24T18:22:57.087Z",
"answer": 1009
},
{
"... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
7ea21b | geo_count_lattice_rect_v1_1520064083_7950 | Let $a = 169$ and $b = 357$. Let $R$ be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Compute the remainder when $88499 \cdot R$ is divided by $79548$. | 13,156 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(357),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(88499),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(79548)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T09:22:54.356337Z | {
"verified": true,
"answer": 13156,
"timestamp": "2026-02-08T09:22:54.357486Z"
} | b2b514 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1662
},
"timestamp": "2026-02-24T11:17:33.349Z",
"answer": 13156
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
d9f1b7 | nt_sum_divisors_mod_v1_677425708_2079 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. For each pair $(x, y)$ in $S$, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute the sum of all positive divisors of $n$, and then find the remainder when this sum is divided by $10181$. De... | 2,418 | 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(129600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10181... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:45:32.247348Z | {
"verified": true,
"answer": 2418,
"timestamp": "2026-02-08T04:45:32.249514Z"
} | 047501 | 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": 1715
},
"timestamp": "2026-02-10T05:36:07.056Z",
"answer": 2418
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
ecca90 | comb_count_derangements_v1_124444284_6018 | Let $N = 32785$. Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 32785$ and $\binom{N}{j}$ is odd.
Compute the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_n": Const(32785),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32785)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T06:59:08.044956Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T06:59:08.046301Z"
} | 4d2b70 | 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": 924
},
"timestamp": "2026-02-24T08:50:57.088Z",
"answer": 14833
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
783b65 | nt_count_intersection_v1_168721529_414 | Let $N$ be the largest integer such that $7^N$ divides $30016!$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $\gcd(n, 15) = 1$. Let $Q$ be the multiplicative order of $2$ modulo $2 \cdot Q' + 3$, where $Q'$ is this count. Find the value of $Q$. | 162 | graphs = [
Graph(
let={
"N": MaxKDivides(target=Factorial(Const(30016)), base=Const(7)),
"a": Const(11),
"b": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("... | NT | null | COUNT | sympy | V1 | [
"V1"
] | dae96f | nt_count_intersection_v1 | null | 6 | 0 | [
"V1"
] | 1 | 0.216 | 2026-02-08T13:02:39.054701Z | {
"verified": true,
"answer": 162,
"timestamp": "2026-02-08T13:02:39.270883Z"
} | 399aa9 | 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": 2566
},
"timestamp": "2026-02-09T04:45:43.912Z",
"answer": 162
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
41fbe9 | comb_binomial_compute_v1_601307018_375 | Let $N = \binom{12}{7}$. Compute $N + \varphi(N + 1) + \tau(N + 1)$. | 1,516 | graphs = [
Graph(
let={
"n": Const(12),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(2)))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(1))))),
... | COMB | NT | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"ONE_PHI_2"
] | a76f7e | comb_binomial_compute_v1 | null | 3 | 0 | [
"ONE_PHI_1",
"ONE_PHI_2"
] | 2 | 0.004 | 2026-03-10T00:54:29.402123Z | {
"verified": true,
"answer": 1516,
"timestamp": "2026-03-10T00:54:29.406328Z"
} | f571dc | CC BY 4.0 | null | null | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
9858b5 | geo_count_lattice_rect_v1_2051736721_457 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 105$ and $0 \le y \le 41$, including the boundaries of the rectangle.
Determine the value of this number. | 4,452 | graphs = [
Graph(
let={
"a": Const(105),
"b": Const(41),
"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 | 0.001 | 2026-02-08T15:26:39.764315Z | {
"verified": true,
"answer": 4452,
"timestamp": "2026-02-08T15:26:39.765565Z"
} | 6fd86b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 226
},
"timestamp": "2026-02-24T20:57:20.522Z",
"answer": 4452
},
{
"id... | 1 | [] | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||||
bda29f | antilemma_k2_v1_1820931509_7 | Define $$
X = \sum_{k=1}^{422} \phi(k) \left\lfloor \frac{422}{k} \right\rfloor,
$$ where $\phi$ denotes Euler's totient function.
Let $C$ be the sum of $\phi(d)$ over all positive divisors $d$ of $2222$.
