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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
b550d7 | nt_sum_divisors_compute_v1_1520064083_3000 | Compute the sum of all positive divisors of $36100$. | 82,677 | graphs = [
Graph(
let={
"n": Const(36100),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K14 | [
"K14/EULER_TOTIENT_SUM",
"OMEGA_ZERO"
] | 902176 | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"EULER_TOTIENT_SUM",
"K14",
"OMEGA_ZERO"
] | 3 | 0.003 | 2026-02-08T05:24:21.736442Z | {
"verified": true,
"answer": 82677,
"timestamp": "2026-02-08T05:24:21.739844Z"
} | 8f96c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 59,
"completion_tokens": 803
},
"timestamp": "2026-02-12T08:36:49.041Z",
"answer": 82677
},
{
... | 1 | [
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
03d9ee | geo_count_lattice_rect_v1_1978505735_4436 | Let $a = 29$ and $b = 92$. Define $L$ as the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $c = 78408$. Compute the remainder when $c \cdot L$ is divided by $92623$. | 75,417 | graphs = [
Graph(
let={
"a": Const(29),
"b": Const(92),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(78408),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(92623)),
},
goal=Ref("Q"),
)
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T18:14:42.117973Z | {
"verified": true,
"answer": 75417,
"timestamp": "2026-02-08T18:14:42.119205Z"
} | 18435f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1274
},
"timestamp": "2026-02-18T15:37:57.027Z",
"answer": 75417
},
... | 1 | [] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||||
2daab0 | diophantine_fbi2_count_v1_153355830_1600 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 3600$. Determine the number of positive integers $d$ such that $6 \leq d \leq 71$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 70$. | 7 | 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(3600)))), expr=Sum(Var("x"), Var("y")))),
"result": CountOve... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T06:31:36.596376Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T06:31:36.605945Z"
} | 08d078 | 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": 1237
},
"timestamp": "2026-02-13T00:54:17.947Z",
"answer": 7
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
27eb87 | modular_min_modexp_v1_1742523217_266 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $b = 4$ and $m = 127$. Determine the value of the smallest positive integer $x \leq 7$ such that $a^x \equiv b \pmod{m}$. Let $Q$ be the remainder when $55387$ times this ... | 4,036 | graphs = [
Graph(
let={
"a": 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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), L... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_min_modexp_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.006 | 2026-02-08T02:57:28.313691Z | {
"verified": true,
"answer": 4036,
"timestamp": "2026-02-08T02:57:28.319883Z"
} | 94cd3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 773
},
"timestamp": "2026-02-09T15:40:21.393Z",
"answer": 4036
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -3.88,
"mid": -1.29,
"hi": 0.91
} | ||
4098ff | nt_num_divisors_compute_v1_1520064083_5168 | Let $n = 3600$ and $m = 11$. Let $d(n)$ denote the number of positive divisors of $n$. Let $p$ be the largest prime number less than or equal to $m$. Compute the Bell number of the remainder when $|d(n)|$ is divided by $p$. | 1 | graphs = [
Graph(
let={
"_n": Const(11),
"n": Const(3600),
"result": NumDivisors(n=Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), Is... | NT | COMB | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_num_divisors_compute_v1 | bell_mod | 4 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.033 | 2026-02-08T06:40:03.269130Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T06:40:03.302037Z"
} | 58fa3a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 509
},
"timestamp": "2026-02-13T03:00:58.505Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": ... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
ee59a0 | antilemma_sum_primes_v1_1125832087_1102 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 169$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum element of $T$. Let $X$ be the set of all prime numbers $n$ such that $2 \leq n \leq m$. Compute the sum of all elements in $X$. | 100 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | COMPUTE | sympy | B3 | [
"B3/SUM_PRIMES",
"SUM_PRIMES"
] | c1b432 | antilemma_sum_primes_v1 | null | 3 | 0 | [
"B3",
"SUM_PRIMES"
] | 2 | 0.012 | 2026-02-08T03:31:14.909842Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T03:31:14.921574Z"
} | fca892 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 434
},
"timestamp": "2026-02-18T02:30:51.293Z",
"answer": 100
}
] | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
"lemma": "V5... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
cc2372 | comb_count_partitions_v1_1978505735_8424 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 97$ and $\gcd(n_1, 14) = 1$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $44121 \cdot p(n)$ is divided by $70780$. | 16,174 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(97)), Eq(GCD(a=Var("n1"), b=Const(14)), Const(1))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(va... | NT | COMB | COUNT | sympy | C4 | [
"C4"
] | 08d162 | comb_count_partitions_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-08T20:49:29.409282Z | {
"verified": true,
"answer": 16174,
"timestamp": "2026-02-08T20:49:29.410256Z"
} | d08a3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1490
},
"timestamp": "2026-02-19T01:13:04.673Z",
"answer": 16174
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ba88d | algebra_poly_eval_v1_124444284_10384 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 5$. Compute the value of $a \cdot 11^2 - 5 \cdot 11 + 1$. | 551 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(11),
"result": Sum(Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))), Pow(Ref("n"), Const(2))), Mul(Const(-5), Ref("n")), Const(1)),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:02:26.021645Z | {
"verified": true,
"answer": 551,
"timestamp": "2026-02-08T13:02:26.023936Z"
} | 12e85f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 170
},
"timestamp": "2026-02-16T04:24:17.897Z",
"answer": 549
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
531c64 | nt_sum_divisors_mod_v1_1125832087_266 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 18$ and $1 \leq j \leq 20$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by $10453$. | 1,170 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(20)))),
"M": Const(10453),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T02:59:35.320298Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T02:59:35.323786Z"
} | 1fa92c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2218
},
"timestamp": "2026-02-10T12:23:34.988Z",
"answer": 127
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
10c14d | diophantine_fbi2_min_v1_1125832087_1819 | Define $k$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy$ equals the number of nonnegative integers $j \leq 288$ for which $\binom{288}{j}$ is odd. Let $d$ be an integer satisfying $6 \leq d \leq 58$ such that $d$ divides $k$ and $\frac{k}{d} \geq 2$. Determine th... | 6 | graphs = [
Graph(
let={
"_n": Const(2),
"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")), SumOverSet(set=SolutionsSet(var=Var("j"), conditio... | NT | null | EXTREMUM | sympy | V8 | [
"V8/B3"
] | b4fc86 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.011 | 2026-02-08T03:58:00.475301Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T03:58:00.486327Z"
} | 2bd738 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 3620
},
"timestamp": "2026-02-10T14:52:35.216Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
f8197f | v7_endings_v1_124444284_854 | Let $k$ be a nonnegative integer such that $0 \le k \le 2837$ and the exponent of the highest power of 3 that divides $\binom{2837}{k}$ is exactly 1. Let $r$ be the number of such integers $k$. Compute the remainder when $6490 \cdot r$ is divided by 76313.
Find the value of $x$. | 54,610 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(2837)), Eq(MaxKDivides(target=Binom(n=Const(2837), k=Var("k")), base=Const(3)), Const(1))))),
"_scale_k": Const(6490),
"_scaled"... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 6 | null | [
"V7"
] | 1 | 0.003 | 2026-02-08T03:32:59.469507Z | {
"verified": true,
"answer": 54610,
"timestamp": "2026-02-08T03:32:59.472018Z"
} | 2e872d | 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": 6818
},
"timestamp": "2026-02-09T23:02:18.476Z",
"answer": 54610
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
ab1cde | nt_count_divisible_and_v1_1742523217_446 | Let $d_1$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Let $d_2 = 12$. Determine the number of positive integers $n$ such that $1 \le n \le 168720$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 2,812 | graphs = [
Graph(
let={
"_n": Const(25),
"upper": Const(168720),
"d1": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n"))))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 5 | 0 | [
"B3"
] | 1 | 8.225 | 2026-02-08T03:03:11.450717Z | {
"verified": true,
"answer": 2812,
"timestamp": "2026-02-08T03:03:19.675234Z"
} | 784fd0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 540
},
"timestamp": "2026-02-09T18:03:15.093Z",
"answer": 2812
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
7c326a | nt_count_divisible_v1_677425708_4209 | Let $\phi(n)$ denote Euler's totient function. Compute the sum
$$
\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor.
