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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
d476f8 | sequence_count_fib_divisible_v1_1520064083_6020 | Let $m=24$ and $M=36514$. For each positive integer $n\le 15480$, consider the Fibonacci number $F_n$, where $F_1=1$, $F_2=1$, and $F_{n+2}=F_{n+1}+F_n$ for all $n\ge1$. Let $A$ be the number of positive integers $n\le15480$ such that $m$ divides $F_n$.
Let $U$ be the number of integers $n$ with $1\le n\le A$ such tha... | 437 | graphs = [
Graph(
let={
"_m": Const(24),
"_n": Const(36514),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(15... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/L3B"
] | e4b8e4 | sequence_count_fib_divisible_v1 | null | 8 | 0 | [
"COUNT_FIB_DIVISIBLE",
"L3B"
] | 2 | 0.03 | 2026-02-08T07:47:59.183520Z | {
"verified": true,
"answer": 437,
"timestamp": "2026-02-08T07:47:59.213169Z"
} | ea4244 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 4264
},
"timestamp": "2026-02-13T12:53:53.143Z",
"answer": 437
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
0a282a | modular_count_residue_v1_1520064083_10125 | Let $n$ be a positive integer such that $1 \leq n \leq 219$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $m$ be the number of such integers $n$.
Let $r$ be the smallest divisor greater than or equal to 2 of 875.
Now consider all positive integers $n$ such that $1 \leq n \leq 45360$ and $n \equ... | 2,388 | graphs = [
Graph(
let={
"_n": Const(219),
"upper": Const(45360),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulu... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"L3C"
] | 156825 | modular_count_residue_v1 | null | 6 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 3.388 | 2026-02-08T11:12:48.443234Z | {
"verified": true,
"answer": 2388,
"timestamp": "2026-02-08T11:12:51.830833Z"
} | eda21f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1124
},
"timestamp": "2026-02-14T10:50:51.804Z",
"answer": 2388
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
090ddd | nt_max_prime_below_v1_151522320_2123 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $P$. Let $S$ be the set of all prime numbers $n$ such that $k \le n \le 32041$. Determine the value of the largest element in $S$. | 32,029 | graphs = [
Graph(
let={
"upper": Const(32041),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.764 | 2026-02-08T04:36:52.913949Z | {
"verified": true,
"answer": 32029,
"timestamp": "2026-02-08T04:36:53.677538Z"
} | 7dc500 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 4282
},
"timestamp": "2026-02-11T21:38:25.744Z",
"answer": 32029
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
8a8424 | antilemma_k3_v1_1978505735_5950 | Let $n = 24245$. Define $x = \sum_{d \mid n} \phi(d)$, where $\phi(d)$ is the number of positive integers at most $d$ that are relatively prime to $d$. Compute the remainder when $45175 \cdot x$ is divided by $66762$. Find the value of this remainder. | 37,265 | graphs = [
Graph(
let={
"_n": Const(24245),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(45175), Ref("x")), modulus=Const(66762)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T19:21:02.202710Z | {
"verified": true,
"answer": 37265,
"timestamp": "2026-02-08T19:21:02.203697Z"
} | a06f6a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 3831
},
"timestamp": "2026-02-18T21:56:41.967Z",
"answer": 37265
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"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
} | ||
e467bc | nt_sum_totient_over_divisors_v1_898971024_1628 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 7868025$. Define $n$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Let $r$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute the remainder when $338... | 35,310 | graphs = [
Graph(
let={
"_n": Const(95403),
"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(7868025)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T16:12:43.949800Z | {
"verified": true,
"answer": 35310,
"timestamp": "2026-02-08T16:12:43.954574Z"
} | 06316c | 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": 6681
},
"timestamp": "2026-02-16T23:37:55.935Z",
"answer": 35310
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
270a2d | comb_bell_compute_v1_1439011603_2921 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \le j \le 8272$ and
$$
\binom{\left| \left\{ n_1 \in \mathbb{Z}^+ \mid 1 \le n_1 \le 165440 \text{ and } 15 \text{ divides } F_{n_1} \right\} \right|}{j} \equiv 1 \pmod{2}.
$$
Let $n$ be the number of elements in $S$. Let $B_n$ denote the $n$th Bell number... | 36,321 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8272)), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(1... | COMB | NT | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/V8"
] | 82a267 | comb_bell_compute_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"V8"
] | 2 | 0.004 | 2026-02-08T17:05:38.987400Z | {
"verified": true,
"answer": 36321,
"timestamp": "2026-02-08T17:05:38.991486Z"
} | 49acfb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1945
},
"timestamp": "2026-02-17T19:13:01.124Z",
"answer": 36321
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
382421 | comb_binomial_compute_v1_865884756_5001 | Let $a = 3$ and $b = 2$. Define $n_2 = a + b$. Let
$$
f = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}.
$$
Let $n_1 = 11$ and define
$$
e = \sum_{k_2=0}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}.
$$
Let $n = 15$ and $k = 6 + e$. Define $\text{result} = \binom{n}{k}$. Compute the remainder when $79410 \cdot \text{result}$ is ... | 21,375 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(2),
"n2": Sum(Ref("a"), Ref("b")),
"f": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Const(11),
"e": Su... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_binomial_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T18:19:10.053176Z | {
"verified": true,
"answer": 21375,
"timestamp": "2026-02-08T18:19:10.055346Z"
} | 714826 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 2096
},
"timestamp": "2026-02-18T16:11:36.881Z",
"answer": 21375
},
... | 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": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
a5c9db | comb_binomial_compute_v1_865884756_5490 | Let $n$ be the number of integers $t$ with $7 \leq t \leq 22$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 6$, and $t = 5a + 2b$.
Let $r = \binom{n}{6}$. Find the value of the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|r| + 2$. | 1,392 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:38:26.556097Z | {
"verified": true,
"answer": 1392,
"timestamp": "2026-02-08T18:38:26.557926Z"
} | e34b74 | 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": 3343
},
"timestamp": "2026-02-18T18:41:01.139Z",
"answer": 1392
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f704b8 | antilemma_cartesian_v1_784195855_4143 | Compute the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 28$ and $1 \leq j \leq 32$. | 896 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), end=Const(32)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T06:52:21.947664Z | {
"verified": true,
"answer": 896,
"timestamp": "2026-02-08T06:52:21.948148Z"
} | e98e22 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 124
},
"timestamp": "2026-02-24T07:12:53.034Z",
"answer": 896
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
454c9d | geo_visible_lattice_v1_1520064083_62 | Let $n = 144$, and let $r$ be the number of ordered pairs of integers $(x, y)$ such that $1 \leq x, y \leq 144$ and $\gcd(x, y) = 1$. Let $Q = (360 - r) \bmod 98467$. Find the value of $Q$. | 86,168 | graphs = [
Graph(
let={
"n": Const(144),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Sub(Const(360), Ref("result")), modulus=Const(98467)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.661 | 2026-02-08T02:58:35.773234Z | {
"verified": true,
"answer": 86168,
"timestamp": "2026-02-08T02:58:36.434709Z"
} | 114195 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 7599
},
"timestamp": "2026-02-23T21:04:53.503Z",
"answer": 86136
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
28dc6a | alg_poly_orbit_count_v1_1218484723_1524 | Let $N \equiv a^3 + 3a^2 + 3a \pmod{89}$ and $M \equiv N^3 + 3N^2 + 3N \pmod{89}$. Find the number of non-negative integers $a$ with $0 \le a \le 62299$ such that $M = a$ and $N \ne a$. | 4,200 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(3), Pow(Var("a"), Const(2))), Mul(Const(3), Var("a"))), modulus=Const(89)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(3), Pow(Ref("p1"), Const(2))), Mul(Const(3), Ref("p1"))), modulus=Const(8... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.013 | 2026-02-25T03:13:23.137684Z | {
"verified": true,
"answer": 4200,
"timestamp": "2026-02-25T03:13:23.150635Z"
} | 92636b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 9262
},
"timestamp": "2026-03-10T04:34:30.140Z",
"answer": 6
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
e61dfc | comb_count_permutations_fixed_v1_153355830_1049 | Let $n$ be the number of integers $t$ such that $21 \leq t \leq 60$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 2$, and
$$
t = 6a + 15b.
