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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0eaaa3 | sequence_count_fib_divisible_v1_1978505735_5205 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 47524$. Let $s_{\min}$ be the minimum value of $x + y$ over all $(x, y) \in S$. Let $d$ be the number of positive integers $n$ at most $9$ that are relatively prime to $20$. Determine the number of positive integers $n_1$ at most $s_{... | 72 | graphs = [
Graph(
let={
"_n": Const(9),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(47524)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3",
"C4"
] | 8d18b3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"C4"
] | 2 | 0.02 | 2026-02-08T18:49:14.014371Z | {
"verified": true,
"answer": 72,
"timestamp": "2026-02-08T18:49:14.034473Z"
} | f2e0da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2936
},
"timestamp": "2026-02-18T19:52:17.217Z",
"answer": 72
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f7f5be | nt_count_divisors_in_range_v1_784195855_4264 | Let $n = 221760$ and let $\ell = 4356$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = \ell$. Let $a$ be the minimum value of $x + y$ over all such pairs. Let $b = 55450$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 114 | graphs = [
Graph(
let={
"_n": Const(4356),
"n": Const(221760),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), e... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.945 | 2026-02-08T06:57:09.026895Z | {
"verified": true,
"answer": 114,
"timestamp": "2026-02-08T06:57:09.972125Z"
} | 0a39f1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 3804
},
"timestamp": "2026-02-13T07:12:22.307Z",
"answer": 114
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
82ab2a | comb_count_surjections_v1_809748730_1244 | Let $S$ be the set of all ordered pairs of integers $(i, j)$ such that $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = 8$. Let $n$ be the number of elements in $S$. Compute the remainder when $69449 \cdot 2! \cdot S(n, 2)$ is divided by $63650$, where $S(n, 2)$ denotes the number of ways to partition a set of $n$ el... | 46,670 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6))))),
"k": Con... | COMB | null | COUNT | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.042 | 2026-02-08T12:17:51.209884Z | {
"verified": true,
"answer": 46670,
"timestamp": "2026-02-08T12:17:51.252264Z"
} | b023a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1310
},
"timestamp": "2026-02-24T15:27:34.482Z",
"answer": 46670
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
2a00ce | comb_count_derangements_v1_2051736721_1875 | Let $n$ be the largest prime number between 2 and 8, inclusive. Let $d_n$ denote the number of derangements of $n$ elements. Let $m$ be the smallest divisor of 1859 that is at least 2. Compute the Bell number $B_k$, where $k$ is the remainder when $|d_n|$ is divided by $m$. Determine the value of $B_k$. | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(8)), IsPrime(Var("n1"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='r... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | d2be59 | comb_count_derangements_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T16:17:14.163162Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T16:17:14.166302Z"
} | 9d2a21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 869
},
"timestamp": "2026-02-17T00:16:30.092Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7e7689 | diophantine_product_count_v1_1742523217_361 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 14$. Let $u$ be the maximum value of $xy$ as $(x, y)$ ranges over $T$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $60$, and $\frac{60}{x} \leq u$. Let $r$ be the number of elements in $... | 53,690 | graphs = [
Graph(
let={
"_n": Const(44121),
"k": Const(60),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(14)))), ... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | diophantine_product_count_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.005 | 2026-02-08T02:59:47.454764Z | {
"verified": true,
"answer": 53690,
"timestamp": "2026-02-08T02:59:47.459989Z"
} | 6b593c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1836
},
"timestamp": "2026-02-09T17:00:03.848Z",
"answer": 53690
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
9aca17 | nt_sum_totient_over_divisors_v1_124444284_4687 | Let $n = 88465$. Define $r$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute the remainder when $63949 \cdot r$ is divided by $57855$. | 12,820 | graphs = [
Graph(
let={
"n": Const(88465),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(63949),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(57855)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | C5 | [
"C5/C5",
"C3/C5"
] | 29a512 | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"C3",
"C5"
] | 2 | 0.059 | 2026-02-08T06:11:38.129559Z | {
"verified": true,
"answer": 12820,
"timestamp": "2026-02-08T06:11:38.188625Z"
} | 7a21ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1363
},
"timestamp": "2026-02-12T21:05:59.254Z",
"answer": 12820
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
aa1272 | modular_sum_quadratic_residues_v1_124444284_3945 | Let $n = 101$. Let $p$ be the largest prime number such that $2 \leq p \leq n$. Define $$
\text{result} = \frac{p(p-1)}{4}.
$$
Compute the value of $\text{result}$. | 2,525 | graphs = [
Graph(
let={
"_n": Const(101),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T05:40:29.157509Z | {
"verified": true,
"answer": 2525,
"timestamp": "2026-02-08T05:40:29.160417Z"
} | 39e310 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 285
},
"timestamp": "2026-02-12T12:51:26.427Z",
"answer": 2525
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
58c8b0 | diophantine_product_count_v1_1520064083_3692 | Let $n$ be a positive integer such that $2 \leq n \leq 63$ and $n$ is prime. Define $k = 480$ and let $p$ be the largest such $n$. Determine the number of positive integers $x$ such that $1 \leq x \leq p$, $x$ divides $k$, and $\frac{k}{x} \leq p$. Compute this number. | 12 | graphs = [
Graph(
let={
"_n": Const(63),
"k": Const(480),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=... | NT | null | COUNT | sympy | L3C | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_product_count_v1 | null | 4 | 0 | [
"L3C",
"MAX_PRIME_BELOW"
] | 2 | 0.025 | 2026-02-08T05:49:17.993482Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T05:49:18.018128Z"
} | d3cf9f | 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": 1304
},
"timestamp": "2026-02-12T14:37:02.172Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8c81b1 | comb_sum_binomial_row_v1_458359167_3136 | Let $n$ be $4$ plus the number of nonnegative integers $j$ such that $0 \leq j \leq 66561$ and the binomial coefficient $\binom{66561}{j}$ is odd. Let $r = 2^n$. Let $Q$ be the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|r| + 2$. Find the value of $Q$. | 684 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(66561)), Eq(Mod(value=Binom(n=Const(66561), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Ref("_n")),... | NT | null | SUM | sympy | V8 | [
"V8"
] | 86348e | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T06:59:19.355804Z | {
"verified": true,
"answer": 684,
"timestamp": "2026-02-08T06:59:19.357261Z"
} | cc7358 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 3733
},
"timestamp": "2026-02-13T07:06:55.094Z",
"answer": 684
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7cbb0b | comb_factorial_compute_v1_1978505735_3299 | Let $N$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \le i \le 8$, $1 \le j \le 9$, and $i + j = 10$. Let $a = 4$ and $b$ be the number of ordered pairs $(p, q)$ such that $1 \le p \le 2$ and $1 \le q \le 2$. Define $n_2 = a + b$. Let $m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 =... | 40,320 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_CARTESIAN/BINOMIAL_ALTERNATING"
] | cdca7b | comb_factorial_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.023 | 2026-02-08T17:32:47.389899Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T17:32:47.413324Z"
} | 02ddd7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 908
},
"timestamp": "2026-02-18T03:48:35.370Z",
"answer": 40320
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
331b86 | modular_modexp_compute_v1_124444284_2867 | Let $a$ be the largest prime number less than or equal to $52$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 640000$. For each pair in $P$, compute $x + y$, and let $e$ be the minimum value among these sums. Define $r = a^e \bmod 10253$. Given that $c = 33856$, compute $c - r$. ... | 25,759 | graphs = [
Graph(
let={
"_n": Const(52),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditi... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | modular_modexp_compute_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.006 | 2026-02-08T05:03:06.845654Z | {
"verified": true,
"answer": 25759,
"timestamp": "2026-02-08T05:03:06.851243Z"
} | 9d5993 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 6093
},
"timestamp": "2026-02-11T22:48:04.114Z",
"answer": 25759
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lem... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
11a1a2 | algebra_poly_eval_v1_1218484723_5310 | Let $F_n$ denote the $n$-th Fibonacci number. Compute $$ \left| \left\{ n : 1 \le n \le 36,\ 6 \mid F_n \right\} \right| \cdot 25 - 30 + 7 $$. | 52 | graphs = [
Graph(
let={
"_n": Const(6),
"b": Const(5),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(36)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))), Pow(Ref("b"), Const(... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | algebra_poly_eval_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-25T06:56:15.323346Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-25T06:56:15.325256Z"
} | 6df3a0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1238
},
"timestamp": "2026-03-29T20:27:42.334Z",
"answer": 52
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
2f59fa | comb_count_partitions_v1_48377204_3060 | Let $m = 42$. Let $P$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 42$. Let $n$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = P$. Find the number of integer partitions of $n$. | 53,174 | graphs = [
Graph(
let={
"_m": Const(42),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_count_partitions_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T17:09:18.407412Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T17:09:18.410839Z"
} | 7479c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 881
},
"timestamp": "2026-02-17T20:36:09.329Z",
"answer": 53174
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b9feb2 | modular_count_residue_v1_717093673_443 | Let $n$ be a positive integer. Define $A$ as the number of positive integers $n$ such that $1 \leq n \leq 76176$ and $n \equiv 6 \pmod{28}$. Define $B$ as the number of positive integers $j$ such that $1 \leq j \leq 3000$ and $j^4 \leq 81000000000000$. Compute $B - A$. | 279 | graphs = [
Graph(
let={
"_n": Const(3000),
"upper": Const(76176),
"m": Const(28),
"r": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulu... | NT | null | COUNT | sympy | C3 | [
"C3"
] | a45c54 | modular_count_residue_v1 | negation_mod | 4 | 0 | [
"C3"
] | 1 | 2.95 | 2026-02-08T15:27:42.631437Z | {
"verified": true,
"answer": 279,
"timestamp": "2026-02-08T15:27:45.581041Z"
} | d3cb4f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1195
},
"timestamp": "2026-02-16T06:53:45.992Z",
"answer": 279
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d4d43c | nt_max_prime_below_v1_349078426_1166 | Let $A$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $n_0$ be the number of elements in $A$.\\
Now, let $B$ be the set of all prime numbers $n$ such that $n_0 \leq n \leq 19321$.\\
Determine the value of the largest elem... | 19,319 | graphs = [
Graph(
let={
"upper": Const(19321),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.505 | 2026-02-08T13:27:13.188576Z | {
"verified": true,
"answer": 19319,
"timestamp": "2026-02-08T13:27:13.693107Z"
} | 90c951 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 3400
},
"timestamp": "2026-02-15T16:06:40.252Z",
"answer": 19319
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
95bfb8 | comb_bell_compute_v1_601307018_9654 | Let $B_n$ denote the $n$-th Bell number. Compute the remainder when $1069 \cdot B_9$ is divided by $67780$. | 35,403 | graphs = [
Graph(
let={
"n": Const(9),
"result": Bell(Ref("n")),
"_c": Const(1069),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(67780)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | HALFPLANE_COUNT | [
"HALFPLANE_COUNT/POLY_ORBIT_HENSEL",
"LIN_FORM"
] | e0c8d1 | comb_bell_compute_v1 | affine_mod | 3 | 0 | [
"HALFPLANE_COUNT",
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 3 | 0.115 | 2026-03-10T10:04:46.637294Z | {
"verified": true,
"answer": 35403,
"timestamp": "2026-03-10T10:04:46.752278Z"
} | 8ab897 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 872
},
"timestamp": "2026-04-19T11:44:24.178Z",
"answer": 35403
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "HALFPLANE_COUNT",
"status": "ok"
},
{
"lemma": "LIN_FORM... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
bf8e86 | nt_sum_totient_over_divisors_v1_784195855_6288 | Let $n = 78459$. Define $\phi(d)$ to be Euler's totient function. Compute
$$
\sum_{d \mid n} \phi(d).