$$
Let this sum be $d$. Determine the number of positive integers $n$ such that $1 \leq n \leq 81225$ and $n$ is divisible by $d$. Compute this number. | 27,075 | graphs = [
Graph(
let={
"upper": Const(81225),
"divisor": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_v1 | null | 3 | 0 | [
"K2"
] | 1 | 6.577 | 2026-02-08T06:29:32.632516Z | {
"verified": true,
"answer": 27075,
"timestamp": "2026-02-08T06:29:39.209863Z"
} | 4d4eb2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 486
},
"timestamp": "2026-02-13T00:32:18.531Z",
"answer": 27075
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
4a398c | antilemma_k3_v1_1915831931_1859 | Let $n = 31590$. Compute the remainder when $94087$ times the sum of $\phi(d)$ over all positive divisors $d$ of $n$ is divided by $73428$, where $\phi(d)$ denotes Euler's totient function. | 63,174 | graphs = [
Graph(
let={
"_n": Const(31590),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(94087), Ref("x")), modulus=Const(73428)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:29:19.499924Z | {
"verified": true,
"answer": 63174,
"timestamp": "2026-02-08T16:29:19.500684Z"
} | 5a33ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 3781
},
"timestamp": "2026-02-17T04:50:15.274Z",
"answer": 63174
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
411bb3 | comb_catalan_compute_v1_1918700295_1599 | Let $a$ and $b$ be integers such that $1 \leq a \leq 4$ and $1 \leq b \leq 3$. Let $t$ be an integer satisfying $7 \leq t \leq 24$ and $t = 3a + 4b$. Define $n_2$ to be the number of such integers $t$ that can be expressed in this form. Let $$f = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.$$ Let $a = 3$, $b = 5 + f$, and $... | 228 | graphs = [
Graph(
let={
"_n": Const(5),
"n2": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(n... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_catalan_compute_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T05:54:28.321952Z | {
"verified": true,
"answer": 228,
"timestamp": "2026-02-08T05:54:28.325076Z"
} | 60d42c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 342,
"completion_tokens": 6913
},
"timestamp": "2026-02-24T04:44:01.180Z",
"answer": 228
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
86f39c | comb_count_permutations_fixed_v1_1125832087_701 | Let $n = \sum_{k=1}^{3} k$. Compute $\binom{n}{1} \cdot !(n-1)$, where $!k$ denotes the number of derangements of $k$ elements. | 264 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.003 | 2026-02-08T03:13:47.723816Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T03:13:47.727054Z"
} | f37d43 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 471
},
"timestamp": "2026-02-10T13:31:56.383Z",
"answer": 264
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
235785 | comb_count_derangements_v1_1439011603_2034 | Let $t = \sum_{k=0}^{5} (-1)^k \binom{5}{k}$ and $s = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$. Let $n = 8 + t + s$. Compute the number of derangements of $n$ elements, denoted $!n$. | 14,833 | graphs = [
Graph(
let={
"n2": Const(5),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(10),
"s": Summation(var="k1", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1),... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T16:28:23.827892Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T16:28:23.830019Z"
} | 8b43cc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1043
},
"timestamp": "2026-02-24T21:07:02.875Z",
"answer": 14833
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
d157ec | comb_count_partitions_v1_168721529_1252 | Let $n = 41$ and let $p(n)$ denote the number of integer partitions of $n$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 223729$. Define $c$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $Q$ be the sum of $d_i \cdot (i+1)^2$ over all digits $d_i$ of $p(n)$,... | 1,190 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(41),
"result": Partition(arg=Ref(name='n')),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 8e300c | comb_count_partitions_v1 | digits_weighted_mod | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:33:17.704052Z | {
"verified": true,
"answer": 1190,
"timestamp": "2026-02-08T13:33:17.707342Z"
} | 5d7308 | 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": 1629
},
"timestamp": "2026-02-09T15:01:48.619Z",
"answer": 1190
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||
ab01aa | geo_visible_lattice_v1_349078426_1366 | Let $n = 77$. Define a visible lattice point as a point $(x, y)$ with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points. Compute the remainder when $38599 \cdot R$ is divided by $87873$. | 480 | graphs = [
Graph(
let={
"n": Const(77),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(38599), Ref("result")), modulus=Const(87873)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 1.134 | 2026-02-08T13:34:18.005653Z | {
"verified": true,
"answer": 480,
"timestamp": "2026-02-08T13:34:19.139689Z"
} | 670353 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T18:44:43.032Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
37254b | antilemma_k2_v1_2051736721_735 | Let $x$ be the sum
$$
\sum_{k=1}^{369} \phi(k) \left\lfloor \frac{369}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $c = 30976$. Compute the value of
$$
\sum_{i=0}^{d-1} \left( \text{the } i\text{-th digit of } |x| \right) \cdot (i+1)^2 + c,
$$
where $d$ is the number of decimal digits in ... | 31,301 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(369), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(369), Var("k"))))),
"_c": Const(30976),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const... | NT | COMB | COMPUTE | sympy | K13 | [
"IDENTITY_POW_ZERO",
"K2"
] | fce51d | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_POW_ZERO",
"K13",
"K2"
] | 3 | 0.009 | 2026-02-08T15:39:03.907327Z | {
"verified": true,
"answer": 31301,
"timestamp": "2026-02-08T15:39:03.916449Z"
} | 48ed40 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1020
},
"timestamp": "2026-02-16T10:06:29.242Z",
"answer": 31301
},
... | 1 | [
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cbd7d2 | modular_inverse_v1_1742523217_271 | Let $m = 1109$ and let $a$ be the largest prime number not exceeding $512$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 1108$ and $$ ax \equiv 1 \pmod{m}. $$ Let $c$ be the number of integers $t$ with $10 \leq t \leq 1412$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq... | 74,039 | graphs = [
Graph(
let={
"_m": Const(92609),
"_n": Const(512),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"m": Const(1109),
"upper": Const(1108),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | a71ada | modular_inverse_v1 | affine_mod | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.047 | 2026-02-08T02:57:28.404362Z | {
"verified": true,
"answer": 74039,
"timestamp": "2026-02-08T02:57:28.451346Z"
} | f1d04f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T19:34:17.466Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": 4.56,
"mid": 6.51,
"hi": 9.5
} | ||
bd47c2 | comb_bell_compute_v1_1742523217_2590 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $n$ be the maximum value of $xy$ over all such pairs. Let $B_n$ be the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $67828 \cdot B_n$ is divided by $73911$. | 41,850 | graphs = [
Graph(
let={
"_n": Const(73911),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T04:51:08.143164Z | {
"verified": true,
"answer": 41850,
"timestamp": "2026-02-08T04:51:08.144671Z"
} | 13f3e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1614
},
"timestamp": "2026-02-24T02:09:26.441Z",
"answer": 41850
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
38a565_n | alg_sum_ap_v1_1218484723_5619 | A hiker walks a path split into 131 segments. On segment $k$ (starting at $k=0$), they walk $2k + 30$ meters. After completing the hike, they want to divide the total distance by the smallest possible perimeter of a rectangular plot with area $5707321$ square meters and integer side lengths. What is the remainder of th... | 1,848 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_ap_v1 | null | 3 | null | [
"B3"
] | 1 | 0.023 | 2026-02-25T07:08:09.055583Z | null | 3a7b91 | 38a565 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 7448
},
"timestamp": "2026-03-30T23:50:23.326Z",
"answer": 1848
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
829ba8 | nt_sum_divisors_mod_v1_1520064083_2955 | Let $t = \lambda(361)$, where $\lambda$ denotes the Liouville function. Let $f = \sum_{d \mid 1}$ $\mu(d)$, where $\mu$ is the M\"obius function. Let $n = 120 \cdot t \cdot f$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by 11369. | 360 | graphs = [
Graph(
let={
"n2": Const(361),
"t": LiouvilleLambda(n=Ref(name='n2')),
"n1": Const(1),
"f": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Mul(Const(120), Ref("t"), Ref("f")),
"M": Const(113... | NT | null | COMPUTE | sympy | LIOUVILLE_ONE | [
"LIOUVILLE_ONE",
"MOBIUS_SUM"
] | 6dd3e4 | nt_sum_divisors_mod_v1 | null | 4 | 2 | [
"LIOUVILLE_ONE",
"MOBIUS_SUM"
] | 2 | 0.001 | 2026-02-08T05:21:22.631984Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T05:21:22.633062Z"
} | 88832d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 713
},
"timestamp": "2026-02-18T15:59:14.955Z",
"answer": 360
}
] | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
812dd4 | nt_num_divisors_compute_v1_1520064083_5615 | Let $n = 12100$. Define $r$ to be the number of positive divisors of $n$. Let $p_{\text{max}}$ be the largest prime number $p$ such that $2 \leq p \leq 5005$. Compute the remainder when $r \bmod 293 + p_{\text{max}} \cdot (r \bmod 337)$ is divided by $83055$. | 52,053 | graphs = [
Graph(
let={
"_n": Const(337),
"n": Const(12100),
"result": NumDivisors(n=Ref("n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5005)), IsPrime(Var("n"))))),
"Q": Mod(value=... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_num_divisors_compute_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T07:27:30.873715Z | {
"verified": true,
"answer": 52053,
"timestamp": "2026-02-08T07:27:30.877278Z"
} | 64a280 | 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": 1340
},
"timestamp": "2026-02-13T10:46:40.541Z",
"answer": 52053
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
be090e | modular_mod_compute_v1_971394319_0 | Let $a$ be the largest prime number not exceeding $30$. Let $m$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 108$. Compute the remainder when $a$ is divided by $m$, and let this result be $r$. Find the remainder when $99671 \cdot r$ is divided by $69440$. | 43,419 | graphs = [
Graph(
let={
"_m": Const(30),
"_n": Const(69440),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(element... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B1"
] | 7086d0 | modular_mod_compute_v1 | null | 4 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.016 | 2026-02-08T12:47:29.013533Z | {
"verified": true,
"answer": 43419,
"timestamp": "2026-02-08T12:47:29.029412Z"
} | 6c6abc | 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": 1332
},
"timestamp": "2026-02-15T05:34:27.862Z",
"answer": 43419
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8e12f1 | nt_count_divisible_v1_1874849503_419 | Let $a = 60$ and $b = 72$. Define $w$ to be the sum of $\mu(d)$ over all positive divisors $d$ of $\gcd(a, b)$, where $\mu$ is the M\"obius function. Let $p = 31$ and $q = 97$, and define $n = pq$. Let $m$ be the remainder when the number of positive divisors of $n$ is divided by $2$. Define $u = 45360 + m$ and $d = 24... | 1,890 | graphs = [
Graph(
let={
"a": Const(60),
"b": Const(72),
"w": SumOverDivisors(n=GCD(a=Ref(name='a'), b=Ref(name='b')), var='d', expr=MoebiusMu(n=Var(name='d'))),
"p": Const(31),
"q": Const(97),
"n": Mul(Ref("p"), Ref("q")),
"... | NT | null | COUNT | sympy | DIVISOR_PARITY | [
"DIVISOR_PARITY",
"MOBIUS_COPRIME"
] | 69075e | nt_count_divisible_v1 | null | 4 | 2 | [
"DIVISOR_PARITY",
"MOBIUS_COPRIME"
] | 2 | 1.458 | 2026-02-08T13:03:20.306805Z | {
"verified": true,
"answer": 1890,
"timestamp": "2026-02-08T13:03:21.764918Z"
} | 0b478a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 569
},
"timestamp": "2026-02-09T16:38:17.185Z",
"answer": 1890
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V3",
"... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
392f81_n | alg_poly3_min_v1_1218484723_7590 | A drone's energy consumption is modeled by $-33ab^2 -26a^3 -7b^3 -51a^2b$ joules, where $a$ is speed level and $b$ is payload setting. The payload $b$ must be the smallest integer $\ge 2$ dividing $213443$, and $a$ ranges from $1$ to $461$. Find the minimum energy consumption, then compute its remainder modulo $94101$. | 74,037 | ALG | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_poly3_min_v1 | null | 6 | null | [
"MIN_PRIME_FACTOR"
] | 1 | 0.589 | 2026-02-25T09:01:56.708578Z | null | dd93e1 | 392f81 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T02:38:19.758Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
3d01db | algebra_poly_eval_v1_655260480_2786 | Let $y = 10$. Define $S$ as the set of all ordered pairs $(x, y_1)$ of positive integers such that $x \cdot y_1 = 1742400$. Let $s$ be the minimum value of $x + y_1$ over all such pairs. Compute
\[
\frac{100 \cdot y^6 + 185 \cdot y^5 + 285 \cdot y^4 - 25 \cdot y^3 - 200 \cdot y^2 + 35 \cdot y + 10}{s}.