$$
Let $k = 7$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. | 240 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:22:08.884970Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T04:22:08.886422Z"
} | 4b4920 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 888
},
"timestamp": "2026-02-24T00:15:05.664Z",
"answer": 240
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
a05460 | comb_factorial_compute_v1_1440796553_1150 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 617400$. Compute the remainder when $44121 \cdot n!$ is divided by $52615$. | 45,570 | graphs = [
Graph(
let={
"_n": Const(52615),
"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=617400)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T12:12:21.807112Z | {
"verified": true,
"answer": 45570,
"timestamp": "2026-02-08T12:12:21.808104Z"
} | c9896a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 3984
},
"timestamp": "2026-02-14T23:05:44.025Z",
"answer": 45570
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4ff1f3 | diophantine_fbi2_count_v1_458359167_3978 | Let $d = 6$, $m = 64229$, and $c = 67383$. Let $n$ be the number of integers $t$ such that $31 \leq t \leq 325$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 40$, and $t = 15a + 6b + 10$. Let $k$ be the number of positive integers from 1 to 14280 that are divisible by 17. Define $r$ to be ... | 50,464 | graphs = [
Graph(
let={
"_d": Const(6),
"_m": Const(64229),
"_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... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/VIETA_SUM",
"C2"
] | de4057 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"C2",
"LIN_FORM",
"VIETA_SUM"
] | 3 | 0.016 | 2026-02-08T11:27:42.595416Z | {
"verified": true,
"answer": 50464,
"timestamp": "2026-02-08T11:27:42.611186Z"
} | 1df2ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 3644
},
"timestamp": "2026-02-14T14:26:53.600Z",
"answer": 50464
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemm... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
15ffd0 | comb_count_surjections_v1_124444284_6481 | Let $n_2$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3\}$. Define
$$
s = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 0$ and define
$$
v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 5 \cdot v$ and $k = 2$. Define
$$
\text{result} = k! \cdot S(n, k),
$$
where... | 59,007 | graphs = [
Graph(
let={
"_n": Const(5),
"n2": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"s": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), B... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING"
] | d0de27 | comb_count_surjections_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | 2 | 0.004 | 2026-02-08T08:28:48.931590Z | {
"verified": true,
"answer": 59007,
"timestamp": "2026-02-08T08:28:48.935449Z"
} | 3cc456 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 773
},
"timestamp": "2026-02-24T09:34:37.295Z",
"answer": 59007
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"s... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
2518cb | nt_count_digit_sum_v1_898971024_2373 | Let $u$ be the number of positive integers $n$ such that $n \leq 23329$ and $\gcd(n, 14) = 1$. Determine the number of positive integers $n_1$ such that $n_1 \leq u$ and the sum of the decimal digits of $n_1$ is 20. Let this number be $r$. Find the remainder when $44121 \cdot r$ is divided by $66620$. | 14,813 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(23329)), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"target_sum": Const(20),
"result": CountOverSet(... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.404 | 2026-02-08T16:42:40.737567Z | {
"verified": true,
"answer": 14813,
"timestamp": "2026-02-08T16:42:41.141999Z"
} | 26fc59 | 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": 2408
},
"timestamp": "2026-02-17T09:48:19.983Z",
"answer": 14813
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5ca7d2 | nt_min_coprime_above_v1_717093673_180 | Let $T$ be the set of all integers $t$ such that $34 \leq t \leq 3176$ and $t = 8a + 14b + 12$ for some positive integers $a \leq 28$ and $b \leq 210$. Let $N$ be the number of elements in $T$. Let $u$ be the largest prime number at most $N$. Find the smallest integer $n_1 > 1260$ such that $n_1 \leq u$ and $\gcd(n_1, ... | 9,213 | graphs = [
Graph(
let={
"start": Const(1260),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.077 | 2026-02-08T15:14:00.723022Z | {
"verified": true,
"answer": 9213,
"timestamp": "2026-02-08T15:14:00.799839Z"
} | c58006 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 7291
},
"timestamp": "2026-02-16T01:39:30.210Z",
"answer": 9213
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c0ac37 | comb_bell_compute_v1_677425708_2913 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 15$ for which there exist positive integers $a \leq 3$ and $b \leq 3$ such that $t = 2a + 3b$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of size $n$. Compute the remainder when $44121 \times B_n$ is divided by $83053... | 9,385 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T05:22:41.567727Z | {
"verified": true,
"answer": 9385,
"timestamp": "2026-02-08T05:22:41.571720Z"
} | cf5289 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2321
},
"timestamp": "2026-02-24T03:18:31.289Z",
"answer": 9385
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
19f16d | antilemma_sum_primes_v1_677425708_3310 | Let $x$ be the sum of all prime numbers $n$ such that $2 \leq n \leq 3$. Compute the value of $2^{|x|} + 3969$ modulo $99991$. | 4,001 | graphs = [
Graph(
let={
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3)), IsPrime(Var("n"))))),
"_c": Const(3969),
"Q": Sum(ModExp(base=Const(2), exp=Abs(arg=Ref(name='x')), mod=Const(99991)), Ref("_c")),
... | NT | null | COMPUTE | sympy | SUM_PRIMES | [
"SUM_PRIMES"
] | 83231d | antilemma_sum_primes_v1 | null | 3 | 0 | [
"SUM_PRIMES"
] | 1 | 0.001 | 2026-02-08T05:39:00.114617Z | {
"verified": true,
"answer": 4001,
"timestamp": "2026-02-08T05:39:00.115762Z"
} | 455ec2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 248
},
"timestamp": "2026-02-18T18:19:13.572Z",
"answer": 4001
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
}
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
d35b57 | diophantine_product_count_v1_784195855_3845 | Let $k = 120$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1296$. For each such pair, compute $x + y$, and let $s$ be the minimum value of $x + y$ over all such pairs.
Now consider the set of all positive integers $x$ such that $1 \leq x \leq s$, $x$ divides $k$, and $\frac{k}{x}... | 8,635 | graphs = [
Graph(
let={
"_n": Const(186),
"k": Const(120),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1296)))),... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | 2cc80e | diophantine_product_count_v1 | negation_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.007 | 2026-02-08T06:39:55.746075Z | {
"verified": true,
"answer": 8635,
"timestamp": "2026-02-08T06:39:55.752853Z"
} | d8f893 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1408
},
"timestamp": "2026-02-13T03:04:18.063Z",
"answer": 8635
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": ... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
6af525 | antilemma_k3_v1_898971024_2940 | Let $n = 26084$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $c = 43784$. Compute the remainder when $c \cdot x$ is divided by $73383$. | 2,227 | graphs = [
Graph(
let={
"_n": Const(26084),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(43784),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(73383)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:04:46.754724Z | {
"verified": true,
"answer": 2227,
"timestamp": "2026-02-08T17:04:46.755396Z"
} | 9ccc16 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1861
},
"timestamp": "2026-02-17T18:40:41.712Z",
"answer": 2227
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
28eeac | comb_bell_compute_v1_1218484723_7290 | Let $B_n$ denote the $n$-th Bell number. Let $n$ be the number of integers $a$ with $0 \le a \le 4912$ such that
\[
\Big(\big((a^{3} \bmod 4913)^{3} \bmod 4913\big)^{3} \bmod 4913\Big)^{3} \bmod 4913 = a,
\]
while simultaneously
\[
a^{3} \bmod 4913 \ne a,
\]
\[
(a^{3} \bmod 4913)^{3} \bmod 4913 \ne a,
\]
\[
\big((a^{3}... | 21,120 | graphs = [
Graph(
let={
"_n": Const(4913),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(4912)), Eq(Mod(value=Pow(Mod(value=Pow(Mod(value=Pow(Mod(value=Pow(Var("a"), Const(3)), modulus=Const(4913)), Const(3)), modulus=Cons... | COMB | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_bell_compute_v1 | null | 8 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.002 | 2026-02-25T08:43:47.727486Z | {
"verified": true,
"answer": 21120,
"timestamp": "2026-02-25T08:43:47.729588Z"
} | 940a68 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T03:46:32.714Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
3d118f | nt_min_with_divisor_count_v1_168721529_1135 | Let $d_0$ be the smallest divisor of $2431$ that is at least $2$. Let $u$ be the largest integer $k$ such that $d_0^k$ divides $56265!$. Let $n_0$ be the smallest positive integer $n \leq u$ that has exactly $2$ positive divisors. Compute the remainder when $82147 \cdot n_0$ is divided by $79836$. | 4,622 | graphs = [
Graph(
let={
"_n": Const(56265),
"upper": MaxKDivides(target=Factorial(Ref("_n")), base=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2431)))))),
"div_count": Const(2),
"res... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/V1"
] | 8d33be | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"V1"
] | 2 | 0.231 | 2026-02-08T13:29:29.140592Z | {
"verified": true,
"answer": 4622,
"timestamp": "2026-02-08T13:29:29.371864Z"
} | 8a37ed | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2171
},
"timestamp": "2026-02-10T02:32:12.782Z",
"answer": 4622
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok_later"... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.92
} | ||
df2ac3 | alg_poly4_sum_v1_601307018_8173 | Let $M = \sum_{k=0}^{3} (2k + 29)$. Compute the remainder when $$\sum_{\substack{1 \leq a \leq M \\ 1 \leq b \leq 128}} \min\left\{ |x - y| : x, y > 0,\, xy = 13695 \right\} \cdot a^{4} + 82b^{4} - 328a^{3}b - 328ab^{3} + 492a^{2}b^{2}$$ is divided by $71285$. | 25,452 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Summation(var="k", start=Const(0), end=Const(3), expr=Sum(Mul(Ref("_m"), Var("k")), Const(29))),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a... | ALG | null | COMPUTE | sympy | SUM_AP | [
"SUM_AP/B3_DIFF"
] | f58eb0 | alg_poly4_sum_v1 | null | 7 | 0 | [
"B3_DIFF",
"SUM_AP"
] | 2 | 0.075 | 2026-03-10T08:40:48.490632Z | {
"verified": true,
"answer": 25452,
"timestamp": "2026-03-10T08:40:48.565698Z"
} | 447100 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 7214
},
"timestamp": "2026-04-19T08:25:13.634Z",
"answer": 25452
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
a1ac8a | antilemma_k3_v1_1125832087_1262 | Let $n = 77671$. Compute $\sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. | 77,671 | graphs = [
Graph(
let={
"_n": Const(77671),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:39:04.689733Z | {
"verified": true,
"answer": 77671,
"timestamp": "2026-02-08T03:39:04.690304Z"
} | 197d0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 299
},
"timestamp": "2026-02-10T15:11:37.621Z",
"answer": 77671
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
07d527 | geo_count_lattice_rect_v1_349078426_265 | A rectangle in the coordinate plane has vertices at $(0,0)$, $(19,0)$, $(0,59)$, and $(19,59)$. Compute the number of lattice points that lie inside or on the boundary of this rectangle. Let $Q$ be $2437$ times this number. Find the remainder when $Q$ is divided by $50224$. | 11,408 | graphs = [
Graph(
let={
"a": Const(19),
"b": Const(59),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(2437),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(50224)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T12:54:38.350602Z | {
"verified": true,
"answer": 11408,
"timestamp": "2026-02-08T12:54:38.352449Z"
} | b5ed05 | 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": 702
},
"timestamp": "2026-02-24T16:36:50.110Z",
"answer": 11408
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
7fce86 | comb_count_derangements_v1_153355830_72 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 61740$. Let $Q$ be the remainder when $!n \cdot 44121$ is divided by $98180$, where $!n$ denotes the subfactorial of $n$. Compute $Q$. | 77,093 | graphs = [
Graph(
let={
"_n": Const(44121),
"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=61740)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T02:52:59.489174Z | {
"verified": true,
"answer": 77093,
"timestamp": "2026-02-08T02:52:59.491227Z"
} | c2fa18 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 4630
},
"timestamp": "2026-02-23T17:31:19.845Z",
"answer": 77093
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": 2.18,
"mid": 4.01,
"hi": 5.72
} | ||
65d31f | antilemma_sum_primes_v1_1918700295_41 | Let $n$ be an integer satisfying $2 \leq n \leq d$, where $d$ is the smallest divisor of $2205$ that is at least $2$. Suppose $n$ is prime. Let $x$ be the sum of all such integers $n$.