Compute the remainder when $C - X$ is divided by $65818$. | 44,605 | graphs = [
Graph(
let={
"_n": Const(2222),
"x": Summation(var="k", start=Const(1), end=Const(422), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(422), Var("k"))))),
"_c": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(val... | NT | COMB | COMPUTE | sympy | K3 | [
"K3",
"K2"
] | dd2711 | antilemma_k2_v1 | negation_mod | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T11:16:55.990585Z | {
"verified": true,
"answer": 44605,
"timestamp": "2026-02-08T11:16:55.992506Z"
} | 1e4cb9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 885
},
"timestamp": "2026-02-14T12:07:44.548Z",
"answer": 44605
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
20136d | alg_poly_orbit_hensel_v1_1218484723_223 | Let $N \equiv a^2 + 10 \pmod{2209}$, $M \equiv N^2 + 10 \pmod{2209}$, $R \equiv M^2 + 10 \pmod{2209}$, $S \equiv R^2 + 10 \pmod{2209}$, $T \equiv S^2 + 10 \pmod{2209}$, and $K \equiv T^2 + 10 \pmod{2209}$. Find the number of non-negative integers $a$ with $0 \le a \le 2880535$ such that $K = a$, but $N \ne a$, $M \ne a... | 7,824 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(10)), modulus=Const(2209)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(10)), modulus=Const(2209)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(10)), modulus=Const(2209)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.053 | 2026-02-25T01:54:51.583771Z | {
"verified": true,
"answer": 7824,
"timestamp": "2026-02-25T01:54:51.637001Z"
} | 2f2ae6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T21:57:21.010Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.85,
"mid": 5.71,
"hi": 7.83
} | ||
6b47d2 | nt_count_divisors_in_range_v1_717093673_2967 | Let $n = 7560$, $a = 1$, and $b = 1082$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 58 | graphs = [
Graph(
let={
"n": Const(7560),
"a": Const(1),
"b": Const(1082),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
},
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.091 | 2026-02-08T17:18:24.047609Z | {
"verified": true,
"answer": 58,
"timestamp": "2026-02-08T17:18:24.139009Z"
} | 5df0c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 2018
},
"timestamp": "2026-02-17T23:14:40.363Z",
"answer": 58
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
93e01e | comb_count_surjections_v1_124444284_8013 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Let $k$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2\}$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 24 | graphs = [
Graph(
let={
"_n": Const(8),
"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")), Ref... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COMB1"
] | e44290 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T09:30:12.803040Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T09:30:12.805216Z"
} | c625dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 550
},
"timestamp": "2026-02-24T11:23:54.917Z",
"answer": 24
},
{
"id":... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
18fb18 | geo_count_lattice_rect_v1_2051736721_552 | Compute the number of lattice points in the rectangle $[0, 80] \times [0, 28]$. | 2,349 | graphs = [
Graph(
let={
"a": Const(80),
"b": Const(28),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T15:31:22.640422Z | {
"verified": true,
"answer": 2349,
"timestamp": "2026-02-08T15:31:22.641368Z"
} | 94a495 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 228
},
"timestamp": "2026-02-24T18:03:47.571Z",
"answer": 2349
},
{
"i... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
57df55 | geo_count_lattice_triangle_v1_1218484723_6397 | Let
$$M = \left|111 \cdot 121 + 33 \cdot (0 - 12)\right|,$$
and
$$R = \gcd(111, 12) + \gcd\!\left(\left|\left|\{(a, b) : 1 \le a \le 40,\ 1 \le b \le 40,\ 5b^{2} + 10ab + 5a^{2} = 11520\}\right| - 111\right|,\ \left|121 - 12\right|\right) + \gcd\!\left(\left|0 - 33\right|,\ \left|0 - 121\right|\right).$$
Define
$$S = \... | 6,511 | graphs = [
Graph(
let={
"_n": Const(111),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=121)), Mul(Const(value=33), Sub(left=Const(value=0), right=Const(value=12))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=12))), GCD(a=Abs(arg=S... | GEOM | NT | COUNT | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.006 | 2026-02-25T07:58:14.146490Z | {
"verified": true,
"answer": 6511,
"timestamp": "2026-02-25T07:58:14.152215Z"
} | 637900 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 303,
"completion_tokens": 1690
},
"timestamp": "2026-03-30T01:32:53.843Z",
"answer": 6511
},
{
"i... | 1 | [
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
bd0673 | modular_mod_compute_v1_168721529_1374 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq=54$, $\gcd(p,q)=1$, and $p<q$.
Let $n$ be the smallest positive integer $d$ such that $d\ge m$ and $d$ divides $31603$.