\]
Let $c = \sum... | 65,715 | graphs = [
Graph(
let={
"_m": Const(73563),
"_n": Const(2),
"y": Const(10),
"result": Div(Sum(Mul(Const(100), Pow(Ref("y"), Const(6))), Mul(Const(185), Pow(Ref("y"), Const(5))), Mul(Const(285), Pow(Ref("y"), Const(4))), Mul(Const(-25), Pow(Ref("y"), Const(3)))... | NT | null | COMPUTE | sympy | K2 | [
"K2",
"B3"
] | f7e709 | algebra_poly_eval_v1 | quadratic_mod | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.01 | 2026-02-08T17:01:07.888722Z | {
"verified": true,
"answer": 65715,
"timestamp": "2026-02-08T17:01:07.899162Z"
} | 282cb3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 3530
},
"timestamp": "2026-02-17T16:54:53.767Z",
"answer": 65715
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3100fb | antilemma_sum_equals_v1_809748730_328 | Let $ S $ be the set of all integers $ t $ such that $ 35 \leq t \leq 239 $ and there exist integers $ a $ and $ b $ with $ 1 \leq a \leq 11 $, $ 1 \leq b \leq 5 $, and $ t = 12a + 21b + 2 $. Let $ n $ be the number of elements in $ S $. Let $ X $ be the set of all ordered pairs $ (i, j) $ of integers such that $ 1 \le... | 61,028 | graphs = [
Graph(
let={
"_m": Const(78941),
"_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=11)), Geq(left=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T11:28:29.481939Z | {
"verified": true,
"answer": 61028,
"timestamp": "2026-02-08T11:28:29.488975Z"
} | 389f76 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T14:04:13.959Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
6e8388 | nt_count_digit_sum_v1_2080023795_111 | Let $p$ be a positive integer for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 8004150$. Let $s$ be the number of such integers $p$. Compute the remainder when $15933$ times the number of integers $n$ with $1 \leq n \leq 99999$ and digit sum equal to $s$ is divided by ... | 20,511 | graphs = [
Graph(
let={
"_n": Const(79954),
"upper": Const(99999),
"target_sum": 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=8... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"ONE_PHI_1",
"ONE_PHI_2"
] | 5c139a | nt_count_digit_sum_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_1",
"ONE_PHI_2"
] | 3 | 33.665 | 2026-02-08T11:33:16.535262Z | {
"verified": true,
"answer": 20511,
"timestamp": "2026-02-08T11:33:50.199778Z"
} | a2053b | 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": 3480
},
"timestamp": "2026-02-08T20:44:57.969Z",
"answer": 20511
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
... | {
"lo": 1.29,
"mid": 4.19,
"hi": 6.61
} | ||
aca4b7 | diophantine_fbi2_min_v1_2051736721_3543 | Let $d$ be an integer satisfying $3 \leq d \leq 25$, such that $d$ divides $15$ and $\frac{15}{d} \geq 5$. Determine the smallest such $d$. Compute the remainder when $44121$ times this value is divided by $62278$. | 7,807 | graphs = [
Graph(
let={
"k": Const(15),
"upper": Const(25),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(5))))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T17:24:15.461588Z | {
"verified": true,
"answer": 7807,
"timestamp": "2026-02-08T17:24:15.469578Z"
} | 296b77 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 566
},
"timestamp": "2026-02-16T09:41:01.983Z",
"answer": 7807
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
2db42f | antilemma_sum_equals_v1_1353956133_747 | Let $m = 83046$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 48$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 23$ and $1 \leq j \leq 24$ such that $i + j = n$. Compute the remainder when $57455 \cdot x$ is divided by $m$. | 75,775 | graphs = [
Graph(
let={
"_m": Const(83046),
"_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"))... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.018 | 2026-02-08T11:49:52.483186Z | {
"verified": true,
"answer": 75775,
"timestamp": "2026-02-08T11:49:52.501347Z"
} | f3af74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1427
},
"timestamp": "2026-02-24T14:46:40.760Z",
"answer": 75775
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"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... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
f285b4 | lte_diff_endings_v1_1742523217_693 | Let $a = 2511$, $b = 11$, $p = 5$, and $n = 875$. Let $d$ be the largest integer $k$ such that $p^k$ divides $a^n - b^n$. Let $k_0 = 18884$ and let $M = 100000$. Find the remainder when $k_0 \cdot d$ is divided by $M$. | 32,188 | graphs = [
Graph(
let={
"a_val": Const(2511),
"b_val": Const(11),
"p_val": Const(5),
"n_val": Const(875),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref(... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 5 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:10:57.906304Z | {
"verified": true,
"answer": 32188,
"timestamp": "2026-02-08T03:10:57.907078Z"
} | aa864a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 984
},
"timestamp": "2026-02-09T21:21:17.011Z",
"answer": 32188
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
8bfa83 | diophantine_fbi2_min_v1_655260480_3279 | Let $k = 60$. Compute the smallest integer $d$ such that $2 \leq d \leq 70$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. | 2 | graphs = [
Graph(
let={
"k": Const(60),
"a": Const(1),
"b": Const(4),
"upper": Const(70),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | B3 | [
"LIN_FORM",
"K13"
] | 11ea0b | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"K13",
"LIN_FORM"
] | 3 | 0.076 | 2026-02-08T17:18:32.939600Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T17:18:33.015641Z"
} | 09ce1c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 466
},
"timestamp": "2026-02-17T23:37:51.743Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
95c26f | comb_binomial_compute_v1_1915831931_2649 | Let $n = 12$. Let $k$ be the number of positive integers $j$ such that $1 \le j \le 7$ and $j^2 \le 49$. Compute the remainder when $\binom{n}{k}$ is multiplied by 68623 and then divided by 54915. | 38,481 | graphs = [
Graph(
let={
"n": Const(12),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(7)), Leq(Pow(Var("j"), Const(2)), Const(49))), domain='positive_integers')),
"result": Binom(n=Ref("n"), k=Ref("k")),
... | ALG | COMB | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | comb_binomial_compute_v1 | null | 2 | 0 | [
"C3"
] | 1 | 0.006 | 2026-02-08T17:00:57.371406Z | {
"verified": true,
"answer": 38481,
"timestamp": "2026-02-08T17:00:57.377371Z"
} | d61198 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 4731
},
"timestamp": "2026-02-17T17:20:57.422Z",
"answer": 38481
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
398360 | algebra_poly_eval_v1_1439011603_2360 | Let $z$ be the number of integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, $5 \leq t \leq 14$, and $t = 3a + 2b$. Let $P$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 90$, $\gcd(p, q) = 1$, and $p < ... | 64,184 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(3),
"z": 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=Cons... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM",
"K2"
] | 01a264 | algebra_poly_eval_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"K2",
"LIN_FORM"
] | 3 | 0.007 | 2026-02-08T16:44:44.290542Z | {
"verified": true,
"answer": 64184,
"timestamp": "2026-02-08T16:44:44.297881Z"
} | aac445 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 1774
},
"timestamp": "2026-02-17T10:09:17.830Z",
"answer": 64184
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
759aea | comb_sum_binomial_row_v1_1526740231_13 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $n = 11$. Compute the value of $|S|^n$. | 2,048 | graphs = [
Graph(
let={
"n": Const(11),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T11:18:28.473894Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T11:18:28.474937Z"
} | 1b2749 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 905
},
"timestamp": "2026-02-14T11:48:34.549Z",
"answer": 2048
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
7c0c75 | geo_count_lattice_triangle_v1_898971024_1370 | Let $A$ be the set of all integers $t$ such that $9 \leq t \leq 194$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 90$, and $t = 7a + 2b$. Let $c$ be the number of elements in $A$. Let $B$ be the set of all integers $t_1$ such that $31 \leq t_1 \leq 565$ and there exist integers $a$ ... | 2,196 | graphs = [
Graph(
let={
"_d": Const(136),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3",
"B3/B3"
] | a40c9e | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.041 | 2026-02-08T16:05:28.234289Z | {
"verified": true,
"answer": 2196,
"timestamp": "2026-02-08T16:05:28.275091Z"
} | 169f6e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 330,
"completion_tokens": 2573
},
"timestamp": "2026-02-16T20:19:18.724Z",
"answer": 2196
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
91381e | antilemma_sum_equals_v1_2051736721_284 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 14$ and $1 \leq i, j \leq 13$. Compute $256 - x$. | 243 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(14)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(13))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T15:19:29.515773Z | {
"verified": true,
"answer": 243,