Let $Q$ be the remainder when $44121 \cdot x$ is divided by $79367$.
Compute $Q$. | 61,871 | graphs = [
Graph(
let={
"_n": Const(79367),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2205)))))), IsPrim... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/SUM_PRIMES",
"SUM_PRIMES"
] | 58b99d | antilemma_sum_primes_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_PRIMES"
] | 2 | 0.001 | 2026-02-08T02:57:31.240645Z | {
"verified": true,
"answer": 61871,
"timestamp": "2026-02-08T02:57:31.241806Z"
} | ac119b | 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": 586
},
"timestamp": "2026-02-08T22:00:30.807Z",
"answer": 61871
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
ffe818 | nt_count_divisible_and_v1_865884756_2552 | Let $S$ be the set of all integers $t$ with $5 \le t \le 12$ that can be expressed as $2a + 3b$ for positive integers $a \in \{1,2,3\}$ and $b \in \{1,2\}$. Let $d_1$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = |S|$. Let $d_2 = 12$. Determine the number of positi... | 2,922 | graphs = [
Graph(
let={
"upper": Const(105192),
"d1": 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")), CountOverSet(set=SolutionsSet(var=Var("t"... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 3.587 | 2026-02-08T16:49:23.431283Z | {
"verified": true,
"answer": 2922,
"timestamp": "2026-02-08T16:49:27.018203Z"
} | 5c8db0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 708
},
"timestamp": "2026-02-16T07:54:06.684Z",
"answer": 2922
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"le... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
60fa6d | geo_count_lattice_rect_v1_1439011603_2617 | Let $a = 196$ and $b = 82$. Define a lattice point as a point in the plane with integer coordinates. Consider the rectangle consisting of all points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points contained in this rectangle. | 16,351 | graphs = [
Graph(
let={
"a": Const(196),
"b": Const(82),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T16:53:05.796784Z | {
"verified": true,
"answer": 16351,
"timestamp": "2026-02-08T16:53:05.798739Z"
} | 42e7d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 410
},
"timestamp": "2026-02-17T14:20:02.613Z",
"answer": 16351
},
{... | 1 | [] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||||
cfb5c1 | nt_count_coprime_and_v1_124444284_10200 | Let $k_1$ be the largest prime number $n$ such that $2 \leq n \leq 5$, and let $k_2 = 7$. Let $\text{result}$ be the number of positive integers $n$ not exceeding 17300 such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Compute $\text{result} + \varphi(|\text{result}| + 1) + \tau(|\text{result}| + 1)$, where $\varphi... | 17,799 | graphs = [
Graph(
let={
"upper": Const(17300),
"k1": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"k2": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.883 | 2026-02-08T12:52:39.344629Z | {
"verified": true,
"answer": 17799,
"timestamp": "2026-02-08T12:52:41.227969Z"
} | bf1df2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1416
},
"timestamp": "2026-02-15T06:29:55.898Z",
"answer": 17799
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
17fac0 | nt_count_intersection_v1_865884756_6621 | Let $N = 50000$. Compute the number of positive integers $n \leq N$ such that $9$ divides $n$ and $\gcd(n, 14) = 1$. Let $c$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 178$. Find the value of $c - n$. | 5,540 | graphs = [
Graph(
let={
"N": Const(50000),
"a": Const(9),
"b": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=R... | NT | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | nt_count_intersection_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 1.561 | 2026-02-08T19:19:56.425859Z | {
"verified": true,
"answer": 5540,
"timestamp": "2026-02-08T19:19:57.987141Z"
} | 9f4cb1 | 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": 1388
},
"timestamp": "2026-02-18T21:58:48.790Z",
"answer": 5540
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4e9c6a | nt_sum_divisors_range_v1_1978505735_725 | Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 8000$. Compute the sum of $\tau(n)$ over all $n \in S$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 73,147 | graphs = [
Graph(
let={
"upper": Const(8000),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")))), expr=NumDivisors(n=Var("n")))),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME"
] | 60ba20 | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 0.945 | 2026-02-08T15:34:29.951918Z | {
"verified": true,
"answer": 73147,
"timestamp": "2026-02-08T15:34:30.896913Z"
} | a85eba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 3746
},
"timestamp": "2026-02-16T08:18:13.532Z",
"answer": 73147
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
149356 | comb_factorial_compute_v1_1440796553_682 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Compute $n!$. Let $d_i$ denote the $i$th decimal digit of this factorial (starting from the units digit as $i=0$). Let $k$ be the number of digits in this factorial minus $\binom{7}{7}$. Compute $$\sum_{i=0}^{k} d_i... | 50,721 | graphs = [
Graph(
let={
"_n": Const(2),
"n2": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"w": Summation(var="k", start=Const(0), end=Ref("n1"... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N",
"COMB1"
] | 894a8c | comb_factorial_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"ONE_BINOM_N"
] | 3 | 0.005 | 2026-02-08T11:55:17.013576Z | {
"verified": true,
"answer": 50721,
"timestamp": "2026-02-08T11:55:17.018410Z"
} | 63fa93 | 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": 825
},
"timestamp": "2026-02-24T15:00:30.528Z",
"answer": 50721
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
863389 | nt_min_coprime_above_v1_1520064083_1234 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 5$, $25 \leq t \leq 97$, and $t = 8a + 10b + 7$. Let $m$ be the number of elements in $S$. Let $n$ be the smallest integer such that $55555 < n \leq 55590$ and $\gcd(n, m) = 1$. Compute the remainder... | 55,556 | graphs = [
Graph(
let={
"start": Const(55555),
"upper": Const(55590),
"modulus": 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(n... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T03:52:22.324362Z | {
"verified": true,
"answer": 55556,
"timestamp": "2026-02-08T03:52:22.330876Z"
} | b16ef7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1308
},
"timestamp": "2026-02-10T16:04:12.147Z",
"answer": 55556
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
2d3cfb | comb_count_partitions_v1_397696148_1350 | Let $a = 2$ and $b = 1$. Define $n_2 = a + b$. Let
$$
m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Set $n_1 = m$, and define
$$
c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 41c$. Compute the number of integer partitions of $n$. | 44,583 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(1),
"n2": Sum(Ref("a"), Ref("b")),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("m"),
"c": Summat... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T12:31:18.992140Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T12:31:18.993048Z"
} | afb3a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 778
},
"timestamp": "2026-02-24T15:43:29.032Z",
"answer": 44583
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
ec2900 | sequence_lucas_compute_v1_1978505735_4285 | Let $d=66166$. Let $M$ be the number of positive integers $k$ with $1\le k\le 8640$ such that $27$ divides $k$.