$$
Let $c$ be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 2$ and $1 \le j \le 59$ such that $\gcd(i,j) = 1$. Compute the remainder when $c - \sum_{d \mid n} \phi(d)$ is divided by $78812$. Determi... | 442 | graphs = [
Graph(
let={
"_n": Const(78812),
"n": Const(78459),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | b363a0 | nt_sum_totient_over_divisors_v1 | negation_mod | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T08:32:18.938134Z | {
"verified": true,
"answer": 442,
"timestamp": "2026-02-08T08:32:18.939332Z"
} | 2ce709 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 502
},
"timestamp": "2026-02-13T19:32:56.364Z",
"answer": 442
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
566361 | nt_sum_totient_over_divisors_v1_784195855_1633 | Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq 5968$ and $j^4 \leq 1268572398616576$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 5,968 | graphs = [
Graph(
let={
"_n": Const(5968),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(4)), Const(1268572398616576))), domain='positive_integers')),
"result": SumOverDivisors(n=R... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.004 | 2026-02-08T05:11:02.196719Z | {
"verified": true,
"answer": 5968,
"timestamp": "2026-02-08T05:11:02.200639Z"
} | c40f2a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 3459
},
"timestamp": "2026-02-11T23:02:50.093Z",
"answer": 5968
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4ebd5d | lin_form_endings_v1_124444284_4078 | Let $a = 30$ and $b = 75$. Let $L = \operatorname{lcm}(a, b)$, and define
$$
x = 2L + a + b.
$$
Compute the remainder when $7250 \cdot x$ is divided by $84246$. | 71,886 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(75),
"k_val": Const(2),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:45:15.500923Z | {
"verified": true,
"answer": 71886,
"timestamp": "2026-02-08T05:45:15.501568Z"
} | 57efba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1788
},
"timestamp": "2026-02-12T14:23:06.030Z",
"answer": 71886
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d56aad | nt_count_coprime_and_v1_458359167_690 | Let $ u = 31251 $. Define $ k_1 $ to be the sum of all positive integers $ n $ such that $ 1 \leq n \leq 3 $ and $ n $ is divisible by $ 3 $. Let $ k_2 = 11 $. Let $ S $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq u $, $ \gcd(n, k_1) = 1 $, and $ \gcd(n, k_2) = 1 $. Let $ c $ be the number of el... | 18,940 | graphs = [
Graph(
let={
"upper": Const(31251),
"k1": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(3)), Eq(Mod(value=Var("n"), modulus=Const(3)), Const(0))))),
"k2": Const(11),
"result": CountOverSet(set=S... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 4.126 | 2026-02-08T03:30:22.443446Z | {
"verified": true,
"answer": 18940,
"timestamp": "2026-02-08T03:30:26.569312Z"
} | 4b8c34 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1097
},
"timestamp": "2026-02-10T14:41:00.374Z",
"answer": 18940
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
4e0778 | nt_sum_over_divisible_v1_1125832087_570 | Let $S$ be the set of all positive integers $n$ such that $n \leq 70000$ and $n$ is divisible by 32. Let $R$ be the sum of all elements in $S$. Let $P$ be the largest prime number not exceeding 7003. Compute the remainder when $\left(R \bmod 293\right) + P \cdot \left(R \bmod 337\right)$ is divided by 77877. | 45,747 | graphs = [
Graph(
let={
"upper": Const(70000),
"divisor": Const(32),
"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")), Const(0))))),
"Q": Mod(... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_sum_over_divisible_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.242 | 2026-02-08T03:09:21.795680Z | {
"verified": true,
"answer": 45747,
"timestamp": "2026-02-08T03:09:25.037193Z"
} | 6cfd5f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2362
},
"timestamp": "2026-02-10T13:13:58.015Z",
"answer": 45747
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_V... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
8fd228 | comb_count_permutations_fixed_v1_784195855_10134 | Let $h = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, and let $a = h$, $b = 2$. Define $n_1 = a + b$ and $c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 11 + c$ and $k = 9$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. Then determine the sma... | 36 | graphs = [
Graph(
let={
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Ref("h"),
"b": Const(2),
"n1": Sum(Ref("a"), Ref("b")),
"c": Summat... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T17:28:00.786521Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T17:28:00.787702Z"
} | 860fdc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1407
},
"timestamp": "2026-02-18T01:52:31.223Z",
"answer": 36
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"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... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2cb01c | algebra_quadratic_discriminant_v1_124444284_8066 | Let $c = 2$ and $m = 2$. Let $n$ be the largest prime number satisfying $2 \leq n \leq 7$. Define
$$
b = \sum_{k=1}^{n} \phi(k) \cdot \left\lfloor \frac{d_{\min}}{k} \right\rfloor,
$$
where $d_{\min}$ is the smallest integer $d \geq c$ that divides $77$. Let $a = -2$ and $c = -90$. Compute $b^m - 4ac$. | 64 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"a": Const(-2),
"b": Summation(var="k", start=Const(1), en... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2",
"MAX_PRIME_BELOW/K2"
] | 816350 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"K2",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.006 | 2026-02-08T09:32:48.151368Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T09:32:48.157311Z"
} | 521bdd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 1058
},
"timestamp": "2026-02-15T20:44:08.067Z",
"answer": 64
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemm... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
4c6ce9_n | algebra_poly_eval_v1_1419126231_1203 | A digital artist generates images using binary sequences of length $320$. An image is considered *high-contrast* if the number of ways to choose $j$ pixels to highlight is odd. Let $R$ count how many values of $j$ from $0$ to $320$ produce such images. Separately, a chemist mixes compounds $A$ and $B$ in integer amount... | 1,831 | ALG | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/POLY3_MIN",
"V8/MAX_PRIME_BELOW"
] | 631658 | algebra_poly_eval_v1 | null | 5 | null | [
"MAX_PRIME_BELOW",
"POLY3_MIN",
"V8"
] | 3 | 0.006 | 2026-02-25T10:40:33.011381Z | null | 5da818 | 4c6ce9 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 6348
},
"timestamp": "2026-03-31T04:27:58.061Z",
"answer": 30894
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status"... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
db1f1e | modular_modexp_compute_v1_349078426_828 | Let $a = 31$. Let $e$ be the sum of $\phi(d)$ over all positive divisors $d$ of $128$, where $\phi$ denotes Euler's totient function. Let $m = 30976$.