"timestamp": "2026-02-08T15:19:29.527627Z"
} | fe4bf7 | 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": 383
},
"timestamp": "2026-02-24T20:34:58.746Z",
"answer": 243
},
{
"id"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
ae6015 | algebra_vieta_sum_v1_1978505735_1808 | Let $m = 2$ and let $s$ be the sum of all even positive integers $n$ such that $1 \leq n \leq 2$. Let $p(x) = 2x^4 - 4x^t - 206x^m + 520x + 1800$, where $t$ is the largest prime number satisfying $s \leq t \leq 3$. Find the product of all real roots of the equation $p(x) = 0$. | 900 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2)), Eq(Mod(value=Var("n"), modulus=Const(2)), Const(0))))),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), con... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"SUM_DIVISIBLE/MAX_PRIME_BELOW"
] | caf344 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 3 | 0.043 | 2026-02-08T16:24:13.263384Z | {
"verified": true,
"answer": 900,
"timestamp": "2026-02-08T16:24:13.306585Z"
} | c017ae | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 368
},
"timestamp": "2026-02-16T07:22:02.474Z",
"answer": 900
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
24134d | diophantine_product_count_v1_124444284_211 | Let $k$ be the number of integers $t$ such that $15 \leq t \leq 278$ and there exist positive integers $a \leq 25$ and $b \leq 20$ satisfying $t = 7a + 5b + 3$. Let $S$ be the set of positive integers $x$ such that $1 \leq x \leq 210$, $x$ divides $k$, and $k/x \leq 210$. Compute the remainder when $65245$ times the nu... | 47,986 | graphs = [
Graph(
let={
"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=25)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.01 | 2026-02-08T03:04:42.260489Z | {
"verified": true,
"answer": 47986,
"timestamp": "2026-02-08T03:04:42.270017Z"
} | 45c49e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 9808
},
"timestamp": "2026-02-23T15:55:22.614Z",
"answer": 4144
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
cdb050 | antilemma_k2_v1_1470522791_799 | Let $d=2$. Let $c$ be the sum of all integers $x$ such that
$$x^d-12x-8064=0.$$
Let $m=96934$. For each positive integer $k$, let $\varphi(k)$ denote the number of positive integers at most $k$ that are relatively prime to $k$.
Let
$$n=\sum_{k=1}^{12} \varphi(k)\left\lfloor\frac{12}{k}\right\rfloor.$$
Define
$$S=\sum_... | 35,333 | graphs = [
Graph(
let={
"_d": Const(2),
"_c": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_d")), Mul(Const(-12), Var("x")), Const(-8064)), Const(0)))),
"_m": Const(96934),
"_n": Summation(var="k", start=Const(1), end=Const(12)... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"IDENTITY_DIV_SELF",
"K2/K2",
"K2"
] | c78755 | antilemma_k2_v1 | null | 8 | 0 | [
"IDENTITY_DIV_SELF",
"K13",
"K2",
"VIETA_SUM"
] | 4 | 0.009 | 2026-02-08T13:15:49.008149Z | {
"verified": true,
"answer": 35333,
"timestamp": "2026-02-08T13:15:49.016722Z"
} | e53d40 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 2037
},
"timestamp": "2026-02-15T11:52:00.084Z",
"answer": 35333
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ef912e | nt_count_gcd_equals_v1_1978505735_1721 | Let $k$ be the largest prime number less than or equal to $150$. Compute the number of positive integers $n_1$ such that $1 \le n_1 \le 19321$ and $\gcd(n_1, k) = 149$. Let $Q$ be the remainder when $35877$ times this count is divided by $58984$. Find the value of $Q$. | 27,381 | graphs = [
Graph(
let={
"upper": Const(19321),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(150)), IsPrime(Var("n"))))),
"d": Const(149),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condit... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_gcd_equals_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.934 | 2026-02-08T16:21:54.024419Z | {
"verified": true,
"answer": 27381,
"timestamp": "2026-02-08T16:21:57.958882Z"
} | 9c77b7 | 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": 1122
},
"timestamp": "2026-02-17T02:22:59.463Z",
"answer": 27381
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
43a57b | antilemma_k3_v1_2051736721_5698 | Let $n = 20410$. Compute the remainder when $2108 \cdot \left(\sum_{d \mid n} \phi(d)\right)$ is divided by 84403. | 63,153 | graphs = [
Graph(
let={
"_n": Const(20410),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(2108), Ref("x")), modulus=Const(84403)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T18:44:08.683073Z | {
"verified": true,
"answer": 63153,
"timestamp": "2026-02-08T18:44:08.685328Z"
} | 0eb10f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 1309
},
"timestamp": "2026-02-18T19:20:54.157Z",
"answer": 63153
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f789db | diophantine_fbi2_min_v1_717093673_3925 | Let $k = 12$ and $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $s = |S|$.
Let $T$ be the set of all integers $d$ such that $6 \leq d \leq 22$, $d$ divides $k$, and $\frac{k}{d} \geq s$. Determine the minimum element of ... | 0 | graphs = [
Graph(
let={
"k": Const(12),
"upper": Const(22),
"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")), CountOverSet(set=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.026 | 2026-02-08T17:58:11.402293Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T17:58:11.427945Z"
} | f8cc85 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 627
},
"timestamp": "2026-02-16T11:49:09.676Z",
"answer": null
},
{
"id": 11,... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a4a40c | comb_factorial_compute_v1_1218484723_3342 | Let $N$ be the number of positive integers $t$ such that $t = 15a + 6b$ for some integers $a, b$ with $1 \leq a \leq 411$, $1 \leq b \leq 10$, and $21 \leq t \leq 6225$. Let $R = 7!$. Find the remainder when $N \cdot R$ is divided by $55277$. | 15,524 | graphs = [
Graph(
let={
"_n": Const(55277),
"n": Const(7),
"result": Factorial(Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Cons... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | comb_factorial_compute_v1 | affine_mod | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-25T05:01:58.166880Z | {
"verified": true,
"answer": 15524,
"timestamp": "2026-02-25T05:01:58.168298Z"
} | 4090b3 | 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": 12025
},
"timestamp": "2026-03-29T09:43:56.254Z",
"answer": 15524
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
74dd5d | modular_mod_compute_v1_124444284_7586 | Let $a$ be the number of positive integers $n$ such that $1 \leq n \leq 9$ and $\gcd(n, 20) = 1$. Let $r$ be the remainder when $a$ is divided by $49729$. Compute the remainder when $83260 \cdot r$ is divided by $78051$. | 20,836 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(9)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"m": Const(49729),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": Co... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | modular_mod_compute_v1 | null | 3 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-08T09:11:48.145869Z | {
"verified": true,
"answer": 20836,
"timestamp": "2026-02-08T09:11:48.146885Z"
} | 1f596c | 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": 553
},
"timestamp": "2026-02-14T01:57:25.068Z",
"answer": 20836
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
002e16 | modular_mod_compute_v1_865884756_6842 | Compute the remainder when $-62500$ is divided by the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 80$ and $1 \leq j \leq 80$. | 1,500 | graphs = [
Graph(
let={
"a": Const(-62500),
"m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(80)), right=IntegerRange(start=Const(1), end=Const(80)))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result")... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_mod_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T19:24:59.152694Z | {
"verified": true,
"answer": 1500,
"timestamp": "2026-02-08T19:24:59.153506Z"
} | ca9528 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 616
},
"timestamp": "2026-02-18T22:19:18.953Z",
"answer": 1500
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
36e901 | antilemma_product_of_sums_v1_151522320_1005 | Let $n$ be the largest prime number such that $2 \leq n \leq 28$. Let $S_1$ be the sum of all integers $j$ with $0 \leq j \leq 7$ such that $\binom{7}{j}$ is odd. Let $S_2 = \sum_{k=1}^{n} k$. Define $x = S_1 \cdot S_2$. Compute $\sum_{k=1}^{|x|} \tau(k)$, where $\tau(k)$ denotes the number of positive divisors of $k$. | 70,397 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(28)), IsPrime(Var("n"))))),
"S1": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/PRODUCT_OF_SUMS/SUM_ARITHMETIC"
] | 8df830 | antilemma_product_of_sums_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 3 | 0.004 | 2026-02-08T03:42:25.363055Z | {
"verified": true,
"answer": 70397,
"timestamp": "2026-02-08T03:42:25.367417Z"
} | 478ad4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 401
},
"timestamp": "2026-02-18T05:29:12.887Z",
"answer": 48
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok_... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
276f81 | comb_count_permutations_fixed_v1_655260480_4908 | Let $n = 6$. Let $k$ be the value of
$$
\sum_{k_1=0}^{9} (-1)^{k_1} \binom{m}{k_1},