For each integer $t$, suppose there exist integers $a$ and $b$ such that $1\le a\le 40$, $1\le b\le 2$, $7\le t\le 90$, and
$$t=2a+5b.$$
Let $N$ be the number of integers $t$ for which such integers $a$ and ... | 2,887 | graphs = [
Graph(
let={
"_d": Const(66166),
"_m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(8640)), Divides(divisor=Const(27), dividend=Var("k"))), domain='positive_integers')),
"_n": CountOverSet(set=SolutionsS... | NT | null | COMPUTE | sympy | C2 | [
"C2/LIN_FORM/MAX_DIVISOR/SUM_DIVISIBLE"
] | 33456a | sequence_lucas_compute_v1 | negation_mod | 7 | 0 | [
"C2",
"LIN_FORM",
"MAX_DIVISOR",
"SUM_DIVISIBLE"
] | 4 | 0.008 | 2026-02-08T18:08:36.587546Z | {
"verified": true,
"answer": 2887,
"timestamp": "2026-02-08T18:08:36.595525Z"
} | e6daee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 3384
},
"timestamp": "2026-02-18T14:35:45.222Z",
"answer": 2887
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
08fe03 | nt_num_divisors_compute_v1_865884756_1389 | Let $S$ be the set of all nonnegative integers $j$ such that $j \geq \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, $j \leq 10921$, and $\binom{10921}{j} \equiv 1 \pmod{2}$. Let $n$ be the number of elements in $S$. Compute the number of positive divisors of $n$. | 8 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Const(0), end=Const(7), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(7), k=Var("k"))))), Leq(Var("j"), Const(10921)), Eq(Mod(value=Binom(n... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"V8"
] | efe7d7 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"V8"
] | 2 | 0.003 | 2026-02-08T16:00:09.452999Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T16:00:09.455570Z"
} | 5d29f1 | 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": 1205
},
"timestamp": "2026-02-16T19:59:47.309Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bc6be8 | nt_sum_divisors_mod_v1_124444284_8747 | Let $n = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11597$. | 360 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"M": Const(11597),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"),... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T11:53:31.345258Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T11:53:31.346435Z"
} | 031574 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1502
},
"timestamp": "2026-02-14T20:16:57.117Z",
"answer": 360
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bb7e97 | alg_telescope_v1_1218484723_2504 | Let $s = \min\{x + y : x, y \in \mathbb{Z}^+, xy = 851929\}$. Let $T$ be the set of integers $t$ for which there exist integers $a, b$ with $1 \le a \le 815$, $1 \le b \le 1098$, $t = 5a + 2b + 18$, and $25 \le t \le 6289$. Let $N = |T|$. Define $M = \left( \sum_{k=0}^{s} \left((k+1)^2 - k^2\right) \right) \bmod N$. Fi... | 55,300 | graphs = [
Graph(
let={
"_n": Const(28816),
"result": Mod(value=Summation(var="k", start=Const(0), end=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... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | alg_telescope_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.095 | 2026-02-25T04:16:04.491388Z | {
"verified": true,
"answer": 55300,
"timestamp": "2026-02-25T04:16:04.586711Z"
} | 5376b9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:09:15.860Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
ace2af | algebra_quadratic_discriminant_v1_124444284_4137 | Let $a = 1$, $b = -5$, and $c = 11$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 600$, $\gcd(p, q) = 1$, and $p < q$. Let $r = b^2 - 4ac \cdot |S|$. Compute the Bell number $B_k$, where $k$ is the absolute value of $r$ modulo $11$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(11),
"a": Const(1),
"b": Const(-5),
"c": Const(11),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), co... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T05:48:37.064467Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T05:48:37.067172Z"
} | b0f4bb | 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": 1337
},
"timestamp": "2026-02-12T14:27:00.787Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a12cb7 | modular_modexp_compute_v1_458359167_390 | Let $n = 2$. Let $a$ be the smallest divisor $d$ of $36$ such that $d \geq n$. Let $e$ be the number of integers $t$ in the range $20 \leq t \leq 1610$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 252$, $1 \leq b \leq 7$, and $t = 6a + 14b$. Let $m = 58564$. Compute the remainder when $a^e$ i... | 36,228 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(36))))),
"e": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | modular_modexp_compute_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T03:15:35.816193Z | {
"verified": true,
"answer": 36228,
"timestamp": "2026-02-08T03:15:35.818766Z"
} | 23772a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 6537
},
"timestamp": "2026-02-10T13:08:40.375Z",
"answer": 36228
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d14684 | nt_sum_totient_over_divisors_v1_458359167_853 | Let $n = 99592$ and $m = 62655$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 24373969$. Let $s$ be the minimum value of $x + y$ over all such pairs.
Let $r = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's toti... | 1,183 | graphs = [
Graph(
let={
"_n": Const(62655),
"n": Const(99592),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditio... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | e0298c | nt_sum_totient_over_divisors_v1 | affine_mod | 6 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T03:34:15.749818Z | {
"verified": true,
"answer": 1183,
"timestamp": "2026-02-08T03:34:15.753779Z"
} | df92b1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1427
},
"timestamp": "2026-02-10T15:34:23.315Z",
"answer": 1183
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
caff71 | comb_factorial_compute_v1_677425708_2305 | Let $n = 8$ and $r = n!$. Let $s = \sum_{k=1}^{6} k$. Compute the remainder when $s - r$ is divided by $73788$. | 33,489 | graphs = [
Graph(
let={
"n": Const(8),
"result": Factorial(Ref("n")),
"Q": Mod(value=Sub(Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")), Ref("result")), modulus=Const(73788)),
},
goal=Ref("Q"),
)
] | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | 5c63b0 | comb_factorial_compute_v1 | negation_mod | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T04:59:50.533797Z | {
"verified": true,
"answer": 33489,
"timestamp": "2026-02-08T04:59:50.535174Z"
} | 66f903 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 397
},
"timestamp": "2026-02-24T02:28:33.336Z",
"answer": 33489
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
e1a556 | antilemma_k2_v1_48377204_400 | Let $ n = 205 $. Compute the value of
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$ | 21,115 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(205), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(205), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.003 | 2026-02-08T15:25:37.775949Z | {
"verified": true,
"answer": 21115,
"timestamp": "2026-02-08T15:25:37.778579Z"
} | 171246 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 829
},
"timestamp": "2026-02-16T05:53:26.310Z",
"answer": 21115
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aabd13 | diophantine_sum_product_min_v1_579913215_66 | Let $S = 9$ and $P = 8$. Let $x$ be a positive integer such that $1 \leq x \leq N$, where $N$ is the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 9450$ and $\gcd(p, q) = 1$. Suppose $x(S - x) = P$. Let $r$ be the smallest such $x$ satisfying these conditions. Define ... | 6,001 | graphs = [
Graph(
let={
"_n": Const(2),
"S": Const(9),
"P": Const(8),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p'... | NT | null | EXTREMUM | sympy | K3 | [
"K3",
"COPRIME_PAIRS"
] | c33e96 | diophantine_sum_product_min_v1 | digits_weighted_mod | 6 | 0 | [
"COPRIME_PAIRS",
"K3"
] | 2 | 0.013 | 2026-02-08T12:50:38.106177Z | {
"verified": true,
"answer": 6001,
"timestamp": "2026-02-08T12:50:38.119349Z"
} | 4147ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 2060
},
"timestamp": "2026-02-15T06:12:05.614Z",
"answer": 6001
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
3def8a | sequence_count_fib_divisible_v1_1520064083_357 | Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_{n} = F_{n-1} + F_{n-2}$ for $n \geq 3$. Let $u$ be the number of positive integers $n \leq 10152$ such that $12$ divides $F_n$. Let $r$ be the number of positive integers $n \leq u$ such that $3$ divides $F_n$. Compute $r$. | 211 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(10152)), Divides(divisor=Const(12), dividend=Fibonacci(arg=Var(name='n')))))),
"d": Const(3),
"result": CountOverSet(set=SolutionsSet(va... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.036 | 2026-02-08T03:16:54.655845Z | {
"verified": true,
"answer": 211,
"timestamp": "2026-02-08T03:16:54.691999Z"
} | 4e6864 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2128
},
"timestamp": "2026-02-10T13:51:12.978Z",
"answer": 211
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
aa7474 | nt_count_intersection_v1_1520064083_2325 | Let $m = 22$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $n$ be the maximum value of $xy$ over all such pairs.
Now consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Let $b$ be the minimum value of $x + y$ over all such pairs.
Dete... | 7,575 | graphs = [
Graph(
let={
"_m": Const(22),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_intersection_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 2.317 | 2026-02-08T04:39:01.519075Z | {
"verified": true,
"answer": 7575,
"timestamp": "2026-02-08T04:39:03.836000Z"
} | 7e4f56 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 2095
},
"timestamp": "2026-02-11T16:11:57.033Z",
"answer": 7575
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3d3d9e | geo_count_lattice_rect_v1_1218484723_7521 | Let $a = \sum_{k=0}^{2} 10^k$. Find the number of lattice points $(x, y)$ with $0 \le x \le a$ and $0 \le y \le 45$, and compute the remainder when $44121$ times this number is divided by $59923$. | 23,453 | graphs = [
Graph(
let={
"_n": Const(59923),
"a": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Const(10), Var("k"))),
"b": Const(45),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("r... | GEOM | GEOM | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | geo_count_lattice_rect_v1 | null | 2 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T08:57:10.418527Z | {
"verified": true,
"answer": 23453,
"timestamp": "2026-02-25T08:57:10.419311Z"
} | 3605cf | 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": 2603
},
"timestamp": "2026-03-30T04:57:10.070Z",
"answer": 23453
},
{
"... | 1 | [
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
03d026 | antilemma_product_of_sums_v1_1125832087_1499 | Let $S_1$ be the sum of $i \cdot j$ over all ordered pairs $(i,j)$ with $1 \leq i \leq 10$ and $1 \leq j \leq 9$. Let $T$ be the set of all integers $t$ such that $10 \leq t \leq 24$ and $t = 6a + 4b$ for some integers $a \in \{1,2\}$ and $b \in \{1,2,3\}$. Let $S_2$ be the sum of all integers $k$ from $\varphi(1)$ to ... | 51,975 | graphs = [
Graph(
let={
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(9)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/SUM_ARITHMETIC",
"PRODUCT_OF_SUMS",
"ONE_PHI_1"
] | 530e1e | antilemma_product_of_sums_v1 | null | 4 | 0 | [
"LIN_FORM",
"ONE_PHI_1",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 4 | 0.002 | 2026-02-08T03:46:12.672060Z | {
"verified": true,
"answer": 51975,
"timestamp": "2026-02-08T03:46:12.674212Z"
} | f1e62d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 626
},
"timestamp": "2026-02-18T06:07:24.567Z",
"answer": 52025
}
] | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status"... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
2bd961 | algebra_vieta_sum_v1_1915831931_3235 | Let $S$ be the set of all real numbers $x$ satisfying
$$
x^3 - 4x^2 - 25x + 28 = 0.