Compute the remainder when $a^e$ is divided by $m$. | 24,577 | graphs = [
Graph(
let={
"a": Const(31),
"e": SumOverDivisors(n=Const(value=128), var='d', expr=EulerPhi(n=Var(name='d'))),
"m": Const(30976),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | modular_modexp_compute_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:18:15.251473Z | {
"verified": true,
"answer": 24577,
"timestamp": "2026-02-08T13:18:15.252343Z"
} | c74683 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 3072
},
"timestamp": "2026-02-15T12:30:41.585Z",
"answer": 24577
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a383e1 | antilemma_sum_equals_v1_784195855_10065 | Let $m = 170$. Define $n$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 85$, and $1 \leq j \leq 85$. Find the remainder when $44121 \cdot x$ is divided by $72113... | 28,401 | graphs = [
Graph(
let={
"_m": Const(170),
"_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 | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.022 | 2026-02-08T17:25:08.148925Z | {
"verified": true,
"answer": 28401,
"timestamp": "2026-02-08T17:25:08.170650Z"
} | ab776f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1200
},
"timestamp": "2026-02-18T01:46:50.261Z",
"answer": 28401
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"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... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
661fbc | algebra_vieta_sum_v1_784195855_1109 | Let $S$ be the set of all real solutions $x$ to the equation $x^3 - 22x^2 + 159x - 378 = 0$. Compute the product of all elements in $S$. | 378 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=3)), Mul(Const(value=-22), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=159), Var(name='x')), Const(value=-378)), right=Const(value=... | NT | null | COMPUTE | sympy | B3 | [
"MOBIUS_SUM"
] | 518e32 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"B3",
"MOBIUS_SUM"
] | 2 | 0.109 | 2026-02-08T04:51:53.340638Z | {
"verified": true,
"answer": 378,
"timestamp": "2026-02-08T04:51:53.450127Z"
} | d0ba19 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 805
},
"timestamp": "2026-02-11T22:15:44.359Z",
"answer": 378
},
{
"id... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CO... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
a2deb0 | alg_sum_powers_v1_1419126231_242 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ such that $$-12ab + 20b^2 + 41a^2 \le 12836.$$ Find the remainder when $\sum_{k=1}^{M} k^2$ is divided by $\min\{x + y : x > 0, y > 0, xy = 5480281\}$. | 3,699 | graphs = [
Graph(
let={
"_m": Const(12836),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Leq(Sum(Mul(Const(-12), Var("a"), Var("b")), M... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/B3"
] | 837d99 | alg_sum_powers_v1 | null | 6 | 0 | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.009 | 2026-02-25T09:47:39.991942Z | {
"verified": true,
"answer": 3699,
"timestamp": "2026-02-25T09:47:40.001030Z"
} | abdfd0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 10689
},
"timestamp": "2026-03-30T07:41:36.751Z",
"answer": 3699
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
69fb36 | algebra_poly_eval_v1_2051736721_3033 | Let $A$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $B$ be the number of positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 q = 1500$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Let $m = 24$. Defin... | 44,037 | graphs = [
Graph(
let={
"_n": Const(2),
"m": Const(24),
"result": Sum(Mul(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=18)), Eq... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T17:04:42.086894Z | {
"verified": true,
"answer": 44037,
"timestamp": "2026-02-08T17:04:42.090726Z"
} | 558629 | 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": 2310
},
"timestamp": "2026-02-17T18:09:10.172Z",
"answer": 44037
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
992712 | nt_num_divisors_compute_v1_397696148_2270 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6350400$. Define $T$ to be the set of all values $x + y$ where $(x,y) \in S$. Let $n$ be the minimum element of $T$. Compute the number of positive divisors of $n$. | 60 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"result": NumDi... | NT | null | COMPUTE | sympy | B1 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.008 | 2026-02-08T13:04:39.305241Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T13:04:39.313321Z"
} | 9da467 | 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": 1440
},
"timestamp": "2026-02-15T09:14:12.431Z",
"answer": 60
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
956a07 | nt_num_divisors_compute_v1_1918700295_193 | Let $n$ be the number of positive integers from 1 to 11553, inclusive, whose digit sum is divisible by 2. Compute the number of positive divisors of $n$. | 15 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11553)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(0))))),
"result": NumDivisors(n=Ref("n")),
},
... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T03:03:13.150967Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T03:03:13.153419Z"
} | 855a45 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2086
},
"timestamp": "2026-02-10T12:37:36.284Z",
"answer": 15
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
b1ad6b | comb_count_surjections_v1_865884756_2433 | Let $n = 4$. Let $k$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 5$, $1 \leq j \leq 5$, and $i + j = 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind.
Compute the value of $k! \cdot S(4, k)$. | 24 | graphs = [
Graph(
let={
"n": Const(4),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(5)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(5... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.014 | 2026-02-08T16:46:26.997819Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T16:46:27.012180Z"
} | 79bd05 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1112
},
"timestamp": "2026-02-24T21:49:19.898Z",
"answer": 24
},
{
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
aa78c4 | antilemma_v7_kummer_260342960_94 | Let $m=9$. Let $N$ be the number of positive integers $j$ with $1\le j\le 110$ and $j^4\le 146410000$.
Consider all ordered triples $(a,b,t)$ of integers such that $1\le a\le 22$, $1\le b\le 2$, $27\le t\le 174$, and
$$t=6a+21b.$$
Let $K$ be the number of distinct integers $t$ for which there exists at least one such ... | 1 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(110)), Leq(Pow(Var("j"), Const(4)), Const(146410000))), domain='positive_integers')),
"x": MaxKDivides(target=Binom(n=Ref("... | NT | null | COMPUTE | sympy | C3 | [
"C3/LIN_FORM/V7",
"MAX_PRIME_BELOW/V7",
"V7"
] | 396411 | antilemma_v7_kummer | null | 7 | null | [
"C3",
"LIN_FORM",
"MAX_PRIME_BELOW",
"V7"
] | 4 | 0.004 | 2026-02-08T11:13:47.939621Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T11:13:47.943925Z"
} | 50e15b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 1740
},
"timestamp": "2026-02-08T20:28:21.204Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"sta... | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
a489a8 | comb_count_derangements_v1_865884756_3703 | Let $v = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and let $n = 7v$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"n2": Const(0),
"w": Summation(var="k", start=Sub(Binom(n=Const(19), k=Const(0)), Const(1)), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"v": Summation(var="k1", start=Const(0), en... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_count_derangements_v1 | null | 2 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.001 | 2026-02-08T17:33:03.874107Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:33:03.875415Z"
} | bf89fb | 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": 1239
},
"timestamp": "2026-02-18T03:42:04.062Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
194844 | nt_sum_totient_over_divisors_v1_238844314_541 | Let $ n $ be the largest prime number less than or equal to 7754. Compute the value of $$ Q = \left( 44121 \times \sum_{d \mid n} \phi(d) \right) \bmod 70402. $$ | 57,197 | graphs = [
Graph(
let={
"_n": Const(70402),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7754)), IsPrime(Var("n"))))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.005 | 2026-02-08T13:23:38.425195Z | {
"verified": true,
"answer": 57197,
"timestamp": "2026-02-08T13:23:38.429824Z"
} | ddc3a9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1470
},
"timestamp": "2026-02-15T15:12:49.383Z",
"answer": 57197
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b7b20d | nt_sum_divisors_mod_v1_1520064083_1858 | Let $n$ be the sum of all positive integers at most $1120$ that are divisible by $140$. Let $\sigma$ be the sum of the positive divisors of $n$. Let $M = 11239$, and let $r$ be the remainder when $\sigma$ is divided by $M$. Let $Q$ be the $r'\!$-th Bell number, where $r'$ is the remainder when $|r|$ is divided by $11$.... | 21,147 | graphs = [
Graph(
let={
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1120)), Eq(Mod(value=Var("n"), modulus=Const(140)), Const(0))))),
"M": Const(11239),
"sigma": SumDivisors(n=Ref("n")),
"result": M... | NT | COMB | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T04:20:31.242149Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T04:20:31.244311Z"
} | dad05c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1093
},
"timestamp": "2026-02-10T16:20:19.208Z",
"answer": 21147
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