$$
where $m$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 18$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. | 265 | graphs = [
Graph(
let={
"n": Const(6),
"k": Summation(var="k1", start=Const(0), end=Const(9), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.004 | 2026-02-08T18:12:14.948124Z | {
"verified": true,
"answer": 265,
"timestamp": "2026-02-08T18:12:14.952253Z"
} | 34c79d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1346
},
"timestamp": "2026-02-18T15:07:49.596Z",
"answer": 265
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
a439f3 | nt_sum_over_divisible_v1_48377204_999 | Let $S$ be the set of all positive integers $n$ such that $n \leq 16384$ and $n$ is divisible by $24$. Let $r$ be the sum of all elements in $S$. Let $d_{\min}$ be the smallest divisor of $114651463$ that is at least $2$. Compute
$$
353702 \cdot (r \bmod 97) + 329703 \cdot \left((r^2 + 1) \bmod d_{\min}\right) + 215534... | 64,898 | graphs = [
Graph(
let={
"_n": Const(93609),
"upper": Const(16384),
"divisor": Const(24),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Con... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | b5b91a | nt_sum_over_divisible_v1 | crt_mix_3 | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.171 | 2026-02-08T15:51:33.410037Z | {
"verified": true,
"answer": 64898,
"timestamp": "2026-02-08T15:51:34.581396Z"
} | 738c5b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 4432
},
"timestamp": "2026-02-16T15:00:21.699Z",
"answer": 64898
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e154ef | algebra_poly_eval_v1_168721529_714 | Let $A$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 164025$. Let $s$ be the minimum value of $x + y$ as $(x,y)$ ranges over $A$. Let $B$ be the set of all integers $n$ with $1 \leq n \leq 10944$ such that $21$ divides the $n$-th Fibonacci number. Let $c$ be the number of elements in $B$... | 1,390 | graphs = [
Graph(
let={
"_c": Const(21),
"_m": Const(2),
"_n": Const(4),
"n": Const(13),
"result": Div(Sum(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPosit... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"COPRIME_PAIRS",
"B3"
] | acec14 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.01 | 2026-02-08T13:12:38.077452Z | {
"verified": true,
"answer": 1390,
"timestamp": "2026-02-08T13:12:38.087398Z"
} | dc9d68 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 333,
"completion_tokens": 5927
},
"timestamp": "2026-02-11T07:38:33.556Z",
"answer": 1390
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},... | {
"lo": -1.84,
"mid": 2.85,
"hi": 7.63
} | ||
c79ac5 | diophantine_fbi2_count_v1_784195855_8263 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 57600$. For each such pair, compute $x + y$, and let $k$ be the minimum value of $x + y$ over all such pairs. Compute the number of positive integers $d$ such that $5 \leq d \leq 54$, $d$ divides $k$, and $\frac{k}{d}$ is an integer b... | 10 | graphs = [
Graph(
let={
"_n": Const(5),
"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(57600)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T15:58:59.493971Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T15:58:59.500663Z"
} | 9a445c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1374
},
"timestamp": "2026-02-16T17:46:09.577Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6434cb | antilemma_k3_v1_784195855_1952 | Let $n = 47722$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Let $y = |x| + 1$. Compute $x + \phi(y) + \tau(y)$, where $\phi$ denotes Euler's totient function and $\tau(y)$ denotes the number of positive divisors of $y$. | 91,766 | graphs = [
Graph(
let={
"_n": Const(47722),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Const(1)))),
},
goa... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T05:24:46.185126Z | {
"verified": true,
"answer": 91766,
"timestamp": "2026-02-08T05:24:46.185857Z"
} | 01904a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1026
},
"timestamp": "2026-02-12T08:10:19.792Z",
"answer": 91766
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2541bc | geo_count_lattice_triangle_v1_971394319_431 | Let $A$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 16384$. Let $s_{\min}$ be the minimum value of $x + y$ over all pairs $(x, y) \in A$. Define $\text{area}_{2x} = \left| 169 \cdot 300 + 128 \cdot (-s_{\min}) \right|$. Define $\text{boundary} = \gcd(|169|, |256|) + \gcd(|128 - 169|, |... | 8,964 | graphs = [
Graph(
let={
"_m": Const(3832),
"_n": Const(8),
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=300)), Mul(Const(value=128), Sub(left=Const(value=0), right=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), c... | ALG | NT | COUNT | sympy | C5 | [
"C5",
"B3"
] | 2a47df | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"C5"
] | 2 | 0.012 | 2026-02-08T13:04:50.229669Z | {
"verified": true,
"answer": 8964,
"timestamp": "2026-02-08T13:04:50.241316Z"
} | 6230de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1204
},
"timestamp": "2026-02-15T09:39:17.598Z",
"answer": 8964
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f8a3b7 | diophantine_fbi2_min_v1_124444284_10107 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 32400$. Let $S$ be the set of all integers $t$ with $10 \le t \le 391$ for which there exist integers $a$ and $b$ such that $1 \le a \le 44$, $1 \le b \le 37$, and $t = 3a + 7b$. Let $u$ be the number of element... | 15 | graphs = [
Graph(
let={
"_n": Const(4),
"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 | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.021 | 2026-02-08T12:50:07.989347Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T12:50:08.010655Z"
} | 24d1c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 5157
},
"timestamp": "2026-02-15T05:36:32.984Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8736dd | antilemma_k3_v1_153355830_2369 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $69417$, where $\phi$ is Euler's totient function. | 69,417 | graphs = [
Graph(
let={
"_n": Const(69417),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T07:05:01.573298Z | {
"verified": true,
"answer": 69417,
"timestamp": "2026-02-08T07:05:01.573682Z"
} | 0ae610 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 571
},
"timestamp": "2026-02-13T07:44:11.072Z",
"answer": 69417
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
00b789 | diophantine_fbi2_count_v1_1978505735_6456 | Let $k = 480$. Define $S$ to be the set of all integers $d$ such that $2 \leq d \leq 152$, $d$ divides $k$, and $$\frac{k}{d} \geq T,$$ where $T$ is the number of ordered pairs $(p, q)$ of positive integers satisfying $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Furthermore, assume $\frac{k}{d} \leq 152$. Compute ... | 30 | graphs = [
Graph(
let={
"k": Const(480),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(152)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), CountOverSet(set=SolutionsSet(var=Var("p"), cond... | NT | null | COUNT | sympy | K2 | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 0.17 | 2026-02-08T19:36:15.837609Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T19:36:16.007757Z"
} | 60fe2a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2996
},
"timestamp": "2026-02-18T22:57:28.269Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
836fdb | nt_count_primes_v1_1742523217_2358 | Let $\ell$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 216$, and $\gcd(p, q) = 1$. Compute the number of prime numbers $n$ such that $\ell \leq n \leq 10153$. | 1,246 | graphs = [
Graph(
let={
"upper": Const(10153),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.319 | 2026-02-08T04:43:03.842427Z | {
"verified": true,
"answer": 1246,
"timestamp": "2026-02-08T04:43:04.161180Z"
} | a394e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 3197
},
"timestamp": "2026-02-12T02:48:12.950Z",
"answer": 1246
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
06407d | antilemma_cartesian_v1_1874849503_1148 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 18$ and $1 \leq b \leq 31$. Compute the value of
$$
x + \varphi(|x| + 0!) + \tau(|x| + \binom{1}{0}).
$$
Here, $\varphi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. | 1,066 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(31)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Factorial(Const(0)))), NumDivisors(n=Sum(Abs(arg=Ref(name='x... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0",
"ONE_BINOM_0"
] | 122c03 | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_0",
"ONE_FACTORIAL_0"
] | 3 | 0.002 | 2026-02-08T13:38:52.660481Z | {
"verified": true,
"answer": 1066,
"timestamp": "2026-02-08T13:38:52.662307Z"
} | 3c89e1 | 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": 549
},
"timestamp": "2026-02-10T01:42:43.369Z",
"answer": 1066
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": ... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
da80ed | alg_qf_psd_count_v1_1218484723_2894 | Let $T$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 20$ such that
$$
10a_1^2 - 18a_1b_1 + 25b_1^2 \le 6730.
$$
Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 366$ and $1 \le b \le T$ such that
$$
41a^2 - 8ab + b^2 = 53125.