Let $a=-23$. Let $M$ be the smallest value of $x+y$ over all ordered pairs $(x,y)$ of posit... | 21,147 | graphs = [
Graph(
let={
"_c": Const(31603),
"_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=54)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | COMB | COMPUTE | sympy | K2 | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/B3"
] | e30b23 | modular_mod_compute_v1 | bell_mod | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"K2",
"MIN_PRIME_FACTOR"
] | 4 | 0.014 | 2026-02-08T13:39:16.387777Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T13:39:16.402136Z"
} | 731421 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 2873
},
"timestamp": "2026-02-09T16:14:15.958Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
44f545 | nt_euler_phi_compute_v1_1874849503_216 | Let $n_2 = 667$ and define $f = \lambda(n_2)$, where $\lambda(n) = (-1)^{\Omega(n)}$ is the Liouville function and $\Omega(n)$ counts the total number of prime factors of $n$ with multiplicity. Let $h = \sum_{d \mid f} \mu(d)$, where $\mu$ is the Möbius function. Define $n = 32761 \cdot h$. Compute $\phi(n)$, where $\p... | 32,580 | graphs = [
Graph(
let={
"n2": Const(667),
"f": LiouvilleLambda(n=Ref(name='n2')),
"n1": Ref("f"),
"h": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Mul(Const(32761), Ref("h")),
"result": EulerPhi(n=R... | NT | null | COMPUTE | sympy | LIOUVILLE_ONE | [
"LIOUVILLE_ONE",
"MOBIUS_SUM"
] | 6dd3e4 | nt_euler_phi_compute_v1 | null | 4 | 2 | [
"LIOUVILLE_ONE",
"MOBIUS_SUM"
] | 2 | 0.002 | 2026-02-08T12:53:11.635748Z | {
"verified": true,
"answer": 32580,
"timestamp": "2026-02-08T12:53:11.637905Z"
} | d993b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1781
},
"timestamp": "2026-02-09T14:44:07.338Z",
"answer": 32580
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"... | {
"lo": -6.51,
"mid": -0.38,
"hi": 5.12
} | ||
aaeed6 | nt_max_prime_below_v1_1470522791_1174 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Compute the largest prime number $n$ such that $n \leq 70000$ and $n \geq k$. | 69,997 | graphs = [
Graph(
let={
"upper": Const(70000),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.805 | 2026-02-08T13:29:05.085901Z | {
"verified": true,
"answer": 69997,
"timestamp": "2026-02-08T13:29:06.890690Z"
} | 9febfe | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 469
},
"timestamp": "2026-02-16T04:36:13.188Z",
"answer": 69971
},
{
"id": 11... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
548e84 | comb_count_derangements_v1_1419126231_1103 | Let $D_n$ denote the number of derangements of $n$ elements, and let $n = \sum_{k=0}^{2} 2^k$. Find the remainder when $73589 \cdot D_n$ is divided by $77738$. | 3,816 | graphs = [
Graph(
let={
"_n": Const(73589),
"n": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=Const(77738)),
},
... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T10:38:04.445507Z | {
"verified": true,
"answer": 3816,
"timestamp": "2026-02-25T10:38:04.446358Z"
} | 49473f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 2885
},
"timestamp": "2026-03-30T11:26:01.689Z",
"answer": 3816
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
04835b | nt_max_prime_below_v1_1470522791_1573 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $P$. Let $n$ be a prime number satisfying $n \geq k$ and $n \leq 11025$. Determine the value of the largest such prime $n$. | 11,003 | graphs = [
Graph(
let={
"upper": Const(11025),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.266 | 2026-02-08T13:45:00.420932Z | {
"verified": true,
"answer": 11003,
"timestamp": "2026-02-08T13:45:00.686656Z"
} | 83847f | 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": 3009
},
"timestamp": "2026-02-15T20:15:56.863Z",
"answer": 11003
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
97e0b3 | diophantine_fbi2_min_v1_1520064083_4538 | Let $k = 33$ and $U = 43$. Let $S$ be the set of all integers $d$ such that $4 \leq d \leq U$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Let $m$ be the smallest element of $S$. Compute $\sum_{n=1}^{|m|} \phi(n)$, where $\phi$ denotes Euler's totient function. | 42 | graphs = [
Graph(
let={
"k": Const(33),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3))))),
... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.005 | 2026-02-08T06:19:04.996968Z | {
"verified": true,
"answer": 42,
"timestamp": "2026-02-08T06:19:05.002130Z"
} | e765e5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 784
},
"timestamp": "2026-02-19T03:34:49.713Z",
"answer": 48
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
6725ec | comb_factorial_compute_v1_601307018_2906 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $$\left|\left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 30,\ 10a_1^2 + 25b_1^2 - 18a_1b_1 \le 1845 \right\}\right| \cdot a^2 b + 64a^3 + 27b^3 + 108ab^2 = 551368.$$ Let $R = n!$. Find the remainder when $44121R$ is divided b... | 59,293 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(CountOverSe... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/POLY3_COUNT"