844170 | nt_sum_gcd_range_mod_v1_458359167_877 | Let $N = 7000$ and $k = 540$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$, and let $\text{result}$ be the remainder when $\text{sum}$ is divided by 10069. Let $P$ be the set of all prime integers $n$ such that $2 \leq n \leq 97$. Compute the remainder when
$$
353702 \cdot (\text{result} \bmod \max(P)) + 329703 \cdo... | 19,173 | graphs = [
Graph(
let={
"_n": Const(16),
"N": Const(7000),
"k": Const(540),
"M": Const(10069),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("M")),... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 045f57 | nt_sum_gcd_range_mod_v1 | crt_mix_3 | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.314 | 2026-02-08T04:08:45.123586Z | {
"verified": true,
"answer": 19173,
"timestamp": "2026-02-08T04:08:45.437885Z"
} | 0e9efb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 3547
},
"timestamp": "2026-02-10T15:34:43.751Z",
"answer": 19173
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
abb8a6 | comb_count_permutations_fixed_v1_898971024_1134 | Let $a = 1$ and $b = 5$. Define $n_1 = a + b$. Let $m = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Define $n = 8 + m$. Compute $\binom{n}{0} \cdot !n$, where $!n$ denotes the number of derangements of $n$ objects. | 14,833 | graphs = [
Graph(
let={
"n2": Const(0),
"w": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"a": Const(1),
"b": Const(5),
"n1": Sum(Ref("a"), Ref("b")),
"m": Sum... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T15:57:14.982499Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T15:57:14.984957Z"
} | b5fb8b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1035
},
"timestamp": "2026-02-24T19:09:33.003Z",
"answer": 14833
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
45f479 | geo_count_lattice_rect_v1_1439011603_1167 | Let $a = 120$ and $b = 50$. Define $R$ as the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Let $N$ be the number of lattice points (points with integer coordinates) that lie inside or on the boundary of $R$. Find the remainder when $89561 \cdot N$ is divided by $54090$. | 43,401 | graphs = [
Graph(
let={
"a": Const(120),
"b": Const(50),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(89561), Ref("result")), modulus=Const(54090)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T15:57:31.154437Z | {
"verified": true,
"answer": 43401,
"timestamp": "2026-02-08T15:57:31.155897Z"
} | b73879 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1375
},
"timestamp": "2026-02-24T19:04:02.377Z",
"answer": 43401
},
{
... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
bab8cb | comb_count_surjections_v1_865884756_4010 | Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 6$ and $1 \le j \le 6$ such that $i + j = 6$. Let $k$ be the number of ordered pairs $(x, y)$ with $1 \le x \le 2$ and $1 \le y \le 2$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 240 | graphs = [
Graph(
let={
"_n": Const(6),
"n": 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(6)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | e4fc6a | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.017 | 2026-02-08T17:41:21.581508Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T17:41:21.598732Z"
} | 7d8d61 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 891
},
"timestamp": "2026-02-18T06:38:44.983Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
4a85c0 | nt_sum_over_divisible_v1_717093673_3045 | Let $d$ be the largest prime number less than or equal to $72$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 5827$ and $n_1$ is divisible by $d$. Let $s$ be the sum of all elements in $S$. Determine the value of the smallest positive integer $k$ such that the $k$-th Fibonacci number is d... | 2,280 | graphs = [
Graph(
let={
"_n": Const(72),
"upper": Const(5827),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": SumOverSet(set=SolutionsSet(var=Var("n1"), cond... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.2 | 2026-02-08T17:20:45.732959Z | {
"verified": true,
"answer": 2280,
"timestamp": "2026-02-08T17:20:45.932479Z"
} | 5544b9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 2099
},
"timestamp": "2026-02-18T00:24:44.858Z",
"answer": 2280
},
{... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a1489 | alg_poly_orbit_count_v1_1218484723_4420 | Let $N \equiv 2a^3 - 4a \pmod{83}$, $M \equiv 2N^3 - 4N \pmod{83}$, $R \equiv 2M^3 - 4M \pmod{83}$, $S \equiv 2R^3 - 4R \pmod{83}$, $T \equiv 2S^3 - 4S \pmod{83}$, and $K \equiv 2T^3 - 4T \pmod{83}$. Find the number of non-negative integers $a$ with $0 \le a \le 51708$ such that $K = a$, $N \neq a$, $M \neq a$, $R \neq... | 3,738 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-4), Var("a"))), modulus=Const(83)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-4), Ref("p1"))), modulus=Const(83)),
"p3": Mod(value=Sum(Mul(Const(2)... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.036 | 2026-02-25T06:02:09.144698Z | {
"verified": true,
"answer": 3738,
"timestamp": "2026-02-25T06:02:09.180580Z"
} | 344f3f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T15:41:22.611Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
84d135 | nt_count_divisible_and_v1_2051736721_4443 | Let $d_1 = 6$ and $d_2 = \sum_{k=1}^{4} k$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq 73080$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 2,436 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(73080),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 2.616 | 2026-02-08T17:59:34.059630Z | {
"verified": true,
"answer": 2436,
"timestamp": "2026-02-08T17:59:36.675264Z"
} | ca3575 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 238
},
"timestamp": "2026-02-16T11:49:49.275Z",
"answer": 1218
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
fdefeb | alg_qf_psd_sum_v1_1218484723_4834 | Evaluate the sum
$$
\sum_{\substack{a=1 \\ b=1}}^{74} \left( \left| \left\{ (a_1, b_1) : 1 \le a_1 \le 30,\ 1 \le b_1 \le 30,\ a_1 \le b_1,\ 2a_1^2 + 2b_1^2 - 4a_1b_1 = 2 \right\} \right| \cdot a^2 + 13b^2 + 32ab \right)
$$
and find the remainder when this sum is divided by $67680$. | 10,500 | graphs = [
Graph(
let={
"_n": Const(74),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(74)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(CountOv... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.016 | 2026-02-25T06:28:35.346042Z | {
"verified": true,
"answer": 10500,
"timestamp": "2026-02-25T06:28:35.362539Z"
} | e84922 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 3273
},
"timestamp": "2026-03-29T17:56:53.153Z",
"answer": 10500
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
55b1b6 | nt_min_with_divisor_count_v1_1353956133_292 | Let $S$ be the set of all ordered pairs $(k, j)$ where $k \in \{1, 2, 3\}$ and $j \in \{1, 2\}$. Let $\sigma$ be the sum of $k$ over all such pairs. Define $d = \frac{7\sigma}{14}$. Find the smallest positive integer $n \le 72900$ such that the number of positive divisors of $n$ is exactly $d$. | 12 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": Const(72900),
"div_count": Div(Mul(Const(7), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3))... | NT | null | EXTREMUM | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 4.85 | 2026-02-08T11:23:08.659309Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T11:23:13.509029Z"
} | 0c7943 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 1140
},
"timestamp": "2026-02-14T13:19:04.135Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a7d5e3 | nt_count_divisible_v1_1520064083_282 | Let $N$ be the number of positive integers $n$ such that $n \leq 65536$ and $n$ is divisible by 30. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 174$. Compute $M - N$. | 5,385 | graphs = [
Graph(
let={
"upper": Const(65536),
"divisor": Const(30),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": M... | NT | null | COUNT | sympy | LIN_FORM | [
"B1"
] | d2b6e1 | nt_count_divisible_v1 | negation_mod | 4 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 6.285 | 2026-02-08T03:09:10.393768Z | {
"verified": true,
"answer": 5385,
"timestamp": "2026-02-08T03:09:16.678578Z"
} | 0fabb1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 359
},
"timestamp": "2026-02-10T13:36:01.286Z",
"answer": 5385
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
7906b2 | antilemma_k3_v1_784195855_1985 | Let
$$x=\sum_{d\mid 25756} \varphi(d),$$
where $\varphi$ denotes Euler's totient function.
Let $S$ be the set of all integers $t$ such that
$$t^2-5476t+92803=0,$$
and let
$$y=\sum_{d\mid\sum_{t\in S} t} \varphi(d).$$
Write $|x|$ in base $10$, and for each integer $i$ with $0\le i\le \bigl(\text{number of decimal digi... | 5,695 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverDivisors(n=Const(value=25756), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=2)), Mul(Const... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K3",
"K3"
] | 9b39e6 | antilemma_k3_v1 | digits_weighted_mod | 8 | 0 | [
"K13",
"K3",
"VIETA_SUM"
] | 3 | 0.006 | 2026-02-08T05:25:07.048959Z | {
"verified": true,
"answer": 5695,
"timestamp": "2026-02-08T05:25:07.055036Z"
} | 4a33d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 918
},
"timestamp": "2026-02-12T08:14:06.541Z",
"answer": 5695
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a0851d | modular_inverse_v1_1248542787_731 | Let $a = 529$. Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 642$.
Let $u$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 20$ and $1 \leq j \leq 32$.
Determine the smallest positive integer $x$ such that $1 \leq x \leq u$ and
$$
a \cdot x \equiv 1 \pmod{m}.