$$
Let $P$ be the product of all elements of $S$. Compute the remainder when $65742 \cdot P$ is divided by $55771$. | 55,438 | graphs = [
Graph(
let={
"_n": Const(28),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=MaxOverSet(set=SolutionsSet(var=Var(name='n'), condition=And(Geq(left=Var(name='n'), right=Const(value=2)), Leq(left=Var(name='n'), ... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.013 | 2026-02-08T17:27:20.079634Z | {
"verified": true,
"answer": 55438,
"timestamp": "2026-02-08T17:27:20.092485Z"
} | 47a0d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 926
},
"timestamp": "2026-02-18T02:54:19.977Z",
"answer": 55438
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
93973d | nt_count_digit_sum_v1_1116507919_490 | Let $s$ be the largest prime number $n$ such that $2 \le n \le 17$. Compute the number of positive integers $n \le 50086$ such that the sum of the decimal digits of $n$ is equal to $s$. | 2,911 | graphs = [
Graph(
let={
"_n": Const(17),
"upper": Const(50086),
"target_sum": 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("n"),... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 404dfd | nt_count_digit_sum_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 2 | 1.674 | 2026-02-08T02:35:34.026549Z | {
"verified": true,
"answer": 2911,
"timestamp": "2026-02-08T02:35:35.700695Z"
} | 1eb03c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 4782
},
"timestamp": "2026-02-09T18:33:09.336Z",
"answer": 2911
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -4.58,
"mid": 0.57,
"hi": 5.69
} | ||
a44a73 | sequence_count_fib_divisible_v1_1520064083_7864 | Let $a$ and $b$ be integers such that $1 \le a \le 21$, $1 \le b \le 204$, and define $t = 14a + 6b$. Let $S$ be the set of all integers $t$ satisfying $20 \le t \le 1518$. Let $N$ be the number of elements in $S$. Determine the value of $Q$, where $Q$ is the remainder when $31163$ multiplied by the number of positive ... | 49,143 | graphs = [
Graph(
let={
"_n": Const(92590),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=21)), Geq(le... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.053 | 2026-02-08T09:21:00.356629Z | {
"verified": true,
"answer": 49143,
"timestamp": "2026-02-08T09:21:00.409391Z"
} | 60e4a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 6353
},
"timestamp": "2026-02-14T03:11:49.535Z",
"answer": 49143
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
29c3f1 | lin_form_endings_v1_124444284_8533 | Let $a = 49$ and $b = 35$. Let $L$ be the least common multiple of $a$ and $b$. Let $k = 11441$ and $M = 95404$. Compute the remainder when $k \cdot L$ is divided by $M$. | 36,329 | graphs = [
Graph(
let={
"a_coeff": Const(49),
"b_coeff": Const(35),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(11441),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(95404),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T09:45:24.699811Z | {
"verified": true,
"answer": 36329,
"timestamp": "2026-02-08T09:45:24.700192Z"
} | 360c44 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 582
},
"timestamp": "2026-02-14T05:51:30.552Z",
"answer": 36329
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a05ac8 | nt_count_divisors_in_range_v1_1520064083_7275 | Let $n = 498960$. Determine the number of positive divisors $d$ of $n$ such that $1 \leq d \leq 6240$. Let this number be $r$. Let $p$ be the largest prime number less than or equal to $11$. Compute the Bell number $B_{|r| \bmod p}$, which is the number of partitions of a set of size $|r| \bmod p$. | 203 | graphs = [
Graph(
let={
"_n": Const(11),
"n": Const(498960),
"a": Const(1),
"b": Const(6240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), R... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_count_divisors_in_range_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.058 | 2026-02-08T08:52:55.286594Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T08:52:55.344507Z"
} | ff6297 | 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": 3946
},
"timestamp": "2026-02-13T22:53:42.164Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5c6b18 | comb_sum_binomial_row_v1_1470522791_368 | Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 22$. Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Compute $m^n$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(22),
"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")), Re... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"COMB1"
] | d35293 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COMB1",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T12:58:32.181948Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T12:58:32.185230Z"
} | f2e5d0 | 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": 656
},
"timestamp": "2026-02-15T08:22:10.776Z",
"answer": 2048
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
9262b0 | comb_sum_binomial_row_v1_601307018_10779 | Let $M$ be the minimum value of $37a^3 + 84a^2b + 48ab^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 26$. Let $n$ be the number of non-negative integers $v$ with $0 \le v \le M$ for which there exist integers $a, b$ with $1 \le a, b \le 5$ such that $4a^2 - 12ab + 9b^2 = v$. Compute $2^n$... | 8,192 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(26)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(26)))), expr=Sum(Mul(Const(84), Pow(Var("a"... | COMB | null | SUM | sympy | POLY3_MIN | [
"POLY3_MIN/QF_PSD_DISTINCT"
] | 0fc231 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"POLY3_MIN",
"QF_PSD_DISTINCT"
] | 2 | 0.005 | 2026-03-10T11:15:23.033111Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-03-10T11:15:23.037683Z"
} | 44b275 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 2437
},
"timestamp": "2026-04-19T14:43:49.828Z",
"answer": 8192
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "V7",
"st... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
38f711 | alg_sym_quad_system_v1_1218484723_3793 | Let $N$ be the sum of $a^3 + b^3 + c^3$ over all positive integer solutions $(a,b,c)$ to the system $$a^2 + b^2 + c^2 = ab + bc + ca \quad \text{and} \quad a + 5b + 2c = 2496.$$ Let $N' = N \bmod 1619$, and let $Q = B_{|N'| \bmod 11}$, where $B_k$ denotes the $k$-th Bell number. Compute $Q$. | 5 | graphs = [
Graph(
let={
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul(Var("b"), Var("c")), Mul(Va... | COMB | COMB | COMPUTE | sympy | K3 | [
"STARS_BARS"
] | f6827c | alg_sym_quad_system_v1 | null | 6 | 0 | [
"K3",
"STARS_BARS"
] | 2 | 0.162 | 2026-02-25T05:26:19.943554Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T05:26:20.105690Z"
} | 8d32d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 784
},
"timestamp": "2026-03-29T12:16:12.180Z",
"answer": 5
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "STARS_BARS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
cddf87 | diophantine_product_count_v1_784195855_9549 | Let $k = \sum_{d \mid 420} \phi(d)$. Let $R$ be the number of positive integers $x$ such that $1 \leq x \leq 221$, $x$ divides $k$, and $\frac{k}{x} \leq 221$. Compute the remainder when $64481 \cdot R$ is divided by 62425. | 45,232 | graphs = [
Graph(
let={
"_n": Const(420),
"k": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"upper": Const(221),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("uppe... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | diophantine_product_count_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.017 | 2026-02-08T16:53:13.546341Z | {
"verified": true,
"answer": 45232,
"timestamp": "2026-02-08T16:53:13.563548Z"
} | a00b42 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1262
},
"timestamp": "2026-02-17T15:28:28.570Z",
"answer": 45232
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
06b88e | alg_sum_powers_v1_1419126231_913 | Let $M = \left( \sum_{k=1}^{930} k^2 \right) \bmod \left( \sum_{k1=0}^{4} (3k1 + 913) \right)$. Compute $|M|$. | 1,425 | graphs = [
Graph(
let={
"_n": Const(913),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(930), expr=Pow(Var("k"), Const(2))), modulus=Summation(var="k1", start=Const(0), end=Const(4), expr=Sum(Mul(Const(3), Var("k1")), Ref("_n")))),