$$
Find $... | 11 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(366)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_count_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.219 | 2026-02-25T04:39:23.497957Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-25T04:39:23.716765Z"
} | 1846d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:12:51.331Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
1b0451 | nt_sum_totient_over_divisors_v1_238844314_1019 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 14953$ and $\gcd(k, 14) = 1$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 6,409 | graphs = [
Graph(
let={
"_n": Const(14953),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.006 | 2026-02-08T13:51:08.894845Z | {
"verified": true,
"answer": 6409,
"timestamp": "2026-02-08T13:51:08.901183Z"
} | 0a23c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 789
},
"timestamp": "2026-02-15T21:21:19.557Z",
"answer": 6409
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c7159c | nt_count_divisible_v1_865884756_1747 | Let $n = 26$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 231361$. Let $S$ be the set of all values of $x + y$ for such pairs. Let $m$ be the minimum element of $S$. Find the number of positive integers $d$ such that $1 \leq d \leq n$ and $d$ divides $m$. Let $d_{\text{max}}$ be t... | 1,632 | graphs = [
Graph(
let={
"_n": Const(26),
"upper": Const(42436),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(el... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | nt_count_divisible_v1 | null | 6 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 1.35 | 2026-02-08T16:17:03.006679Z | {
"verified": true,
"answer": 1632,
"timestamp": "2026-02-08T16:17:04.356784Z"
} | af139d | 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": 1184
},
"timestamp": "2026-02-17T00:20:40.502Z",
"answer": 1632
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
82c72f | lin_form_endings_v1_1520064083_4493 | Let $a = 56$ and $b = 42$. Define $g$ to be the greatest common divisor of $a$ and $b$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 48$ and $B = 4$. Compute the value of
$$
(12874 \cdot (a' \cdot A + b' \cdot B - a' \cdot b')) \mod 57562.
$$ | 54,204 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(42),
"A_val": Const(48),
"B_val": Const(4),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:18:00.131104Z | {
"verified": true,
"answer": 54204,
"timestamp": "2026-02-08T06:18:00.132046Z"
} | 100862 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 961
},
"timestamp": "2026-02-12T22:13:55.879Z",
"answer": 54204
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e8af34 | sequence_fibonacci_compute_v1_124444284_8868 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Define $T$ to be the set of all values $x + y$ where $(x, y) \in S$. Let $n$ be the minimum element of $T$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $c$... | 71,680 | graphs = [
Graph(
let={
"_n": Const(73696),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(144)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 74c9a3 | sequence_fibonacci_compute_v1 | affine_mod | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T11:56:28.018516Z | {
"verified": true,
"answer": 71680,
"timestamp": "2026-02-08T11:56:28.020958Z"
} | 7a7478 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 5583
},
"timestamp": "2026-02-14T20:40:16.307Z",
"answer": 71680
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
841ef4 | nt_min_coprime_above_v1_1874849503_287 | Let $n$ be a positive integer. Define $m$ to be the number of positive integers $n \leq 288$ such that $16$ divides the $n$-th Fibonacci number. Let $S$ be the set of integers $n$ satisfying $35344 < n \leq 35378$ and $\gcd(n, m) = 1$. Compute the minimum element of $S$. | 35,345 | graphs = [
Graph(
let={
"_n": Const(288),
"start": Const(35344),
"upper": Const(35378),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(16), dividend=Fibonacci(arg=Va... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_min_coprime_above_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.01 | 2026-02-08T12:55:51.986425Z | {
"verified": true,
"answer": 35345,
"timestamp": "2026-02-08T12:55:51.996593Z"
} | effa0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1688
},
"timestamp": "2026-02-09T15:22:57.042Z",
"answer": 35345
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"statu... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
f77b71 | modular_min_linear_v1_1978505735_6078 | Let $a$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 18470$. Let $b$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 149769$. Let $m = 11574$, and let $r$ be the smallest positive integer $x_3 \leq m$ such that $a \cdot ... | 15,480 | graphs = [
Graph(
let={
"_n": Const(95693),
"a": 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")),... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1",
"B3"
] | 44bb30 | modular_min_linear_v1 | null | 7 | 0 | [
"B3",
"COMB1"
] | 2 | 0.432 | 2026-02-08T19:24:32.989863Z | {
"verified": true,
"answer": 15480,
"timestamp": "2026-02-08T19:24:33.421670Z"
} | 64f48a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 5905
},
"timestamp": "2026-02-18T22:10:44.846Z",
"answer": 15480
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
32c0ba | nt_sum_divisors_mod_v1_1439011603_1095 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. For each pair, compute $x + y$. Let $n$ be the smallest value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Let $M = 11903$, and define $r$ to be the remainder when $\sigma$ is div... | 4,994 | 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(14288400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(119... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T15:54:34.076874Z | {
"verified": true,
"answer": 4994,
"timestamp": "2026-02-08T15:54:34.081862Z"
} | 806567 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1557
},
"timestamp": "2026-02-16T16:34:34.503Z",
"answer": 4994
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bac6c3 | comb_count_permutations_fixed_v1_809748730_1765 | Let $n$ be the largest prime number not exceeding $5$. Let $k = 0$ and define $D = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $C = 43264$. Compute $C - D$. | 43,220 | graphs = [
Graph(
let={
"_n": Const(5),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:41:21.290286Z | {
"verified": true,
"answer": 43220,
"timestamp": "2026-02-08T12:41:21.292659Z"
} | a0d82e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 764
},
"timestamp": "2026-02-15T03:51:44.778Z",
"answer": 43220
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
20b913 | modular_sum_quadratic_residues_v1_124444284_846 | Let $m = 4$ and $n = 2$. Define $T$ to be the set of all integers $t$ such that $8 \leq t \leq 442$ and there exist positive integers $a \leq 47$ and $b \leq 69$ satisfying $t = 5a + 3b$. Let $p$ be the largest prime number $n$ such that $2 \leq n \leq |T|$. Compute $\frac{p(p-1)}{4}$. Determine the value of this quant... | 44,205 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'),... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T03:32:55.788401Z | {
"verified": true,
"answer": 44205,
"timestamp": "2026-02-08T03:32:55.791996Z"
} | 0be4b2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 8175
},
"timestamp": "2026-02-23T20:19:03.303Z",
"answer": 44205
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status"... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
c4e6af | antilemma_v7_kummer_548369836_350 | Let $m = 152$ and $n = 44$. Let $A$ be the set of all positive integers $k$ such that $k$ divides some multiple of $n$ that is at most $1520$. Let $N$ be the number of elements in $A$. Define $x$ to be the largest integer $k$ such that $3^k$ divides $\binom{N}{76}$. Find the value of $x$. | 3 | graphs = [
Graph(
let={
"_m": Const(152),
"_n": Const(44),
"x": MaxKDivides(target=Binom(n=CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"SUM_DIVISIBLE/C2/V7",
"V7"
] | e31ef7 | antilemma_v7_kummer | null | 7 | null | [
"C2",
"COUNT_PRIMES",
"SUM_DIVISIBLE",
"V7"
] | 4 | 0.025 | 2026-02-08T02:52:55.369166Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T02:52:55.394461Z"
} | 4c3479 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 3980
},
"timestamp": "2026-02-09T23:05:57.986Z",
"answer": 4
},
{
"i... | 0 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
... | {
"lo": 4.29,
"mid": 7.01,
"hi": 10
} | ||
6b19c1 | antilemma_k3_v1_784195855_2912 | Compute $\sum_{d \mid 10999} \phi(d)$, where $\phi$ denotes Euler's totient function. | 10,999 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=10999), 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 | 2026-02-08T06:07:29.637397Z | {
"verified": true,
"answer": 10999,
"timestamp": "2026-02-08T06:07:29.637718Z"
} | b88821 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 722
},
"timestamp": "2026-02-15T17:03:51.603Z",
"answer": 10999
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
c7c87f | nt_count_digit_sum_v1_1978505735_7072 | Let $m = 483$. Define $A$ as the set of all integers $t$ such that $7 \leq t \leq 10009$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 863$, $1 \leq b \leq 2847$, and $t = 5a + 2b$. Let $u$ be the number of elements in $A$.