$$ | 372 | graphs = [
Graph(
let={
"a": Const(529),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(642)), IsPrime(Var("n"))))),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), rig... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COUNT_CARTESIAN"
] | 68b53e | modular_inverse_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"MAX_PRIME_BELOW"
] | 2 | 0.03 | 2026-02-08T03:21:21.991788Z | {
"verified": true,
"answer": 372,
"timestamp": "2026-02-08T03:21:22.021698Z"
} | 8207f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 3243
},
"timestamp": "2026-02-09T07:38:48.860Z",
"answer": 372
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
0fc783 | comb_count_surjections_v1_1742523217_2109 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i+j = 6$, $1 \le i \le 4$, and $1 \le j \le 5$. Let $k = 4$. Define $\text{result} = k! \cdot S(n,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $65777 \cdot \text{result}$ is divided by $72... | 53,124 | graphs = [
Graph(
let={
"_n": Const(72644),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.016 | 2026-02-08T04:28:36.339490Z | {
"verified": true,
"answer": 53124,
"timestamp": "2026-02-08T04:28:36.355367Z"
} | 2f0ad2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1361
},
"timestamp": "2026-02-24T00:45:01.823Z",
"answer": 53124
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
ac7cbb | algebra_poly_eval_v1_1419126231_763 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1018081$. Let $a = 22$, and define
$$
T = \frac{\min_{\substack{1 \le a1 \le 5 \\ 1 \le b \le 5}} \left( 72a1^3 + 162a1b^2 - 108a1^2b \right) \cdot a^5 - 1678a^4 + \left| \left\{ n : 1 \le n \le 8609,\ \gcd(n, 1... | 20,200 | graphs = [
Graph(
let={
"_d": Const(72),
"_m": Const(2380),
"_n": Const(2),
"a": Const(22),
"result": Div(Sum(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var(... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"QF_PSD_MIN",
"POLY3_MIN",
"C4"
] | 10ddc4 | algebra_poly_eval_v1 | quadratic_mod | 6 | 0 | [
"B3",
"C4",
"POLY3_MIN",
"QF_PSD_MIN"
] | 4 | 0.025 | 2026-02-25T10:15:39.711699Z | {
"verified": true,
"answer": 20200,
"timestamp": "2026-02-25T10:15:39.737116Z"
} | 5b607c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 376,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T09:58:45.012Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "P... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
2c8819 | antilemma_cartesian_v1_1456120455_103 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 29$ and $1 \leq j \leq 33$. Define $m = |x| + 2$. The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. The entry point of $m$ is the smallest positive integer $k$ such that $F_k \equiv 0 \pmod{m}... | 552 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=Const(33)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.004 | 2026-02-08T02:53:45.469310Z | {
"verified": true,
"answer": 552,
"timestamp": "2026-02-08T02:53:45.473763Z"
} | fe1ef6 | 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": 4490
},
"timestamp": "2026-02-08T20:11:32.096Z",
"answer": 552
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": 0.04,
"mid": 1.71,
"hi": 3.18
} | ||
bfd4cf | comb_factorial_compute_v1_1978505735_47 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 1470$, $\gcd(p, q) = 1$, and $p < q$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=1470)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:10:14.228583Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T15:10:14.231001Z"
} | 9dd32d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 686
},
"timestamp": "2026-02-16T00:48:15.903Z",
"answer": 40320
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d279f6 | alg_poly4_sum_v1_601307018_137 | Let $S$ be the set of all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 380$ and $1 \leq b \leq B$, where $B = \min\{ x + y \mid x, y > 0,\, xy = 36100,\, x \leq y \}$. Compute the remainder when $$\sum_{(a,b) \in S} \left( 97a^4 - 280a^3b + 312a^2b^2 - 160ab^3 + 32b^4 \right)$$ is divided by $99512$. | 71,384 | graphs = [
Graph(
let={
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(380)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=Solu... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_sum_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.365 | 2026-03-10T00:46:03.048991Z | {
"verified": true,
"answer": 71384,
"timestamp": "2026-03-10T00:46:03.413507Z"
} | b86d78 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 21072
},
"timestamp": "2026-03-28T22:31:07.101Z",
"answer": 71384
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.98,
"mid": 6.04,
"hi": 8.63
} | ||
dea8dc | alg_poly_orbit_legendre_v1_1419126231_993 | For a non-negative integer $a$, define $N = a^{11} \bmod 23$, $M = (3a^4 - a^3 + 5a^2 - 3a - 3) \bmod 23$, $R = M^{11} \bmod 23$, $S = N + R$, and $T = (3M^4 - M^3 + 5M^2 - 3M - 3) \bmod 23$. Find the number of integers $a$ with $0 \le a \le 32337$ such that $T = a$, $S \equiv 0 \pmod{5}$, and $M \ne a$. | 2,812 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(4))), Mul(Const(-1), Pow(Var("a"), Const(3))), Mul(Const(5), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(-3)), modulus=Const(23)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(4))), ... | NT | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 6 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.039 | 2026-02-25T10:30:20.308843Z | {
"verified": true,
"answer": 2812,
"timestamp": "2026-02-25T10:30:20.347485Z"
} | 3e8e47 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 12316
},
"timestamp": "2026-03-30T11:02:23.808Z",
"answer": 2812
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
b27a6d | comb_sum_binomial_row_v1_1520064083_2837 | Let $n$ be the number of integers $t$ in the range $47 \leq t \leq 110$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 2$, and $t = 6a + 21b + 20$. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(na... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:14:35.821160Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T05:14:35.823086Z"
} | eb8a7a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 940
},
"timestamp": "2026-02-11T23:08:46.518Z",
"answer": 65536
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
74988b | nt_max_prime_below_v1_717093673_3335 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 16384$. Compute this value of $n$. | 16,381 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(16384),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositiv... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_max_prime_below_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.37 | 2026-02-08T17:30:02.146232Z | {
"verified": true,
"answer": 16381,
"timestamp": "2026-02-08T17:30:02.516331Z"
} | 89a251 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 422
},
"timestamp": "2026-02-16T11:20:55.149Z",
"answer": 16377
},
{
"id": 11... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
417c00 | geo_visible_lattice_v1_898971024_21 | Let $n = 99$. 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. Find the remainder when $67706 \cdot r$ is divided by $57033$. | 7,619 | graphs = [
Graph(
let={
"n": Const(99),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(67706),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(57033)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.478 | 2026-02-08T15:09:21.075507Z | {
"verified": true,
"answer": 7619,
"timestamp": "2026-02-08T15:09:21.553226Z"
} | 246144 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 10939
},
"timestamp": "2026-02-24T20:01:55.579Z",
"answer": 7619
},
{
"... | 1 | [] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||||
dad27c | nt_count_gcd_equals_v1_1470522791_984 | Let $n = 49086$. Define $A$ to be the number of integers $j$ with $0 \leq j \leq n$ such that $\binom{n}{j}$ is odd. Let $k = 313$ and $d = 1$. Define $B$ to be the number of positive integers $n'$ with $1 \leq n' \leq A$ such that $\gcd(n', k) = d$. Compute the remainder when $27771 \times B$ is divided by $85514$. | 80,372 | graphs = [
Graph(
let={
"_n": Const(49086),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(49086)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.752 | 2026-02-08T13:21:31.678116Z | {
"verified": true,
"answer": 80372,
"timestamp": "2026-02-08T13:21:32.429755Z"
} | 7b53c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2547
},
"timestamp": "2026-02-15T14:02:14.778Z",
"answer": 80372
},
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cfcbd3 | comb_bell_compute_v1_1439011603_171 | For integers $a$ and $b$ with $1\le a\le 930$ and $1\le b\le 141$, consider all integers $t$ satisfying $8\le t\le 3495$ and
$$t=3a+5b.$$
Let $T$ be the set of all such integers $t$, and let $N$ be the number of elements in $T$.
Consider all integers $n$ with $1\le n\le N$ such that $4$ divides the $n$-th Fibonacci n... | 4,140 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(580),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE/V8"
] | 3da8f5 | comb_bell_compute_v1 | null | 8 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM",
"V8"
] | 3 | 0.007 | 2026-02-08T15:19:09.880410Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T15:19:09.887514Z"
} | 5fadbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 4902
},
"timestamp": "2026-02-16T03:49:52.861Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
96bdc3 | sequence_fibonacci_compute_v1_865884756_3939 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number at most 25 that is at least the number of elements in $S$. Compute the $n$-th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": Const(25),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T17:40:36.269712Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T17:40:36.272542Z"
} | af0370 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 996
},
"timestamp": "2026-02-18T06:36:48.551Z",
"answer": 28657
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
609fa1 | antilemma_k2_v1_1915831931_2548 | Let $n = 405$. Compute the sum
$$
\sum_{k=1}^{\sum_{d \mid n} \phi(d)} \phi(k) \left\lfloor \frac{405}{k} \right\rfloor.