] | 1c021d | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.008 | 2026-03-10T03:31:52.546014Z | {
"verified": true,
"answer": 59293,
"timestamp": "2026-03-10T03:31:52.554335Z"
} | cddfac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 20236
},
"timestamp": "2026-03-29T06:56:37.798Z",
"answer": 59293
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
f0d510 | diophantine_fbi2_count_v1_717093673_3367 | Let $k = 360$. Determine the number of integers $d$ such that $3 \leq d \leq 57$, $d$ divides $360$, and $3 \leq \frac{360}{d} \leq 57$. Compute this number. | 12 | graphs = [
Graph(
let={
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(57)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(Ref("k"), Var("d")), Const(57)... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"K2"
] | 6897ab | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.034 | 2026-02-08T17:30:43.758651Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T17:30:43.792572Z"
} | 449542 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 1491
},
"timestamp": "2026-02-18T03:55:23.744Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0100d5 | modular_mod_compute_v1_2051736721_2735 | Find the remainder when $-66049$ is divided by $16290$. | 15,401 | graphs = [
Graph(
let={
"a": Const(-66049),
"m": Const(16290),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_mod_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.007 | 2026-02-08T16:52:19.284768Z | {
"verified": true,
"answer": 15401,
"timestamp": "2026-02-08T16:52:19.291806Z"
} | 649a20 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 569
},
"timestamp": "2026-02-16T08:05:52.719Z",
"answer": 16241
},
{
"id": 11,... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
cc3768 | comb_sum_binomial_row_v1_1918700295_414 | Let $A$ be the set of positive integers $n$ such that $1 \leq n \leq 38868$ and $3$ divides the $n$-th Fibonacci number. Let $m$ be the number of elements in $A$. Let $B$ be the set of positive integers $n$ such that $1 \leq n \leq m$, $3$ divides $n$, and $\gcd(n, 10) = 1$. Let $c$ be the number of elements in $B$. Co... | 43,278 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(38868)), Divides(divisor=Const(3), dividend=Fibonacci(arg=Var(name='n')))))),
"n": Const(16),
"result": Pow(Co... | NT | null | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/C5"
] | 1997c2 | comb_sum_binomial_row_v1 | negation_mod | 7 | 0 | [
"C5",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.003 | 2026-02-08T03:13:05.904222Z | {
"verified": true,
"answer": 43278,
"timestamp": "2026-02-08T03:13:05.906767Z"
} | e6e6d4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1875
},
"timestamp": "2026-02-10T13:25:23.618Z",
"answer": 43278
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
7a475b | nt_count_primes_v1_971394319_1864 | Let $m$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 6$, and $\gcd(p, q) = 1$. Let $r$ be the number of prime numbers $n$ such that $m \leq n \leq 72900$. Compute the remainder when $36031 \cdot r$ is divided by $90522$. | 22,290 | graphs = [
Graph(
let={
"_n": Const(90522),
"upper": Const(72900),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.92 | 2026-02-08T13:58:17.911050Z | {
"verified": true,
"answer": 22290,
"timestamp": "2026-02-08T13:58:19.831459Z"
} | de0128 | 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": 2838
},
"timestamp": "2026-02-15T22:37:49.230Z",
"answer": 22290
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
01616f | nt_count_digit_sum_v1_1116507919_130 | Let $S$ be the set of all integers $t$ such that $5 \leq t \leq 23$ and there exist positive integers $a \leq 3$ and $b \leq 7$ satisfying $t = 3a + 2b$. Let $T$ be the number of integers $n$ with $1 \leq n \leq 99999$ such that the sum of the decimal digits of $n$ equals $|S|$. Let $c = \sum_{k=1}^{4} k$. Compute the ... | 46,097 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)),... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM",
"ONE_PHI_2"
] | dd74b4 | nt_count_digit_sum_v1 | negation_mod | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_2",
"SUM_ARITHMETIC"
] | 3 | 3.261 | 2026-02-08T02:26:26.606166Z | {
"verified": true,
"answer": 46097,
"timestamp": "2026-02-08T02:26:29.867625Z"
} | 6ebc2a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 3053
},
"timestamp": "2026-02-08T19:06:24.305Z",
"answer": 46097
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
3d464c | nt_count_coprime_v1_1918700295_4657 | Let $n = 39$ and let the upper bound be $87025$. Let $k$ be the largest positive integer $d$ such that $1 \leq d \leq 39$ and $d$ divides $1833$. Define $r$ to be the number of positive integers $n$ with $1 \leq n \leq 87025$ such that $\gcd(n, k) = 1$. Compute the Bell number $B_m$, where $m = |r| \bmod 11$. | 203 | graphs = [
Graph(
let={
"_n": Const(39),
"upper": Const(87025),