"Q": Abs(arg=Ref(name... | ALG | null | COMPUTE | sympy | SUM_AP | [
"SUM_AP"
] | ff6f57 | alg_sum_powers_v1 | null | 2 | 0 | [
"SUM_AP"
] | 1 | 0.033 | 2026-02-25T10:24:13.947205Z | {
"verified": true,
"answer": 1425,
"timestamp": "2026-02-25T10:24:13.979974Z"
} | 3ba695 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1259
},
"timestamp": "2026-03-30T10:39:36.822Z",
"answer": 1425
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
3201b0 | comb_factorial_compute_v1_1520064083_5260 | Let $m = 8$. Let $N$ be the number of positive integers $k$ such that $1 \le k \le 616$ and $m$ divides $k$. Let $n$ be the smallest divisor of $N$ that is greater than or equal to 2. Compute the value of $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(616)), Divides(divisor=Ref("_m"), dividend=Var("k"))), domain='positive_integers')),
"n": MinOverSet(set=SolutionsSet(var=V... | NT | null | COMPUTE | sympy | C2 | [
"C2/MIN_PRIME_FACTOR"
] | 59c94d | comb_factorial_compute_v1 | null | 3 | 0 | [
"C2",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T06:42:34.001127Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T06:42:34.003528Z"
} | b366b0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 375
},
"timestamp": "2026-02-15T17:42:12.308Z",
"answer": 5040
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -10,
"mid": -7.3,
"hi": -4.61
} | ||
355436 | alg_sum_ap_v1_1218484723_1442 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $41a^2 - 12ab + 20b^2 \le 19792$. Let $T = \sum_{\substack{n=1 \\ 121 \mid n}}^{M} n$, and let $P = \min\{x + y : x, y > 0,\ xy = 19158129\}$. Find the remainder when $\sum_{k=0}^{T} (15k + 33)$ is divided by $P$. | 6,408 | graphs = [
Graph(
let={
"_c": Const(19792),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Sum(Mul(Const(41), Pow(Var("a"), Const(2))... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/SUM_DIVISIBLE",
"B3"
] | 7dab22 | alg_sum_ap_v1 | null | 6 | 0 | [
"B3",
"QF_PSD_COUNT_LEQ",
"SUM_DIVISIBLE"
] | 3 | 0.026 | 2026-02-25T03:10:01.301595Z | {
"verified": true,
"answer": 6408,
"timestamp": "2026-02-25T03:10:01.327922Z"
} | f4672b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 15716
},
"timestamp": "2026-03-10T03:43:08.984Z",
"answer": 8270
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
}
] | {
"lo": 3.14,
"mid": 5.37,
"hi": 7.61
} | ||
8504e0 | nt_max_prime_below_v1_677425708_2446 | Let $p$ and $q$ be positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $n_0$ be the number of such pairs $(p, q)$. Let $S$ be the set of all prime numbers $n$ such that $n_0 \leq n \leq 52650$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $... | 16,750 | 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=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"COPRIME_PAIRS/B3"
] | bfccae | nt_max_prime_below_v1 | negation_mod | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 1.461 | 2026-02-08T05:03:44.536113Z | {
"verified": true,
"answer": 16750,
"timestamp": "2026-02-08T05:03:45.997148Z"
} | d6da75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 6726
},
"timestamp": "2026-02-11T22:49:53.847Z",
"answer": 16750
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
99e030 | geo_count_lattice_triangle_v1_1439011603_2313 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(333,300)$, and $(128,120)$, multiplied by 2. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each side of the triangle. Compute the value of $\frac{A + 2 - B}{2}$. Let $Q$ be the remainder w... | 7,461 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=333), Const(value=120)), Mul(Const(value=128), Sub(left=Const(value=0), right=Const(value=300))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=333)), b=Abs(arg=Const(value=300))), GCD(a=Abs(arg=Sub(left=Const(value=128), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.002 | 2026-02-08T16:40:58.117501Z | {
"verified": true,
"answer": 7461,
"timestamp": "2026-02-08T16:40:58.119876Z"
} | 714660 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1453
},
"timestamp": "2026-02-17T10:05:55.801Z",
"answer": 7461
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
614eac | alg_qf_psd_orbit_v1_1218484723_1736 | Let $T$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 30$ such that $10a_1^2 + 25b_1^2 - 18a_1b_1 \le 1873$. Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le T$ satisfying $123a^2 - 240ab + 123b^2 = 78975$. Find $Q$. | 6 | graphs = [
Graph(
let={
"_n": Const(123),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(148)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 1.171 | 2026-02-25T03:24:49.039379Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T03:24:50.210025Z"
} | 164c4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 9816
},
"timestamp": "2026-03-29T01:07:45.737Z",
"answer": 3
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
7b5a94_n | alg_linear_system_2x2_v1_1218484723_487 | A spacecraft's fuel efficiency is modeled by the expression $\frac{M}{\det} + \frac{R}{\det}$, where $\det = 6 \cdot 19$, $R = 6 \cdot 2394$, and $M = 278256 \cdot 19 + 7 \cdot P$. Here, $P$ is the minimum possible sum of two positive dimensions $x$ and $y$ of a solar panel array with total area $1432809$. Compute the ... | 46,649 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_linear_system_2x2_v1 | null | 4 | null | [
"B3"
] | 1 | 0.004 | 2026-02-25T02:10:40.487408Z | null | 879526 | 7b5a94 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 10387
},
"timestamp": "2026-03-30T15:31:33.254Z",
"answer": 46649
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
99814a | antilemma_k3_v1_2051736721_2393 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $6322$. | 6,322 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=6322), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:38:50.945468Z | {
"verified": true,
"answer": 6322,
"timestamp": "2026-02-08T16:38:50.945982Z"
} | daadfc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 699
},
"timestamp": "2026-02-16T07:39:49.390Z",
"answer": 10264
},
{
"id": 11,
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
6ae749 | algebra_poly_eval_v1_601307018_1854 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers with $xy = 343396$. Let $M$ be the minimum value of $|x_1 - y_1|$ over all ordered pairs $(x_1, y_1)$ of positive integers with $x_1 y_1 = 736291$. Let $z = 27$, and let $Q$ be the number of positive integer pairs $(a, b)$ with... | 9,697 | graphs = [
Graph(
let={
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(343396)))), expr=Sum(Var("x"), Var("y")))),
"_n": MinOverSe... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF/QF_PSD_COUNT_LEQ",
"B3/B3_DIFF"
] | d32426 | algebra_poly_eval_v1 | null | 6 | 0 | [
"B3",
"B3_DIFF",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.031 | 2026-03-10T02:36:07.353506Z | {
"verified": true,
"answer": 9697,
"timestamp": "2026-03-10T02:36:07.384596Z"
} | f668a1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 22752
},
"timestamp": "2026-03-29T03:35:54.320Z",
"answer": 8697
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
571013 | nt_min_crt_v1_865884756_1386 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y$ equals the number of integers $t$ with $9 \leq t \leq 44$ for which there exist integers $a'$ and $b'$ satisfying $1 \leq a' \leq 15$, $1 \leq b' \leq 2$, and $t = 2a' + 7b'$. Let $P$ be the set of all products $xy$ where $(x,y) \in ... | 79,116 | graphs = [
Graph(
let={
"_n": Const(19779),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/B1/MIN_PRIME_FACTOR"
] | fbd179 | nt_min_crt_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.012 | 2026-02-08T16:00:04.495261Z | {
"verified": true,
"answer": 79116,
"timestamp": "2026-02-08T16:00:04.507414Z"
} | c5e5e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 1142
},
"timestamp": "2026-02-16T18:01:05.836Z",
"answer": 79116
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8a2d53 | modular_inverse_v1_865884756_1110 | Let $a = 270$ and $m = 383$. Let $u$ be the number of prime numbers $n$ such that $2 \leq n \leq 2633$. Find the smallest positive integer $x$ such that $1 \leq x \leq u$ and
\[
270x \equiv 1 \pmod{383}.