$$ | 82,215 | graphs = [
Graph(
let={
"_n": Const(405),
"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(405), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.004 | 2026-02-08T16:56:34.083932Z | {
"verified": true,
"answer": 82215,
"timestamp": "2026-02-08T16:56:34.087599Z"
} | 02f403 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 645
},
"timestamp": "2026-02-17T17:06:59.637Z",
"answer": 82215
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21f5d0 | lte_diff_endings_v1_1742523217_358 | Let $a = 31$, $b = 11$, $p = 2$, $K = 3$, and $N = 138074$. Let $d = a - b$. Define $v_p(d)$ to be the largest integer $k$ such that $p^k$ divides $d$. Let $m = K - v_p(d)$ and let $p^m$ be the $m$-th power of $p$. Compute the value of $\left\lfloor \frac{N}{p^m} \right\rfloor$. | 69,037 | graphs = [
Graph(
let={
"a_val": Const(31),
"b_val": Const(11),
"p_val": Const(2),
"K_val": Const(3),
"N_val": Const(138074),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_va... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 5 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:59:43.966402Z | {
"verified": true,
"answer": 69037,
"timestamp": "2026-02-08T02:59:43.967129Z"
} | 35d2bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 392
},
"timestamp": "2026-02-09T16:52:26.413Z",
"answer": 69037
},
{
"i... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
3b6ef6 | nt_count_coprime_v1_151522320_268 | Let $n$ 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 $k$ be the number of integers $t$ such that $18\le t\le 82$ and there exist integers $a$ and $b$ with $1\le a\le 3$ and $1\le b\le 10$ satisfying
$$t=14a+4b.$$
Let $N$ be... | 46,817 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM/ONE_PHI_2",
"ONE_PHI_1"
] | c946e0 | nt_count_coprime_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"ONE_PHI_1",
"ONE_PHI_2"
] | 4 | 5.477 | 2026-02-08T03:07:01.927999Z | {
"verified": true,
"answer": 46817,
"timestamp": "2026-02-08T03:07:07.404762Z"
} | b0ef5b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 2002
},
"timestamp": "2026-02-09T01:01:43.787Z",
"answer": 46817
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
2c1058 | comb_count_permutations_fixed_v1_601307018_10072 | Let $n = \sum_{k=0}^{2} 2^k$ and define $D_n$ as the number of derangements of $n$ elements. Let $R = \binom{n}{0} \cdot D_{n}$. Find the remainder when $56983 \cdot R$ is divided by $59962$. | 53,400 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k1", start=Const(0), end=Ref("_n"), expr=Pow(Const(2), Var("k1"))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-03-10T10:34:32.350272Z | {
"verified": true,
"answer": 53400,
"timestamp": "2026-03-10T10:34:32.352545Z"
} | b375a7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 2062
},
"timestamp": "2026-04-19T12:54:51.080Z",
"answer": 53400
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
72c42f | comb_bell_compute_v1_784195855_872 | Let $x$ and $y$ be positive integers such that $x + y = 6$. Consider the set of all such ordered pairs $(x, y)$, and let $P$ be the set of products $xy$ corresponding to these pairs. Let $n$ be the maximum value in $P$. Define $Q$ to be the remainder when $15482 \cdot B_n$ is divided by $77145$, where $B_n$ denotes the... | 71,619 | graphs = [
Graph(
let={
"_n": Const(77145),
"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 | SUM_ARITHMETIC | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 6 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.014 | 2026-02-08T04:39:59.432462Z | {
"verified": true,
"answer": 71619,
"timestamp": "2026-02-08T04:39:59.446181Z"
} | 638bb8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1835
},
"timestamp": "2026-02-24T01:29:59.264Z",
"answer": 71619
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
1e13ca | algebra_poly_eval_v1_397696148_1741 | Let $b = 11$. Let $p$ range over all positive integers for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $t$ be the number of such integers $p$. Compute the remainder when $9 \cdot 11^t + 8 \cdot 11 + 2$ is multiplied by 44121 and then divided by 72020. | 20,219 | graphs = [
Graph(
let={
"b": Const(11),
"result": Sum(Mul(Const(9), Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(lef... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T12:44:04.493645Z | {
"verified": true,
"answer": 20219,
"timestamp": "2026-02-08T12:44:04.495547Z"
} | 4fc979 | 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": 1333
},
"timestamp": "2026-02-15T04:55:43.895Z",
"answer": 20219
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
619ea5 | alg_sym_quad_system_v1_1218484723_2923 | Let $m = \min\{ x + y : x > 0, y > 0,\ xy = 6441444 \}$. Find the remainder when $$\sum_{\substack{a, b, c \ge 1 \\ a^2 + b^2 + c^2 = ab + bc + ca \\ a + 9b + 2c = m}} (a^4 + b^4 + c^4)$$ is divided by $7211$. | 5,265 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Ref("_n")), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mu... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sym_quad_system_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.014 | 2026-02-25T04:40:48.704000Z | {
"verified": true,
"answer": 5265,
"timestamp": "2026-02-25T04:40:48.718180Z"
} | c7c132 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 7462
},
"timestamp": "2026-03-29T07:17:49.691Z",
"answer": 5265
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
3d6fea | diophantine_product_count_v1_898971024_2914 | Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq 81$, $x$ divides $120$, and $\frac{120}{x} \leq 81$. Let $T$ be the set of all primes between $2$ and $15959$, inclusive. Let $d$ be the smallest integer greater than or equal to $2$ that divides the number of elements in $T$. Compute the Bell num... | 5 | graphs = [
Graph(
let={
"_n": Const(15959),
"k": Const(120),
"upper": Const(81),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref... | NT | COMB | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MIN_PRIME_FACTOR"
] | cd8e34 | diophantine_product_count_v1 | bell_mod | 7 | 0 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 2 | 0.018 | 2026-02-08T17:03:10.479434Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T17:03:10.497414Z"
} | 9de333 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2858
},
"timestamp": "2026-02-17T18:37:40.179Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c75285 | nt_count_coprime_and_v1_2051736721_5700 | Let $n$ be a positive integer such that $1 \leq n \leq 44624$, $\gcd(n, 3) = 1$, and $\gcd(n, 11) = 1$. Let $A$ be the number of such integers $n$. Let $B$ be the maximum prime $p$ satisfying $2 \leq p \leq 6$. Compute the remainder when $B - A$ is divided by 82481. | 55,440 | graphs = [
Graph(
let={
"upper": Const(44624),
"k1": Const(3),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | nt_count_coprime_and_v1 | negation_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.425 | 2026-02-08T18:44:08.689946Z | {
"verified": true,
"answer": 55440,
"timestamp": "2026-02-08T18:44:13.115212Z"
} | b701c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1122
},
"timestamp": "2026-02-18T19:20:53.542Z",
"answer": 55440
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dd3de8 | geo_count_lattice_triangle_v1_717093673_2045 | Let the vertices of a triangle be $(0,0)$, $(128,99)$, and $(8,120)$. Let $A$ be twice the area of this triangle, and let $B$ be the number of lattice points on the boundary of the triangle, including the vertices. Compute $\left| \frac{A + 2 - B}{2} \right|$. Find the value of this result. | 7,279 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=120)), Mul(Const(value=8), Sub(left=Const(value=0), right=Const(value=99))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=99))), GCD(a=Abs(arg=Sub(left=Const(value=8), right=C... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T16:28:17.284765Z | {
"verified": true,
"answer": 7279,
"timestamp": "2026-02-08T16:28:17.287693Z"
} | a3cad0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1974
},
"timestamp": "2026-02-17T05:37:18.889Z",
"answer": 7279
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
c2f509 | diophantine_fbi2_min_v1_1978505735_7366 | Let $k = 72$ and let $u = 82$. Let $D$ be the set of all integers $d$ such that $7 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Let $r$ be the minimum element of $D$. Compute the remainder when $37679 \cdot r$ is divided by $99154$. | 3,970 | graphs = [
Graph(
let={
"k": Const(72),
"upper": Const(82),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(7)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3))))),
... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.021 | 2026-02-08T20:13:16.840499Z | {
"verified": true,
"answer": 3970,
"timestamp": "2026-02-08T20:13:16.861542Z"
} | 45aed0 | 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": 1047
},
"timestamp": "2026-02-19T00:07:35.124Z",
"answer": 3970
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c06551 | lin_form_endings_v1_1978505735_3549 | Let $a = 32$ and $b = 56$. Define $d = \gcd(a, b)$. Let $k = 15218$ and $M = 68956$. Compute the remainder when $k \cdot d$ is divided by $M$. | 52,788 | graphs = [
Graph(
let={
"a_coeff": Const(32),
"b_coeff": Const(56),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(15218),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(68956),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:43:02.560447Z | {
"verified": true,
"answer": 52788,
"timestamp": "2026-02-08T17:43:02.561066Z"
} | f811a5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 307
},
"timestamp": "2026-02-16T11:34:04.269Z",
"answer": 52788
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
a1c069 | algebra_quadratic_discriminant_v1_1978505735_6198 | Let $A$ be the number of positive integers $p$ such that $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Let $B$ be the number of positive integers $p_1$ such that $p_1 < q$, $p_1 q = 1350$, and $\gcd(p_1, q) = 1$. Compute the value of $\Delta = (-7)^A - 4(-1)(3)B$. Define $x = 2$ if $\Delta > 0$, and $x = 1$ if $\Delta = 0... | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": Const(-7),