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1833))))),
"result": CountOverSet(set=Solut... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MAX_DIVISOR"
] | 51757e | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_DIVISOR",
"MIN_PRIME_FACTOR"
] | 2 | 12.449 | 2026-02-08T09:30:02.804849Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T09:30:15.253873Z"
} | 7a82d9 | 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": 1410
},
"timestamp": "2026-02-14T04:35:44.132Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1d4daf | geo_visible_lattice_v1_1918700295_3075 | For a positive integer $n$, define $f(n)$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $29273 \cdot f(81)$ is divided by $58167$. | 38,303 | graphs = [
Graph(
let={
"n": Const(81),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(29273), Ref("result")), modulus=Const(58167)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.203 | 2026-02-08T08:22:32.646840Z | {
"verified": true,
"answer": 38303,
"timestamp": "2026-02-08T08:22:32.849610Z"
} | f7fb85 | 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": 7190
},
"timestamp": "2026-02-24T09:26:22.259Z",
"answer": 38303
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
003944 | nt_sum_divisors_mod_v1_784195855_9800 | Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1587600$. Let $n$ be the minimum value of $x + y$ over all such pairs.
Let $\sigma$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11171$. | 9,360 | 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(1587600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1117... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:05:45.114453Z | {
"verified": true,
"answer": 9360,
"timestamp": "2026-02-08T17:05:45.116663Z"
} | b6e854 | 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": 2493
},
"timestamp": "2026-02-17T21:16:22.217Z",
"answer": 9360
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5ce823 | diophantine_product_count_v1_655260480_5846 | Let $k = 120$ and $n = 2116$. Let $\text{upper}$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 2116$. Compute the number of positive integers $x_1$ such that $1 \leq x_1 \leq \text{upper}$, $x_1$ divides $120$, and $\frac{120}{x_1} \leq \text{upper}$. | 14 | graphs = [
Graph(
let={
"_n": Const(2116),
"k": Const(120),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T18:40:51.051247Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T18:40:51.057668Z"
} | ce5ce9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 2750
},
"timestamp": "2026-02-18T18:33:26.523Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
26b625 | nt_num_divisors_compute_v1_809748730_803 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x,y)$ such that $x + y = 86$. Compute the number of positive divisors of $n$. | 3 | graphs = [
Graph(
let={
"_n": Const(86),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T11:46:07.412881Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T11:46:07.415372Z"
} | 83f334 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 503
},
"timestamp": "2026-02-16T03:22:06.376Z",
"answer": 3
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
75e5b2 | antilemma_cartesian_v1_865884756_3911 | Let $A$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 38$ and $1 \leq j \leq 38$ and $i + j = 38$. Let $B$ be the set of all ordered pairs $(i, j)$ such that $1 \leq i \leq 12$ and $1 \leq j \leq 16$. Compute the remainder when $|A| - |B|$ is divided by $91312$. | 91,157 | graphs = [
Graph(
let={
"_n": Const(38),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(16)))),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")])... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | f8dfda | antilemma_cartesian_v1 | negation_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.019 | 2026-02-08T17:39:48.010858Z | {
"verified": true,
"answer": 91157,
"timestamp": "2026-02-08T17:39:48.029951Z"
} | c7c7b6 | 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": 594
},
"timestamp": "2026-02-18T05:34:50.360Z",
"answer": 91157
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
ae695f | nt_count_gcd_equals_v1_48377204_281 | Let $d$ be the largest prime number not exceeding $500$. Determine the value of $d$. Then, compute the number of positive integers $n_1$ not exceeding $31684$ such that $\gcd(n_1, 499) = d$. | 63 | graphs = [
Graph(
let={
"_n": Const(500),
"upper": Const(31684),
"k": Const(499),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=Solut... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.451 | 2026-02-08T15:19:57.153484Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T15:19:59.604791Z"
} | c93d07 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 405
},
"timestamp": "2026-02-16T05:22:49.483Z",
"answer": 63
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
c93976 | comb_count_derangements_v1_1431428450_158 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$.