\]
Multiply this value of $x$ by 3083, then find the remainder when the result is divided by 93693. | 677 | graphs = [
Graph(
let={
"a": Const(270),
"m": Const(383),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2633)), IsPrime(Var("n"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), conditio... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | modular_inverse_v1 | null | 6 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.038 | 2026-02-08T15:47:36.918799Z | {
"verified": true,
"answer": 677,
"timestamp": "2026-02-08T15:47:36.956398Z"
} | c306ae | 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": 1603
},
"timestamp": "2026-02-16T13:33:55.065Z",
"answer": 677
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
26c919 | comb_count_derangements_v1_124444284_1943 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 16$. Let $Q$ be the remainder when $12517 \cdot !n$ is divided by $78932$, where $!n$ denotes the number of derangements of $n$ objects. Compute $Q$. | 16,597 | graphs = [
Graph(
let={
"_n": Const(12517),
"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(16)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_derangements_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T04:12:53.112610Z | {
"verified": true,
"answer": 16597,
"timestamp": "2026-02-08T04:12:53.113575Z"
} | 324427 | 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": 2001
},
"timestamp": "2026-02-23T23:42:11.624Z",
"answer": 16597
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
746d0e | modular_sum_quadratic_residues_v1_971394319_532 | Let $p = 509$ and define $\text{result} = \frac{p(p-1)}{4}$. Let $\_c$ be the number of positive integers $t$ such that $14 \leq t \leq 500$ and $t = 4a + 10b$ for some positive integers $a \leq 80$ and $b \leq 18$. Let $Q$ be the remainder when $\_c - \text{result}$ is divided by $88853$. Determine the value of $Q$. | 24,450 | graphs = [
Graph(
let={
"_n": Const(88853),
"p": Const(509),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=An... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | modular_sum_quadratic_residues_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T13:09:44.139360Z | {
"verified": true,
"answer": 24450,
"timestamp": "2026-02-08T13:09:44.144060Z"
} | baf366 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 4039
},
"timestamp": "2026-02-15T09:52:49.332Z",
"answer": 24450
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d042e2_n | modular_modexp_compute_v1_601307018_3988 | A cryptographic sequence uses a base exponentiation step where the exponent is $\sum_{k=0}^{3} 7^k$. The system computes $43$ raised to this exponent, modulo $16384$, resulting in a value $M$. Later, this value is scaled by $93953$, and the final output is the remainder when this product is divided by $86690$. What is ... | 20,283 | NT | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | modular_modexp_compute_v1 | null | 3 | null | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-03-10T04:34:23.025218Z | null | b8da77 | d042e2 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 4584
},
"timestamp": "2026-03-29T18:16:00.907Z",
"answer": 20283
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
b6dd74 | nt_count_divisible_v1_1978505735_2822 | Let $x$ and $y$ be positive integers such that $xy = 49$. Define $s$ to be the minimum value of $x + y$ over all such pairs. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 40804$ and $n$ is divisible by $s$. Compute the remainder when $37085 \cdot N$ is divided by $92791$. | 56,966 | graphs = [
Graph(
let={
"upper": Const(40804),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(49)))), expr=Sum(Var("x"), Var(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 3 | 0 | [
"B3"
] | 1 | 1.494 | 2026-02-08T17:11:29.579880Z | {
"verified": true,
"answer": 56966,
"timestamp": "2026-02-08T17:11:31.074109Z"
} | c5796a | 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": 931
},
"timestamp": "2026-02-17T21:34:22.418Z",
"answer": 56966
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5768cd | comb_factorial_compute_v1_601307018_10084 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $$64a^3 + 144a^2b + 108ab^2 + 27b^3 = 857375.$$ Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(27),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(64), Pow(Var("a"), Const(3))), Mu... | COMB | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_factorial_compute_v1 | null | 4 | 0 | [
"POLY3_COUNT"
] | 1 | 0.006 | 2026-03-10T10:34:38.976499Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-03-10T10:34:38.982737Z"
} | df2813 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1319
},
"timestamp": "2026-04-19T12:57:01.619Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
eae3d6 | comb_sum_binomial_row_v1_124444284_5824 | Let $n$ be the number of nonnegative integers $j$ with $0 \le j \le 1046$ such that $\binom{1046}{j}$ is odd. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(1046),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1046)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | ALG | COMB | SUM | sympy | V8 | [
"V8"
] | 86348e | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T06:53:21.377841Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T06:53:21.379343Z"
} | 519e84 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 801
},
"timestamp": "2026-02-24T07:17:42.209Z",
"answer": 65536
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
e261cd | alg_sum_ap_v1_601307018_8892 | Let $M$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 729$. Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ satisfying $Mab + 26a^2 + 29b^2 \le 96561$. Let $S = \sum_{k=0}^{140} (14k + 31) \bmod 5445$. Compute $R - S$. | 388 | graphs = [
Graph(
let={
"_m": Const(5445),
"_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(729)))), expr=Sum(Var("x"), Var("y")))),... | ALG | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_COUNT_LEQ"
] | 01ca16 | alg_sum_ap_v1 | negation_mod | 6 | 0 | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.015 | 2026-03-10T09:19:22.394568Z | {
"verified": true,
"answer": 388,
"timestamp": "2026-03-10T09:19:22.409316Z"
} | cfb4ec | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 11085
},
"timestamp": "2026-04-19T10:07:11.745Z",
"answer": 388
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
5e01a8 | alg_sym_quad_system_v1_601307018_4161 | Let $S$ be the sum of $a^4 + b^4 + c^4$ over all triples $(a, b, c)$ of positive integers satisfying $a^2 + b^2 + c^2 = ab + bc + ca$ and $17a + 4b + 6c = 3619$, where $17 = \max\{ n \leq 10 : n\ \text{is prime}\}$ and $3619 = \max\{ d \mid 13253234 : d^2 \leq 13253234 \}$. Let $Q = |S|$. Compute $Q$ modulo $\min\{ x +... | 4,548 | graphs = [
Graph(
let={
"_c": Const(10),
"_m": Const(4),
"_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"), Const(2)), Pow(Var("b"), Const(2)), P... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3_CLOSEST",
"B3"
] | a83ddb | alg_sym_quad_system_v1 | null | 7 | 0 | [
"B3",
"B3_CLOSEST",
"MAX_PRIME_BELOW"
] | 3 | 0.027 | 2026-03-10T04:47:26.875142Z | {
"verified": true,
"answer": 4548,
"timestamp": "2026-03-10T04:47:26.901850Z"
} | 6bfa78 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T11:15:58.469Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
297d75 | nt_max_prime_below_v1_124444284_9521 | Let $n$ be an integer. Define $A$ as the set of all prime numbers $p$ such that $2 \leq p \leq 3$. Let $k$ be the number of elements in $A$. Now, define $B$ as the set of all prime numbers $q$ such that $k \leq q \leq 11491$. Let $m$ be the maximum element of $B$. Compute $m$. | 11,491 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(11491),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n")))))... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_max_prime_below_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.276 | 2026-02-08T12:33:16.944795Z | {
"verified": true,
"answer": 11491,
"timestamp": "2026-02-08T12:33:17.220349Z"
} | 274a59 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 270
},
"timestamp": "2026-02-16T03:59:11.666Z",
"answer": 11473
},
{
"id": 11,... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
3c5cb3 | comb_factorial_compute_v1_784195855_512 | Let $c$ be the maximum value of $xy$ over all positive integers $x$ and $y$ such that $x + y = 98$. Compute the remainder when $c - 7!$ is divided by $69654$. | 67,015 | graphs = [
Graph(
let={
"_n": Const(69654),
"n": Const(7),
"result": Factorial(Ref("n")),
"_c": 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(... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | comb_factorial_compute_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T04:25:06.561832Z | {
"verified": true,
"answer": 67015,
"timestamp": "2026-02-08T04:25:06.563551Z"
} | 97fb71 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 556
},
"timestamp": "2026-02-24T00:31:46.656Z",
"answer": 67015
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
037faa | nt_sum_totient_over_divisors_v1_1520064083_5621 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 5938969$. Let $n$ be the minimum value of $x + y$ over all such pairs. Define $r = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number... | 216 | 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(5938969)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T07:27:44.769076Z | {
"verified": true,
"answer": 216,
"timestamp": "2026-02-08T07:27:44.770522Z"
} | 9b16eb | 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": 3611
},
"timestamp": "2026-02-13T10:45:57.408Z",
"answer": 216
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1f98ee | algebra_poly_eval_v1_1520064083_2059 | Let $b = \sum_{k=1}^{6} k$. Compute the value of $\left( \sum_{k=1}^{3} k \right) \cdot b^3 + 8 \cdot b^2 + 4 \cdot b - 2$, and then take its absolute value. | 59,176 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(8),
"b": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": Sum(Mul(Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")), Pow(Ref("b"), Const(3))), Mul(Ref("_n"), Pow(Ref("b... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.004 | 2026-02-08T04:29:42.590935Z | {
"verified": true,
"answer": 59176,
"timestamp": "2026-02-08T04:29:42.594988Z"
} | d63c0a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 452
},
"timestamp": "2026-02-10T16:55:32.001Z",
"answer": 59176
},
{
"... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"stat... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
e978cf | nt_count_intersection_v1_124444284_1609 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 25000000$. Define $N$ to be the minimum value of $x + y$ over all such pairs. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $9$ divides $n$, and $\gcd(n, 10) = 1$. Let $c = |A|$. Compute the remainder wh... | 12,429 | graphs = [
Graph(
let={
"_n": Const(76052),
"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(25000000)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.681 | 2026-02-08T04:02:26.370055Z | {
"verified": true,
"answer": 12429,
"timestamp": "2026-02-08T04:02:27.051406Z"
} | 5ea0f6 | 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": 4368
},
"timestamp": "2026-02-11T15:48:21.728Z",
"answer": 12429
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