"c": Const(3),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=M... | NT | null | COMPUTE | sympy | B3 | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.007 | 2026-02-08T19:28:18.832330Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T19:28:18.838970Z"
} | 001d80 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 3720
},
"timestamp": "2026-02-18T22:31:49.018Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4ba8f8 | geo_visible_lattice_v1_397696148_1522 | Let $n = 66$. A lattice point $(x, y)$ is called visible if $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $v$ be the number of visible lattice points in this range. Compute $45360 - v$. | 42,705 | graphs = [
Graph(
let={
"n": Const(66),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(45360), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 2.658 | 2026-02-08T12:36:50.467004Z | {
"verified": true,
"answer": 42705,
"timestamp": "2026-02-08T12:36:53.124870Z"
} | 715470 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T16:02:58.168Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
c3322c | nt_sum_totient_over_divisors_v1_1918700295_3722 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 10562500$. Let $n$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 6,500 | 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(10562500)))), expr=Sum(Var("x"), Var("y")))),
"result": SumO... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:50:09.614048Z | {
"verified": true,
"answer": 6500,
"timestamp": "2026-02-08T08:50:09.615511Z"
} | c0fc69 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1211
},
"timestamp": "2026-02-13T21:46:15.833Z",
"answer": 6500
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a140bf | alg_linear_system_2x2_v1_1218484723_656 | Let $\det = 17 \cdot 5 - 20 \cdot 15$, $S = 1326159 \cdot 5 - 1563450 \cdot 15$, and
$$
T = \left|\left\{ (a, b) : \begin{array}{l}
1 \le a \le \left|\left\{ (a1, b1) : 1 \le a1, b1 \le 30,\, -189a1^3 = -1512 \right\}\right|, \\
1 \le b \le 30, \\
68ab^3 + 17b^4 + 102a^2b^2 + \left|\left\{ (a2, b2) : 1 \le a2, b2 \le 4... | 77,979 | graphs = [
Graph(
let={
"_c": Const(17),
"_m": Const(3),
"_n": Const(17),
"num_x": Sub(Mul(Const(1326159), Const(5)), Mul(Const(1563450), Const(15))),
"num_y": Sub(Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), conditio... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/POLY4_COUNT",
"POLY4_COUNT/POLY4_COUNT"
] | ebb791 | alg_linear_system_2x2_v1 | null | 7 | 0 | [
"POLY3_COUNT",
"POLY4_COUNT"
] | 2 | 0.028 | 2026-02-25T02:24:11.924730Z | {
"verified": true,
"answer": 77979,
"timestamp": "2026-02-25T02:24:11.953020Z"
} | 615785 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 413,
"completion_tokens": 27785
},
"timestamp": "2026-03-28T23:43:10.194Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
a7aa2b_n | sequence_fibonacci_compute_v1_601307018_1728 | A botanist studies a plant species whose leaf count follows the Fibonacci sequence: the number of leaves on the $n$-th stem is $F_n$. On the 21st stem, there are $R = F_{21}$ leaves. Separately, a conservation team maps a forest of 30,869,135 trees and seeks the largest possible square plot (with side length $d$) such ... | 44,407 | ALG | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | d8bbcd | sequence_fibonacci_compute_v1 | quadratic_mod | 3 | null | [
"B3_CLOSEST"
] | 1 | 0.003 | 2026-03-10T02:27:59.809244Z | null | 3ed630 | a7aa2b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 14184
},
"timestamp": "2026-03-29T15:25:34.545Z",
"answer": 44407
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
ff305b | nt_min_with_divisor_count_v1_784195855_2241 | Let $U$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 69$, $1 \leq j \leq 126$, and $\gcd(i, j) = 1$. Let $n$ be the smallest positive integer such that $1 \leq n \leq U$ and $n$ has exactly 9 positive divisors. Compute the value of $32768 - n$. | 32,732 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(69)), right=IntegerRange(start=Const(1), end=Const(126))))),
... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_min_with_divisor_count_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.213 | 2026-02-08T05:37:16.018654Z | {
"verified": true,
"answer": 32732,
"timestamp": "2026-02-08T05:37:16.231219Z"
} | babaf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 3680
},
"timestamp": "2026-02-12T12:07:37.096Z",
"answer": 32732
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
86be0a | alg_poly_orbit_count_v1_601307018_3804 | Let $N = (3a^4 + a^3 - a + 5) \bmod 43$, $M = (3N^4 + N^3 - N + 5) \bmod 43$, $R = (3M^4 + M^3 - M + 5) \bmod 43$, $S = (3R^4 + R^3 - R + 5) \bmod 43$, and $T = (3S^4 + S^3 - S + 5) \bmod 43$. Find the number of non-negative integers $a$ with $0 \le a \le 40462$ such that $T = a$, $N \ne a$, $M \ne a$, $R \ne a$, and $... | 4,705 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(4))), Pow(Var("a"), Const(3)), Mul(Const(-1), Var("a")), Const(5)), modulus=Const(43)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(4))), Pow(Ref("p1"), Const(3)), Mul(Const(-1), Ref("p1")), Cons... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.05 | 2026-03-10T04:23:55.159423Z | {
"verified": true,
"answer": 4705,
"timestamp": "2026-03-10T04:23:55.209381Z"
} | 09ca06 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 9687
},
"timestamp": "2026-03-29T10:07:37.318Z",
"answer": 4705
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
e08bf6 | algebra_poly_eval_v1_1915831931_3314 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $P$. Let $d$ be the smallest positive divisor of $105875$ that is at least $c$. Compute the value of $10d^2 - 10d - 5$. | 195 | graphs = [
Graph(
let={
"_n": Const(10),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q'... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T17:32:43.150141Z | {
"verified": true,
"answer": 195,
"timestamp": "2026-02-08T17:32:43.153749Z"
} | 9404aa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1393
},
"timestamp": "2026-02-18T04:33:01.078Z",
"answer": 195
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cd3860 | nt_sum_totient_over_divisors_v1_784195855_9170 | Let $n = 37285$ and define $\text{result} = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. Compute the remainder when $$\sum_{k=1}^{123} \phi(k) \left\lfloor \frac{123}{k} \right\rfloor - \text{result}$$ is divided by $99830$. | 70,171 | graphs = [
Graph(
let={
"n": Const(37285),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Summation(var="k", start=Const(1), end=Const(123), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(123), Var("k"))))), Ref("re... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 9468ae | nt_sum_totient_over_divisors_v1 | negation_mod | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T16:34:31.852422Z | {
"verified": true,
"answer": 70171,
"timestamp": "2026-02-08T16:34:31.853499Z"
} | 64dbe5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 675
},
"timestamp": "2026-02-17T07:29:36.388Z",
"answer": 70171
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f24322 | comb_count_partitions_v1_1439011603_355 | Let $n = 45$. Let $P$ be the number of integer partitions of $n$. Let $S$ be the set of all positive integers $n_2$ such that $1 \leq n_2 \leq 95$ and $n_2 \equiv \left\lfloor \frac{n_2}{2} \right\rfloor \pmod{3}$. Let $c$ be the largest prime number that is at most the size of $S$. Compute the remainder when $c - P$ i... | 66,397 | graphs = [
Graph(
let={
"_n": Const(77750),
"n": Const(45),
"result": Partition(arg=Ref(name='n')),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("n2"), condition=A... | NT | COMB | COUNT | sympy | L3C | [
"L3C/MAX_PRIME_BELOW"
] | 5ebbb2 | comb_count_partitions_v1 | negation_mod | 7 | 0 | [
"L3C",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T15:25:29.045159Z | {
"verified": true,
"answer": 66397,
"timestamp": "2026-02-08T15:25:29.048507Z"
} | 2705d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1274
},
"timestamp": "2026-02-16T06:29:03.015Z",
"answer": 66397
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1703a3 | diophantine_fbi2_min_v1_151522320_81 | Let $k = 21$ and let $u$ be the largest prime number such that $2 \leq u \leq 32$. Find the smallest integer $d$ such that $3 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. Give the value of $d$. | 3 | graphs = [
Graph(
let={
"k": Const(21),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(32)), IsPrime(Var("n"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.024 | 2026-02-08T02:57:28.890430Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T02:57:28.914895Z"
} | 17ba33 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 326
},
"timestamp": "2026-02-10T11:58:42.298Z",
"answer": 3
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
02084d | diophantine_fbi2_min_v1_1526740231_197 | Let $n = 1225$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Determine the smallest integer $d \geq 6$ such that $d \leq s$, $d$ divides 60, and $\frac{60}{d} \geq \sum_{k=1}^{3} k$. Compute the value of $d$. | 6 | graphs = [
Graph(
let={
"_n": Const(1225),
"k": Const(60),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), e... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | dee757 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.007 | 2026-02-08T11:23:39.573936Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T11:23:39.580925Z"
} | 9b0b86 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 791
},
"timestamp": "2026-02-14T13:06:46.173Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
03dd95 | algebra_poly_eval_v1_677425708_4321 | Let $t = 6$. Let $m$ be the minimum value of $d$ over all integers $d \geq 2$ that divide $245$. Define
\[
Q = 5t^4 + 8t^3 + 6t^2 + m \cdot t - 2.