Let $n$ be the smallest positive divisor of $11011$ that is at least $m$.
Let $r = !n$, where $!n$ denotes the number of derangements ... | 336 | graphs = [
Graph(
let={
"_n": Const(11011),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), 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=... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T13:16:57.886504Z | {
"verified": true,
"answer": 336,
"timestamp": "2026-02-08T13:16:57.889583Z"
} | 72b8fc | 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": 2840
},
"timestamp": "2026-02-15T12:03:43.687Z",
"answer": 336
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_la... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5c7af6 | comb_binomial_compute_v1_601307018_1663 | For each integer $a$ with $0 \le a \le 5040$, define the sequence $M = (a^3 + 5a) \bmod 5041$, $R = (M^3 + 5M) \bmod 5041$, $S = (R^3 + 5R) \bmod 5041$, $T = (S^3 + 5S) \bmod 5041$, $K = (T^3 + 5T) \bmod 5041$, $L = (K^3 + 5K) \bmod 5041$. Let $n$ be the number of values of $a$ for which $L = a$ but $a$ does not appear... | 924 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(5040)), Eq(Ref("_po_p6"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a")), Neq(Ref("... | COMB | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_binomial_compute_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.004 | 2026-03-10T02:24:50.166821Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-03-10T02:24:50.171168Z"
} | af91a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 17205
},
"timestamp": "2026-03-29T03:04:12.708Z",
"answer": 924
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
45e1d6 | diophantine_fbi2_min_v1_48377204_1300 | Let $\mathcal{P}$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 18$. For each such pair, compute the product $x \cdot y$. Let $s$ be the maximum value among all such products. Let $k = \sum_{d \mid s} \phi(d)$, where $\phi$ is Euler's totient function. Let $\_m = 2$ and $\_n = 4$. Fin... | 5 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"k": SumOverDivisors(n=MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Sum(Var(name='... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"B1/K3"
] | 759f54 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B1",
"K3",
"SUM_ARITHMETIC"
] | 3 | 0.09 | 2026-02-08T16:01:08.970085Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T16:01:09.060340Z"
} | f3ba4c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 701
},
"timestamp": "2026-02-16T19:47:36.043Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cb20f7 | modular_count_residue_v1_458359167_5668 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Let $r$ be the number of integers $t$ with $14 \leq t \leq 48$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 7$, $1 \leq b \leq 2$, and $t = 4a + 10b$. Let $N$ be the number of positi... | 76,850 | graphs = [
Graph(
let={
"_n": Const(144),
"upper": Const(30493),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | modular_count_residue_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 3.892 | 2026-02-08T12:38:48.192074Z | {
"verified": true,
"answer": 76850,
"timestamp": "2026-02-08T12:38:52.083731Z"
} | 1fbfe2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 2062
},
"timestamp": "2026-02-15T03:12:54.268Z",
"answer": 76850
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
072fd7_l | comb_bell_compute_v1_397696148_2059 | Let $v = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$ and $h = \sum_{k=0}^{6} (-1)^k \binom{6}{k}$. Define $n = 9 + h$. Let $B_n$ denote the $n$th Bell number, which is the number of partitions of a set of $n$ elements. Compute the remainder when $1286 \cdot B_n$ is divided by $74313 + v$. | 1,286 | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_bell_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T12:55:55.991764Z | {
"verified": false,
"answer": 70797,
"timestamp": "2026-02-08T12:55:55.992754Z"
} | 9d72cf | 072fd7 | 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": 221,
"completion_tokens": 1366
},
"timestamp": "2026-02-24T16:42:51.488Z",
"answer": 70797
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | |
a29f75 | sequence_count_fib_divisible_v1_865884756_6204 | Let $u$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 18$, $1 \leq j \leq 45$, and $\gcd(i, j) = 1$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $12$ divides the $n$-th Fibonacci number. Let $c = 21099$ and let $t$ be the number of elements in ... | 4,321 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(45))))),
... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.028 | 2026-02-08T19:03:36.981958Z | {
"verified": true,
"answer": 4321,
"timestamp": "2026-02-08T19:03:37.009651Z"
} | 0d0faf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 4676
},
"timestamp": "2026-02-18T21:14:15.626Z",
"answer": 4321
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bc209a | antilemma_k3_v1_168721529_1105 | Let $n = 70889$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 70,889 | graphs = [
Graph(
let={
"_n": Const(70889),
"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 | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:27:58.981773Z | {
"verified": true,
"answer": 70889,