Let $B$ be the set of all positive integers $k$ such that $1 \leq k \leq m$... | 71,776 | graphs = [
Graph(
let={
"_m": Const(483),
"_n": Const(82432),
"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'), ... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"C2"
] | c556ae | nt_count_digit_sum_v1 | null | 5 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 3.893 | 2026-02-08T20:02:15.422334Z | {
"verified": true,
"answer": 71776,
"timestamp": "2026-02-08T20:02:19.314961Z"
} | ff03da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 5999
},
"timestamp": "2026-02-18T23:52:04.071Z",
"answer": 71776
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bbe499 | comb_factorial_compute_v1_1915831931_2999 | Let $m = 11011$. Consider the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $n_0$ be the number of elements in this set. Define $n$ to be the largest prime number that is at least $n_0$ and at most the smallest divisor of $m... | 5,040 | graphs = [
Graph(
let={
"_m": Const(11011),
"_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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 21b694 | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.006 | 2026-02-08T17:17:15.796916Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T17:17:15.802589Z"
} | 1e524f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1279
},
"timestamp": "2026-02-17T23:54:34.610Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
570b66 | antilemma_sum_equals_v1_784195855_2994 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 16$, $1 \leq j \leq 17$, and $i + j = 17$. Let $y$ be the number of integers $t$ such that $14 \leq t \leq 70$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 5$, and $t = 4a + 10b$. Comput... | 706 | graphs = [
Graph(
let={
"_n": Const(17),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | a464cd | antilemma_sum_equals_v1 | quadratic_mod | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.049 | 2026-02-08T06:10:55.663989Z | {
"verified": true,
"answer": 706,
"timestamp": "2026-02-08T06:10:55.713406Z"
} | 985019 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 2120
},
"timestamp": "2026-02-24T05:35:13.437Z",
"answer": 706
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
4a3c79 | nt_max_prime_below_v1_677425708_1088 | Let $P$ be the set of all ordered pairs $(p, q)$ of positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $\ell$ be the number of such pairs. Let $\mathcal{S}$ be the set of all prime numbers $n$ such that $\ell \leq n \leq 26244$. Let $r$ be the largest element of $\mathcal{S}$. Find the remainder ... | 48,385 | graphs = [
Graph(
let={
"_n": Const(68799),
"upper": Const(26244),
"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 | 0.578 | 2026-02-08T04:00:04.159774Z | {
"verified": true,
"answer": 48385,
"timestamp": "2026-02-08T04:00:04.737602Z"
} | a075f9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 4565
},
"timestamp": "2026-02-10T15:00:43.483Z",
"answer": 48385
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f98f72 | nt_count_gcd_equals_v1_151522320_1133 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 15554$. Define $u$ to be the number of such pairs. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $\gcd(n, 277) = 277$. Compute the number of elements in $T$. | 28 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(15554))))),
... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 3.934 | 2026-02-08T03:49:02.870283Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T03:49:06.804088Z"
} | 264c5f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1157
},
"timestamp": "2026-02-10T15:49:51.654Z",
"answer": 28
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
5498bf | geo_count_lattice_rect_v1_809748730_271 | Let $R$ be the rectangle with vertices at $(0,0)$, $(27,0)$, $(0,83)$, and $(27,83)$. Compute the number of lattice points contained in $R$ (including the boundary). Let $N$ be this number. Find the value of $\sum_{n=1}^{N} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 18,640 | graphs = [
Graph(
let={
"a": Const(27),
"b": Const(83),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Summation(var="n", start=Div(Const(70), Const(70)), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n"))),
},
g... | GEOM | NT | COUNT | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF"
] | b48fad | geo_count_lattice_rect_v1 | null | 4 | 0 | [
"IDENTITY_DIV_SELF"
] | 1 | 0.002 | 2026-02-08T11:25:35.579006Z | {
"verified": true,
"answer": 18640,
"timestamp": "2026-02-08T11:25:35.580782Z"
} | 12e072 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 4085
},
"timestamp": "2026-02-24T13:48:46.739Z",
"answer": 18640
},
{
"... | 1 | [
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e11e36 | diophantine_sum_product_min_v1_458359167_4449 | Let $S = 52$ and $P = 676$. Consider the set of all integers $x$ such that $1 \leq x \leq 51$ and $x(S - x) = P$. Compute the minimum value of $x$ in this set. | 26 | graphs = [
Graph(
let={
"S": Const(52),
"P": Const(676),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(51)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_SQUAREFREE"
] | d4ca42 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"LIN_FORM",
"MOBIUS_SQUAREFREE"
] | 2 | 0.083 | 2026-02-08T11:47:48.391501Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T11:47:48.474284Z"
} | d0b902 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 381
},
"timestamp": "2026-02-14T18:39:36.882Z",
"answer": 26
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
0da26a | comb_catalan_compute_v1_865884756_2454 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 40$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 4a + 10b$. Define $C_n$ to be the $n$th Catalan number. Compute the remainder when $76037 \cdot C_n$ is divided by $51927$. | 24,814 | 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=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T16:47:04.223718Z | {
"verified": true,
"answer": 24814,
"timestamp": "2026-02-08T16:47:04.227678Z"
} | 716e52 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2201
},
"timestamp": "2026-02-17T11:48:06.784Z",
"answer": 24814
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
22493e | nt_min_with_divisor_count_v1_124444284_1811 | Let $N=8256$. For each integer $j$ with $0\le j\le N$, consider the binomial coefficient $\binom{N}{j}$. Let $P$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=72,\quad \gcd(p,q)=1,\quad p<q.$$
Let $C$ be the number of integers $j$ with $0\le j\le N$ such that
$$\bi... | 6 | graphs = [
Graph(
let={
"_n": Const(8256),
"upper": Const(78961),
"div_count": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Coun... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8/B3"
] | efa8e6 | nt_min_with_divisor_count_v1 | null | 8 | 0 | [
"B3",
"COPRIME_PAIRS",
"V8"
] | 3 | 3.238 | 2026-02-08T04:09:32.281061Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T04:09:35.518839Z"
} | bc0558 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 1610
},
"timestamp": "2026-02-11T23:35:39.457Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
... | {
"lo": -3.81,
"mid": -1.11,
"hi": 1.33
} | ||
7da5ad | antilemma_k2_v1_238844314_369 | Compute the value of
$$
\sum_{k=1}^{250} \phi(k) \left\lfloor \frac{250}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 31,375 | graphs = [
Graph(
let={
"_n": Const(250),
"x": Summation(var="k", start=Const(1), end=Const(250), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2"
] | 2 | 0.004 | 2026-02-08T13:18:22.676294Z | {
"verified": true,
"answer": 31375,
"timestamp": "2026-02-08T13:18:22.680496Z"
} | a46772 | 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": 505
},
"timestamp": "2026-02-15T12:59:28.136Z",
"answer": 31375
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4a7e45 | nt_sum_divisors_mod_v1_1918700295_1315 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 705600$. Let $\sigma$ be the sum of the positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10613$. | 5,952 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10613... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:46:36.224299Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T05:46:36.225415Z"
} | 538993 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1506
},
"timestamp": "2026-02-12T14:09:17.046Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
918862 | antilemma_cartesian_v1_1440796553_386 | Let $N$ be the number of ordered pairs $(u,v)$ of integers such that $1\le u\le 34$ and $1\le v\le 46$.
Let $T$ be the set of all integers $t$ such that $17\le t\le 29$ and there exist integers $a$ and $b$ with $1\le a\le 4$, $1\le b\le 3$, and
$$t=2a+3b+12.$$
Let $M$ be the number of elements of $T$.
Let
$$S=|N|+\bi... | 2,816 | graphs = [
Graph(
let={
"_n": Const(11),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(34)), right=IntegerRange(start=Const(1), end=Const(46)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Binom(n=CountOverSet(set=Soluti... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/ONE_BINOM_N",
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 833a19 | antilemma_cartesian_v1 | arith_invariants | 4 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM",
"ONE_BINOM_N",
"ONE_FACTORIAL_0"
] | 4 | 0.002 | 2026-02-08T11:45:41.508142Z | {
"verified": true,
"answer": 2816,
"timestamp": "2026-02-08T11:45:41.510374Z"
} | 92e106 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 1725
},
"timestamp": "2026-02-24T14:38:00.141Z",
"answer": 2816
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "ONE_BINOM_N",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
367069 | algebra_poly_eval_v1_48377204_1348 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. For each such pair, compute $x + y$, and let $m$ be the minimum value of $x + y$ over all such pairs. Compute the value of $$\frac{m \cdot 17^4 - 14 \cdot 17^3 + 3 \cdot 17^2 - 30 \cdot 17 - 8}{47}.$$ | 41,193 | graphs = [
Graph(
let={
"_n": Const(2),
"b": Const(17),
"result": Div(Sum(Mul(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... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T16:03:04.064505Z | {
"verified": true,
"answer": 41193,
"timestamp": "2026-02-08T16:03:04.068455Z"
} | 514fa5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 769
},
"timestamp": "2026-02-16T19:56:27.714Z",
"answer": 41193
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2aee50 | algebra_quadratic_discriminant_v1_48377204_2451 | Let $\Delta = b^2 - 4ac$ where $a = -2$, $b = 26$, and $c = -72$. Let $p$ be the largest prime number less than or equal to $7874$. Compute the remainder when $p \cdot \Delta$ is divided by $65530$. | 940 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(26),
"c": Const(-72),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Mod(value=Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=A... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 183c11 | algebra_quadratic_discriminant_v1 | affine_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:46:36.256405Z | {
"verified": true,
"answer": 940,
"timestamp": "2026-02-08T16:46:36.258105Z"
} | dfaf75 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 988
},
"timestamp": "2026-02-17T10:45:39.333Z",
"answer": 940
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
56007a | lin_form_endings_v1_151522320_2281 | Let $a = 45$ and $b = 105$. Define $k = \left\lfloor \frac{105}{\gcd(a, b)} \right\rfloor$. Let $x = (13971 \cdot k) \mod 97621$.
Find the value of $x$. | 176 | graphs = [
Graph(
let={
"a_coeff": Const(45),
"b_coeff": Const(105),
"_inner_result": Floor(Div(Const(105), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(13971),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mo... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T04:43:18.761759Z | {
"verified": true,
"answer": 176,
"timestamp": "2026-02-08T04:43:18.762126Z"
} | d3141d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 232
},
"timestamp": "2026-02-11T21:43:40.420Z",
"answer": 176
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
609cce | modular_modexp_compute_v1_1125832087_93 | Let $a = 43$. Let $e$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 66$. Let $m = 26569$.