\]
Compute $57121 - Q$. | 48,669 | graphs = [
Graph(
let={
"_n": Const(57121),
"t": Const(6),
"result": Sum(Mul(Const(5), Pow(Ref("t"), Const(4))), Mul(Const(8), Pow(Ref("t"), Const(3))), Mul(Const(6), Pow(Ref("t"), Const(2))), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.006 | 2026-02-08T06:33:14.925158Z | {
"verified": true,
"answer": 48669,
"timestamp": "2026-02-08T06:33:14.931580Z"
} | fd6468 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 433
},
"timestamp": "2026-02-15T17:34:37.995Z",
"answer": 48669
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
5915c4 | v7_endings_v1_124444284_1311 | Compute
$$
\sum_{k=0}^{4119} v_2\left(\binom{4119}{k}\right),
$$
where $v_2(n)$ denotes the highest power of $2$ that divides $n$. | 28,704 | graphs = [
Graph(
let={
"total": Summation(var="k", start=Const(0), end=Const(4119), expr=MaxKDivides(target=Binom(n=Const(4119), k=Var("k")), base=Const(2))),
},
goal=Ref("total"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.008 | 2026-02-08T03:49:06.257941Z | {
"verified": true,
"answer": 28704,
"timestamp": "2026-02-08T03:49:06.265857Z"
} | 4d2c0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 4924
},
"timestamp": "2026-02-10T06:04:02.596Z",
"answer": 28704
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
13ecf2 | diophantine_fbi2_count_v1_809748730_16 | Let $k = 840$. Define $r$ to be the number of positive integers $d$ such that $3 \leq d \leq 146$, $d$ divides $k$, $$
\frac{k}{d} \geq \sum_{d'\mid 5} \phi(d'),$$ and $$
\frac{k}{d} \leq \text{the number of integers } t \text{ with } 10 \leq t \leq 308 \text{ such that } t = 6a + 4b \text{ for some integers } a, b \te... | 55,418 | graphs = [
Graph(
let={
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(146)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), SumOverDivisors(n=Const(value=5), var='d', expr=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"K3"
] | 688117 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T11:17:28.564762Z | {
"verified": true,
"answer": 55418,
"timestamp": "2026-02-08T11:17:28.574947Z"
} | d4db59 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 4249
},
"timestamp": "2026-02-14T11:36:56.839Z",
"answer": 55418
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
977c0e | sequence_count_fib_divisible_v1_601307018_289 | Let $F_n$ denote the $n$-th Fibonacci number. Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers with $1 \le x \le y$ and $xy = 35344$. Let $M$ be the number of positive integers $n$ with $1 \le n \le N$ such that $10 \mid F_n$. Find the smallest positive integer $Q$ such that ... | 36 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(35344)), Leq(Var("x"), Var("y")))), expr=Sum(Var("x"), Var("y")))),
... | NT | NT | COUNT | sympy | POLY_ORBIT_HENSEL | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"POLY_ORBIT_HENSEL"
] | 2 | 0.231 | 2026-03-10T00:50:10.853540Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-03-10T00:50:11.084849Z"
} | 01ed9f | CC BY 4.0 | null | null | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
319399 | comb_factorial_compute_v1_124444284_2192 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 7x - 3294 = 0$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-7), Var("x")), Const(-3294)), Const(0)))),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | comb_factorial_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.001 | 2026-02-08T04:30:36.481994Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T04:30:36.483055Z"
} | 2a2369 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 296
},
"timestamp": "2026-02-24T00:55:47.517Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
3a952d | comb_count_permutations_fixed_v1_124444284_1093 | Let $n = 9$ and $k = 5$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute
$$
\sum_{i=1}^{|r|} \tau(i),
$$
where $\tau(i)$ denotes the number of positive divisors of $i$. | 8,161 | graphs = [
Graph(
let={
"n": Const(9),
"k": Const(5),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Summation(var="n", start=EulerPhi(n=Const(1)), end=Abs(arg=Ref(name='result')), expr=NumDiv... | NT | COMB | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 0.001 | 2026-02-08T03:40:58.414213Z | {
"verified": true,
"answer": 8161,
"timestamp": "2026-02-08T03:40:58.415286Z"
} | 7531c2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 3194
},
"timestamp": "2026-02-09T09:33:37.468Z",
"answer": 8161
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
b297aa | alg_poly_orbit_hensel_v1_1218484723_1800 | Let $N = (2a^5 - a^4 + 4a^3 - 2) \bmod 289$ and $M = (2N^5 - N^4 + 4N^3 - 2) \bmod 289$. Find the number of non-negative integers $a$ with $0 \leq a \leq 573086$ such that $M = a$ and $N \neq a$. | 3,966 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(5))), Mul(Const(-1), Pow(Var("a"), Const(4))), Mul(Const(4), Pow(Var("a"), Const(3))), Const(-2)), modulus=Const(289)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(5))), Mul(Const(-1), Pow(Ref("p... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.033 | 2026-02-25T03:26:46.760122Z | {
"verified": true,
"answer": 3966,
"timestamp": "2026-02-25T03:26:46.792828Z"
} | 867426 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 14970
},
"timestamp": "2026-03-29T01:27:21.211Z",
"answer": 2
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
74ba3b | comb_count_surjections_v1_1978505735_4916 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 7$. Let $k = 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. | 1,800 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(nam... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T18:37:58.196530Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T18:37:58.198774Z"
} | 9e8588 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1170
},
"timestamp": "2026-02-18T18:46:40.906Z",
"answer": 1800
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
c55805 | nt_sum_gcd_range_mod_v1_124444284_2533 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1022121$. Let $k = 288$ and $M = 10903$. Define $$S = \sum_{n=1}^{N} \gcd(n, k).$$ Compute the remainder when $44121 \cdot (S \bmod M)$ is divided by $70802$. | 69,988 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1022121)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(288)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.143 | 2026-02-08T04:44:47.929070Z | {
"verified": true,
"answer": 69988,
"timestamp": "2026-02-08T04:44:48.071697Z"
} | 08ef6d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 4446
},
"timestamp": "2026-02-11T22:02:23.620Z",
"answer": 69988
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8e1de4 | alg_poly3_sum_v1_1419126231_363 | Let $S$ be the set of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 25$ such that $10a_1^2 - 18a_1b_1 + 25b_1^2 \leq 3922$. Find the remainder when $$\sum_{\substack{(a,b) \\ 1 \leq a \leq |S| \\ 1 \leq b \leq 314}} \left(-72a^3 - 132ab^2 - 120a^2b - 19b^3\right)$$ is divided by $70168$. | 49,686 | graphs = [
Graph(
let={
"_n": Const(25),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=A... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.182 | 2026-02-25T09:52:43.614505Z | {
"verified": true,
"answer": 49686,
"timestamp": "2026-02-25T09:52:43.796176Z"
} | 7d9fca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 6477
},
"timestamp": "2026-03-30T08:15:28.799Z",
"answer": 13542
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
ecacb5 | comb_bell_compute_v1_809748730_1681 | Let $n$ be the number of integers $t$ with $6 \leq t \leq 16$ for which there exist positive integers $a$ and $b$, each at most 3, such that $t = 2a + 3b + 1$. Compute the $n$th Bell number. | 21,147 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:37:33.538264Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T12:37:33.539085Z"
} | 2d3752 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1003
},
"timestamp": "2026-02-24T15:59:57.473Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
372591 | antilemma_k3_v1_1125832087_1023 | Let $n = 66254$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $Q$ be the remainder when $70019 \cdot x$ is divided by $97762$. Compute $Q$. | 36,402 | graphs = [
Graph(
let={
"_n": Const(66254),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(70019), Ref("x")), modulus=Const(97762)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:27:18.599365Z | {
"verified": true,
"answer": 36402,
"timestamp": "2026-02-08T03:27:18.600554Z"
} | a48a0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 2316
},
"timestamp": "2026-02-10T14:29:59.465Z",
"answer": 14022
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
010fc4 | nt_count_intersection_v1_2051736721_1857 | Let $N$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 200$. Let $a = 5$ and $b = 12$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. | 667 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(200)))), expr=Mul(Var("x"), Var("y")))),
"a": Const(5),
... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_intersection_v1 | null | 5 | 0 | [
"B1"
] | 1 | 2.049 | 2026-02-08T16:16:43.125712Z | {
"verified": true,
"answer": 667,
"timestamp": "2026-02-08T16:16:45.174512Z"
} | ecd996 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 931
},
"timestamp": "2026-02-17T00:13:06.257Z",
"answer": 667
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
147a00_n | comb_count_permutations_fixed_v1_1218484723_1661 | A teacher assigns 7 students to present topics, ensuring no one gets their own preferred topic. She selects one student to assign first (in $\binom{7}{1}$ ways), then assigns the remaining 6 students to topics such that none receives their own, in $D_6$ ways. Let $N$ be the total number of such assignment sequences. Co... | 64,643 | COMB | null | COUNT | sympy | ONE_BINOM_N | [
"ONE_BINOM_N"
] | 9c72e5 | comb_count_permutations_fixed_v1 | null | 2 | null | [
"ONE_BINOM_N"
] | 1 | 0.002 | 2026-02-25T03:21:51.328896Z | null | bc8048 | 147a00 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 22978
},
"timestamp": "2026-03-30T17:12:22.314Z",
"answer": 64043
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
bc189d | modular_count_residue_v1_397696148_1436 | Let $m = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 38809$ and $n \equiv 0 \pmod{m}$. Compute the number of elements in $S$. | 2,587 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(38809),
"m": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"r": Const(0),
"result": CountOverSet(set=SolutionsSet(var=Var("n... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 6 | 0 | [
"K2"
] | 1 | 2.734 | 2026-02-08T12:33:07.274656Z | {
"verified": true,
"answer": 2587,
"timestamp": "2026-02-08T12:33:10.009008Z"
} | a5f7c8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 502
},
"timestamp": "2026-02-16T03:48:00.240Z",
"answer": 2587
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
8c60de | nt_count_digit_sum_v1_1125832087_673 | Let $ T $ be the set of all integers $ t $ such that $ 26 \leq t \leq 51 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 5 $, $ 1 \leq b \leq 4 $, and $ t = 4a + 3b + 19 $. Let $ s $ be the number of elements in $ T $. Let $ N $ be the number of positive integers $ n $ such that $ 1 \leq n \leq... | 20,086 | graphs = [
Graph(
let={
"upper": Const(398161),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 33.136 | 2026-02-08T03:11:59.867237Z | {
"verified": true,
"answer": 20086,
"timestamp": "2026-02-08T03:12:33.003122Z"
} | 637963 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 6242
},
"timestamp": "2026-02-10T13:03:23.689Z",
"answer": 20086
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.