"timestamp": "2026-02-08T13:27:58.982912Z"
} | ce9a86 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 598
},
"timestamp": "2026-02-09T13:44:46.475Z",
"answer": 70889
},
{
"i... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -2.15,
"hi": 1.85
} | ||
dc7e90 | geo_count_lattice_rect_v1_601307018_5240 | Let $a = \sum_{k=1}^{15} \varphi(k) \left\lfloor \frac{15}{k} \right\rfloor$. Find the number $M$ of lattice points $(x,y)$ with $0 \le x \le a$ and $0 \le y \le 163$, then compute the remainder when $44121M$ is divided by $64252$. | 39,372 | graphs = [
Graph(
let={
"_n": Const(15),
"a": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"b": Const(163),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": M... | GEOM | GEOM | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_count_lattice_rect_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.004 | 2026-03-10T05:55:09.215160Z | {
"verified": true,
"answer": 39372,
"timestamp": "2026-03-10T05:55:09.219311Z"
} | f46021 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1671
},
"timestamp": "2026-04-19T01:36:04.865Z",
"answer": 39372
},
{
... | 1 | [
{
"lemma": "K2",
"status": "ok"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
477435 | antilemma_product_of_sums_v1_458359167_191 | Let $n=41327$. Consider all ordered pairs $(k,j)$ of integers with $1\le k\le5$ and $1\le j\le2$. Let $A$ be the sum of all values of $k$ over these pairs.
Let $d_0$ be the minimum element of the set of all integers $d\ge2$ such that $d$ divides $n$. Let
$$T=\sum_{d\mid \gcd(7,d_0)} \mu(d),$$
where $\mu$ is the functi... | 30,240 | graphs = [
Graph(
let={
"_n": Const(41327),
"x": Mul(SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(2)))), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME/SUM_FACTOR_CARTESIAN",
"PRODUCT_OF_SUMS"
] | 7f69ce | antilemma_product_of_sums_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME",
"PRODUCT_OF_SUMS",
"SUM_FACTOR_CARTESIAN"
] | 4 | 0.002 | 2026-02-08T03:03:23.325652Z | {
"verified": true,
"answer": 30240,
"timestamp": "2026-02-08T03:03:23.327891Z"
} | 180c2a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 407
},
"timestamp": "2026-02-17T17:59:25.077Z",
"answer": 15120
}
] | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "PRODUCT_OF_SUMS",
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
8f29f9 | comb_count_surjections_v1_48377204_2235 | Let $k$ be the number of integers $t$ with $15 \leq t \leq 36$ that can be expressed as $t = 9a + 6b$ for positive integers $a \leq 2$ and $b \leq 3$. Compute $k! \cdot S(7, k)$, where $S(7, k)$ is the Stirling number of the second kind. | 15,120 | graphs = [
Graph(
let={
"n": Const(7),
"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=2)), Geq(left=Var(nam... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:40:57.042561Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T16:40:57.045436Z"
} | 4ff76c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 702
},
"timestamp": "2026-02-17T09:19:00.825Z",
"answer": 15120
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
f5e7b3 | comb_sum_binomial_row_v1_458359167_3967 | Let $a$ be the number of unordered pairs of positive integers $(p, q)$ such that $p < q$, $pq = 72$, and $\gcd(p, q) = 1$. Let $b$ be the number of unordered pairs of positive integers $(p, q)$ such that $p < q$, $pq = 8385300$, and $\gcd(p, q) = 1$. Compute $a^b$. | 65,536 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T11:27:32.940179Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T11:27:32.942962Z"
} | 04ba56 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1638
},
"timestamp": "2026-02-14T14:24:48.227Z",
"answer": 65536
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
639089 | comb_count_partitions_v1_601307018_2538 | Let $n = \sum_{k=\binom{13}{13} - 1}^{2} 6^{k}$. Compute $p(n)$, the number of integer partitions of $n$. | 63,261 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Sub(Binom(n=Const(13), k=Const(13)), Const(1)), end=Const(2), expr=Pow(Ref("_n"), Var("k"))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_partitions_v1 | null | 3 | 0 | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-03-10T03:14:03.483259Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-03-10T03:14:03.485123Z"
} | 621926 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1176
},
"timestamp": "2026-03-29T05:39:12.829Z",
"answer": 63261
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
b4e8de | geo_count_lattice_rect_v1_2051736721_5790 | Compute the number of lattice points in the rectangle $[0, 225] \times [0, 340]$, including the boundary. | 77,066 | graphs = [
Graph(
let={
"a": Const(225),
"b": Const(340),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T18:47:57.746712Z | {
"verified": true,
"answer": 77066,
"timestamp": "2026-02-08T18:47:57.749146Z"
} | 41e992 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 76,
"completion_tokens": 534
},
"timestamp": "2026-02-18T19:37:30.624Z",
"answer": 77066
},
{
... | 1 | [] | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||||
424ad6 | nt_min_coprime_above_v1_2051736721_2192 | Let $A$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 62$, $1 \le j \le 143$, and $\gcd(i, j) = 1$. Let $N$ be the number of elements in $A$.