Compute the remainder when $a^e$ is divided by $m$. | 11,169 | graphs = [
Graph(
let={
"a": Const(43),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(66)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T02:51:59.043027Z | {
"verified": true,
"answer": 11169,
"timestamp": "2026-02-08T02:51:59.044518Z"
} | f679ff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T16:57:17.297Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.88,
"mid": 3.52,
"hi": 5.13
} | ||
9ccae4 | antilemma_cartesian_v1_1439011603_280 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 30$ and $1 \leq b \leq 45$. Compute the remainder when $44121 \cdot x$ is divided by $52642$. | 25,248 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(30)), right=IntegerRange(start=Const(1), end=Const(45)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(52642)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T15:23:39.622060Z | {
"verified": true,
"answer": 25248,
"timestamp": "2026-02-08T15:23:39.623061Z"
} | 153a1d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T20:46:56.840Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
0f818f | sequence_lucas_compute_v1_1248542787_619 | Let $L_{19}$ denote the 19th Lucas number. Let $c$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 23520$ and $\binom{23520}{j}$ is odd. Compute the value of
$$
\sum_{i=0}^{\lfloor \log_{10} L_{19} \rfloor} \left( \text{the } i\text{-th digit of } L_{19} \right) \cdot (i+1)^2 + c.
$$ | 452 | graphs = [
Graph(
let={
"_n": Const(23520),
"n": Const(19),
"result": Lucas(arg=Ref(name='n')),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result')), k=... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86b5fc | sequence_lucas_compute_v1 | digits_weighted_mod | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T03:16:00.900977Z | {
"verified": true,
"answer": 452,
"timestamp": "2026-02-08T03:16:00.903121Z"
} | 03aefa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1955
},
"timestamp": "2026-02-23T21:56:40.801Z",
"answer": 457
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
03bd22 | comb_count_permutations_fixed_v1_153355830_770 | Let $n$ be the smallest divisor of 245 that is at least 2. Compute the remainder when $31868 \cdot \binom{n}{0} \cdot !\left(n - 0\right)$ is divided by 54077, where $!k$ denotes the number of derangements of $k$ elements. | 50,267 | graphs = [
Graph(
let={
"_n": Const(245),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(l... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T04:09:56.946737Z | {
"verified": true,
"answer": 50267,
"timestamp": "2026-02-08T04:09:56.948011Z"
} | 6e7f78 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1133
},
"timestamp": "2026-02-10T15:39:07.418Z",
"answer": 50267
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
31441f | nt_count_coprime_v1_1116507919_220 | Let $S$ be the set of all positive integers $n \leq 27556$ such that $\gcd(n, 34) = 1$. Let $C$ be the number of elements in $S$. Compute the remainder when $86563 \cdot C$ is divided by $57172$. | 33,936 | graphs = [
Graph(
let={
"upper": Const(27556),
"k": Const(34),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
"_c": Const(86563... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_coprime_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 1.923 | 2026-02-08T02:29:13.832798Z | {
"verified": true,
"answer": 33936,
"timestamp": "2026-02-08T02:29:15.756035Z"
} | bfdae7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 2476
},
"timestamp": "2026-02-08T19:15:15.843Z",
"answer": 33936
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
6b7838 | diophantine_fbi2_min_v1_784195855_1468 | Let $n = 28561$. Determine the largest integer $e$ such that $13^e$ divides $n^5$. Let $S$ be the set of all integers $d$ satisfying: $2 \leq d \leq e$, $d$ divides 10, and $\frac{10}{d} \geq 3$. Find the minimum value of $d$ in $S$. | 2 | graphs = [
Graph(
let={
"_n": Const(28561),
"k": Const(10),
"upper": MaxKDivides(target=Pow(Ref("_n"), Const(5)), base=Const(13)),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(d... | NT | null | EXTREMUM | sympy | V8 | [
"ONE_PHI_2",
"K14"
] | 551817 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"K14",
"ONE_PHI_2",
"V8"
] | 3 | 0.016 | 2026-02-08T05:01:59.246908Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T05:01:59.262737Z"
} | f185e1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 311
},
"timestamp": "2026-02-18T15:01:31.343Z",
"answer": 2
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status":... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
6fd210 | alg_poly4_min_v1_1218484723_1589 | For positive integers $a,b$ with $1 \le a \le 171$ and $1 \le b \le 171$, consider the expression
$$-3720ab^{3} + 7440a^{3}b + C\,a^{4} + 31341b^{4} + 29016\,a^{D} b^{2},$$
where
\begin{align*}
C &= \left|\{ (a_1, b_1) : 1 \le a_1 \le 40,\ 1 \le b_1 \le 40,\ 2a_1^{2} - 2a_1 b_1 + 41b_1^{2} \le 65000 \}\right|, \\
D &= ... | 65,658 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(171)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(171)))), e... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"POLY4_COUNT"
] | c72518 | alg_poly4_min_v1 | null | 8 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.089 | 2026-02-25T03:19:06.484973Z | {
"verified": true,
"answer": 65658,
"timestamp": "2026-02-25T03:19:06.574139Z"
} | 71baba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 411,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T07:20:51.786Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 4.43,
"mid": 6.62,
"hi": 9.7
} | ||
61948b | nt_max_prime_below_v1_1439011603_503 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $n \geq m$ and $n \leq 42436$. Let $r$ be the largest element of $T$. Let $U$... | 28,604 | graphs = [
Graph(
let={
"upper": Const(42436),
"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 | B3 | [
"B3",
"COPRIME_PAIRS"
] | fec8c0 | nt_max_prime_below_v1 | affine_mod | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 1.955 | 2026-02-08T15:31:55.871984Z | {
"verified": true,
"answer": 28604,
"timestamp": "2026-02-08T15:31:57.826998Z"
} | 5da95b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 5158
},
"timestamp": "2026-02-16T07:57:24.644Z",
"answer": 28604
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3a6049 | antilemma_k2_v1_151522320_648 | Let $n = 381$. Define
$$
x = \sum_{k=1}^{\sum_{d \mid n} \phi(d)} \phi(k) \left\lfloor \frac{381}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $Q$ be the remainder when $44121x$ is divided by $68842$.
Compute $Q$. | 7,253 | graphs = [
Graph(
let={
"_n": Const(381),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(381), Var("k"))))),
"Q": Mod(value=Mul(Const(44121), Ref("x")),... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T03:26:49.272946Z | {
"verified": true,
"answer": 7253,
"timestamp": "2026-02-08T03:26:49.273734Z"
} | 52b050 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 4665
},
"timestamp": "2026-02-10T14:30:59.458Z",
"answer": 27419
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
e2d4ac | nt_min_coprime_above_v1_153355830_130 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 7496644$. Define $T$ to be the set of all values $x + y$ where $(x,y) \in S$. Let $m$ be the minimum value in $T$. Let $U$ be the set of all integers $n$ such that $m < n \leq 5956$ and $\gcd(n, 470) = 1$. Compute the smallest element ... | 5,477 | graphs = [
Graph(
let={
"start": 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(7496644)))), expr=Sum(Var("x"), Var("y")))),
"upper": Co... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.04 | 2026-02-08T02:54:02.170237Z | {
"verified": true,
"answer": 5477,
"timestamp": "2026-02-08T02:54:02.209972Z"
} | 770ba3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 10240
},
"timestamp": "2026-02-23T19:01:30.177Z",
"answer": 5477
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -2.24,
"mid": 0.01,
"hi": 1.87
} | ||
f9a651 | nt_count_with_divisor_count_v1_655260480_2566 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 6287$ and $\gcd(n, 14) = 1$. Let $d$ be the smallest integer greater than or equal to 2 that divides the number of elements in $A$. Define
$$
\text{div\_count} = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{d}{k} \right\rfloor.
$$
Let $B$ be the set ... | 48,549 | graphs = [
Graph(
let={
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6287)), Eq(GCD(a=Var("n"), b=Const(14)), Const(... | NT | null | COUNT | sympy | C4 | [
"C4/MIN_PRIME_FACTOR/K2"
] | 6e0996 | nt_count_with_divisor_count_v1 | null | 7 | 0 | [
"C4",
"K2",
"MIN_PRIME_FACTOR"
] | 3 | 6.283 | 2026-02-08T16:49:56.327832Z | {
"verified": true,
"answer": 48549,
"timestamp": "2026-02-08T16:50:02.611264Z"
} | 53e4bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 3155
},
"timestamp": "2026-02-17T13:23:41.144Z",
"answer": 48549
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CON... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fbdd75 | antilemma_cartesian_v1_151522320_1797 | Let $x$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 23$ and $1 \leq j \leq 36$. Compute the remainder when $\sum_{n = (1 - 2 + 1)!}^{|x|} \phi(n)$ is divided by $62922$, where $\phi(n)$ denotes Euler's totient function. | 19,770 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Const(36)))),
"Q": Mod(value=Summation(var="n", start=Factorial(Summation(var="k", start=Const(0), end=Const(2), expr=Mul(Pow(Const(... | COMB | GEOM | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 12185f | antilemma_cartesian_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 3 | 0.017 | 2026-02-08T04:23:01.793247Z | {
"verified": true,
"answer": 19770,
"timestamp": "2026-02-08T04:23:01.810253Z"
} | 75f486 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T00:26:01.271Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} |
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