Let $B$ be the set of all integers $n$ such that $5000 < n \le N$ and $\gcd(n, 463) = 1$. Determine the value of the smallest element in $... | 5,001 | graphs = [
Graph(
let={
"start": Const(5000),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(62)), right=IntegerRange(start=Const... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.073 | 2026-02-08T16:31:54.661387Z | {
"verified": true,
"answer": 5001,
"timestamp": "2026-02-08T16:31:54.734237Z"
} | 5b62ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3407
},
"timestamp": "2026-02-17T05:24:58.137Z",
"answer": 5001
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2a394f | nt_max_prime_below_v1_1915831931_761 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $m \leq n \leq 78961$. | 78,941 | graphs = [
Graph(
let={
"upper": Const(78961),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.018 | 2026-02-08T15:39:48.769389Z | {
"verified": true,
"answer": 78941,
"timestamp": "2026-02-08T15:39:50.787620Z"
} | 433f39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 5695
},
"timestamp": "2026-02-16T11:28:24.086Z",
"answer": 78941
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8281d2 | modular_count_residue_v1_2051736721_4170 | Let $r$ be the largest prime number at most $22$. Determine the number of positive integers $n_1$ at most $56169$ such that $n_1$ leaves a remainder of $r$ when divided by $24$. | 2,340 | graphs = [
Graph(
let={
"upper": Const(56169),
"m": Const(24),
"r": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(22)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.854 | 2026-02-08T17:47:44.123525Z | {
"verified": true,
"answer": 2340,
"timestamp": "2026-02-08T17:47:45.977300Z"
} | e43c58 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 748
},
"timestamp": "2026-02-18T07:59:11.874Z",
"answer": 2340
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9a8217 | sequence_fibonacci_compute_v1_124444284_4386 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 121$. Compute the remainder when $44121 \cdot F_n$ is divided by $79705$, where $F_n$ denotes the $n$th Fibonacci number.
Find the value of this remainder. | 78,916 | graphs = [
Graph(
let={
"_n": Const(121),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T05:58:45.980694Z | {
"verified": true,
"answer": 78916,
"timestamp": "2026-02-08T05:58:45.982294Z"
} | 2915cc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1189
},
"timestamp": "2026-02-12T18:13:45.643Z",
"answer": 78916
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
00440c | algebra_quadratic_discriminant_v1_1439011603_2873 | Let $p$ range over the positive integers. Define $\alpha = 1$ if there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$; otherwise, $\alpha = 0$. Let $\beta$ be the number of such $p$ for which this condition holds. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers su... | 12,769 | graphs = [
Graph(
let={
"a": Const(-4),
"b": Const(2),
"c": Const(-1),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.004 | 2026-02-08T17:03:08.387705Z | {
"verified": true,
"answer": 12769,
"timestamp": "2026-02-08T17:03:08.391778Z"
} | e22940 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 1555
},
"timestamp": "2026-02-17T17:48:14.734Z",
"answer": 12769
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
035aab | antilemma_k2_v1_2051736721_6178 | Compute the value of
$$
\sum_{k=1}^{186} \phi(k) \left\lfloor \frac{186}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 17,391 | graphs = [
Graph(
let={
"_n": Const(186),
"x": Summation(var="k", start=Const(1), end=Const(186), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T18:58:33.278928Z | {
"verified": true,
"answer": 17391,
"timestamp": "2026-02-08T18:58:33.279531Z"
} | 9be41f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 701
},
"timestamp": "2026-02-18T21:01:47.095Z",
"answer": 17391
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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