204e21 | comb_count_surjections_v1_1915831931_2656 | 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 $k$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 3$ and $1 \le j \le 4$ such that $i + j = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set o... | 540 | 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 | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.023 | 2026-02-08T17:02:37.720463Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T17:02:37.743607Z"
} | 36a7be | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1352
},
"timestamp": "2026-02-17T17:18:10.505Z",
"answer": 540
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
af58d8 | comb_sum_binomial_row_v1_1218484723_5078 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $b^2 - 8ab + 16a^2 = 9$. Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(9),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Pow(Var("b"), Const(2)), Mul(Const(-8), Var(... | COMB | null | SUM | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.001 | 2026-02-25T06:42:51.788687Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-25T06:42:51.790051Z"
} | 00931c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1224
},
"timestamp": "2026-03-29T19:22:22.646Z",
"answer": 4096
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"s... | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
e8b7a0 | antilemma_k2_v1_397696148_1199 | Let $S$ be the set of positive divisors of 340. Define $x = \sum_{k=1}^{\sum_{d \mid 340} \phi(d)} \phi(k) \left\lfloor \frac{340}{k} \right\rfloor$. Find the value of $x$. | 57,970 | graphs = [
Graph(
let={
"_n": Const(340),
"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(340), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T12:25:01.211376Z | {
"verified": true,
"answer": 57970,
"timestamp": "2026-02-08T12:25:01.211973Z"
} | bc417c | 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": 762
},
"timestamp": "2026-02-15T01:03:50.621Z",
"answer": 57970
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b1e87e | nt_num_divisors_compute_v1_784195855_2326 | Let $m = 576$. Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq m$ and $12$ divides the $n$-th Fibonacci number. Let $n = 56644$, and let $d$ be the number of positive divisors of $n$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = k$. Define $Q = d^2 + 8d... | 1,521 | graphs = [
Graph(
let={
"_m": Const(576),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Divides(divisor=Const(12), dividend=Fibonacci(arg=Var(name='n')))))),
"n": Const(56644),
"result": NumD... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/B1"
] | 8b2515 | nt_num_divisors_compute_v1 | quadratic_mod | 5 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.002 | 2026-02-08T05:40:12.265188Z | {
"verified": true,
"answer": 1521,
"timestamp": "2026-02-08T05:40:12.267522Z"
} | 254dcd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1678
},
"timestamp": "2026-02-12T12:12:39.812Z",
"answer": 1521
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fb9d43 | comb_factorial_compute_v1_124444284_1283 | Let $m = 2$ and let $n$ be the sum $\sum_{k=1}^{4} k$. Define $p$ to be the largest prime number satisfying $m \leq p \leq n$. Compute $p!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Fact... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | bde608 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.001 | 2026-02-08T03:48:25.828799Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T03:48:25.830187Z"
} | 93b561 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 159
},
"timestamp": "2026-02-10T05:32:41.324Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": ... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
25da9e | alg_qf_psd_orbit_v1_601307018_3315 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b$ and $1 \leq b \leq 274$ such that $50a^2 + 100ab + 50b^2 = 5281250$. | 112 | graphs = [
Graph(
let={
"_n": Const(41),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const... | ALG | null | COUNT | sympy | B3_DIFF | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_orbit_v1 | null | 7 | 0 | [
"B3_DIFF",
"QF_PSD_COUNT_LEQ"
] | 2 | 1.922 | 2026-03-10T03:51:30.748671Z | {
"verified": true,
"answer": 112,
"timestamp": "2026-03-10T03:51:32.670254Z"
} | fa9249 | 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": 715
},
"timestamp": "2026-03-29T08:11:23.931Z",
"answer": 112
},
{
"id"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.24
} | ||
8671e8 | comb_catalan_compute_v1_784195855_10388 | Let $ S $ be the set of all integers $ t $ such that $ 7 \leq t \leq 30 $ and there exist integers $ a $ and $ b $ with $ 1 \leq a \leq 5 $, $ 1 \leq b \leq 4 $, and $ t = 2a + 5b $. Let $ n $ be the number of ordered pairs $ (x_1, x_2) $ of positive odd integers such that $ x_1 + x_2 = |S| $. Compute the $ n $-th Cata... | 16,796 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T17:49:13.252118Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T17:49:13.254700Z"
} | 602b84 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1515
},
"timestamp": "2026-02-18T13:35:37.486Z",
"answer": 16796
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
0e39b9 | comb_count_permutations_fixed_v1_1218484723_144 | Let $D_n$ denote the number of derangements of $n$ elements. Let $n = \sum_{k1=\sum_{k2=0}^{6} (-1)^{k2} \binom{6}{k2}}^{2} 2^{k1}$. Compute $50400 - \binom{n}{3} \cdot D_{n - 3}$. | 50,085 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k1", start=Summation(var="k2", start=Const(0), end=Const(6), expr=Mul(Pow(Const(-1), Var("k2")), Binom(n=Const(6), k=Var("k2")))), end=Ref("_n"), expr=Pow(Const(2), Var("k1"))),
"k": Const(3),
"result... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"SUM_GEOM"
] | c3d408 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"SUM_GEOM"
] | 2 | 0.003 | 2026-02-25T01:51:06.281350Z | {
"verified": true,
"answer": 50085,
"timestamp": "2026-02-25T01:51:06.284301Z"
} | 34f9d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1008
},
"timestamp": "2026-03-10T08:31:55.121Z",
"answer": 50085
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"s... | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
99bd55 | nt_count_digit_sum_v1_168721529_786 | Let $\phi(n)$ denote Euler's totient function. Define $U$ as the number of positive integers $n$ such that $1 \leq n \leq 18748$ and $\gcd(n, 15) = 1$. Determine the number of positive integers $n$ such that $1 \leq n \leq U$ and the sum of the decimal digits of $n$ is 14. | 540 | graphs = [
Graph(
let={
"_n": Const(15),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(18748)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"target_sum": Const(14),
"result": CountOverSet(set... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"C4"
] | 1 | 7.598 | 2026-02-08T13:17:28.129851Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T13:17:35.727419Z"
} | 5fe17b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1394
},
"timestamp": "2026-02-09T09:09:10.814Z",
"answer": 540
},
{
"id... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -1.93,
"mid": 2.14,
"hi": 6.33
} | ||
f9f2af | comb_count_permutations_fixed_v1_865884756_5556 | Let $n$ be the smallest divisor of 35 that is at least 2. Compute the value of $\binom{n}{2} \cdot !(n-2)$, where $!k$ denotes the number of derangements of $k$ elements. Multiply this value by 44121 and compute the remainder when the product is divided by 81757. | 64,850 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(35))))),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T18:41:57.383236Z | {
"verified": true,
"answer": 64850,
"timestamp": "2026-02-08T18:41:57.385953Z"
} | 7c6a52 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1213
},
"timestamp": "2026-02-18T18:45:46.021Z",
"answer": 64850
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ee2080 | nt_count_phi_equals_v1_784195855_6446 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 3240000$. Let $m$ be the minimum value of $x + y$ over all such pairs. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq m$ and $\phi(n) = 1228$, where $\phi(n)$ denotes the number of positive integers less than ... | 88,242 | 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(3240000)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.234 | 2026-02-08T08:41:04.146833Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T08:41:04.381232Z"
} | 2e3aa6 | 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": 3904
},
"timestamp": "2026-02-13T20:30:31.960Z",
"answer": 88242
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a0b891 | geo_visible_lattice_v1_124444284_4873 | A lattice point $(x,y)$ is said to be visible from the origin if $\gcd(x,y) = 1$. Let $V$ be the number of visible lattice points $(x,y)$ with $1 \le x, y \le 128$. Compute the remainder when $4963 \cdot V$ is divided by $50485$. | 14,714 | graphs = [
Graph(
let={
"n": Const(128),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(4963), Ref("result")), modulus=Const(50485)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 1.093 | 2026-02-08T06:16:35.233705Z | {
"verified": true,
"answer": 14714,
"timestamp": "2026-02-08T06:16:36.327060Z"
} | 4a6c3d | 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": 6367
},
"timestamp": "2026-02-24T05:51:33.759Z",
"answer": 14714
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
283185 | antilemma_v8_lucas_168721529_651 | Let $m=46$ and let $\varphi$ denote Euler's totient function. For positive integers $x$ and $y$ with $x+y=m$, consider the products $xy$. Let $P$ be the maximum value of $xy$ over all such pairs.
Now consider all ordered pairs $(x,y)$ of positive integers such that $xy=P$. For each such pair, form the sum $x+y$. Let $... | 256 | graphs = [
Graph(
let={
"_m": Const(46),
"_n": Const(34462),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Sub(EulerPhi(n=Const(47)), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositi... | NT | COMB | COMPUTE | sympy | B1 | [
"B1/B3/ZERO_PHI_PRIME/V8",
"V8"
] | b78c35 | antilemma_v8_lucas | null | 6 | 0 | [
"B1",
"B3",
"V8",
"ZERO_PHI_PRIME"
] | 4 | 0.008 | 2026-02-08T13:10:40.775764Z | {
"verified": true,
"answer": 256,
"timestamp": "2026-02-08T13:10:40.784079Z"
} | 494c24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 2743
},
"timestamp": "2026-02-09T07:32:23.116Z",
"answer": 256
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
fa0d25 | alg_poly_orbit_legendre_v1_601307018_1861 | Let $N = a^{23} \bmod 47$, $M = (a^2 + a - 11) \bmod 47$, $R = M^{23} \bmod 47$, $S = (M^2 + M - 11) \bmod 47$, $T = S^{23} \bmod 47$, $K = N + R + T$, and $L = (S^2 + S - 11) \bmod 47$. Find the number of non-negative integers $a$ with $0 \le a \le 34638$ such that $L = a$, $K \equiv 0 \pmod{3}$, $M \ne a$, and $S \ne... | 2,211 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-11)), modulus=Const(47)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-11)), modulus=Const(47)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-11)), ... | NT | null | COUNT | sympy | POLY_ORBIT_LEGENDRE_COUNT | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | b47831 | alg_poly_orbit_legendre_v1 | null | 7 | null | [
"POLY_ORBIT_LEGENDRE_COUNT"
] | 1 | 0.032 | 2026-03-10T02:36:37.977623Z | {
"verified": true,
"answer": 2211,
"timestamp": "2026-03-10T02:36:38.009852Z"
} | 3c5ed8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T03:39:14.587Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE_COUNT",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"... | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
6c38ae | sequence_fibonacci_compute_v1_1918700295_3944 | Let $N = 15011$. Define $n$ to be the number of positive integers $n$ with $1 \leq n \leq 100$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $N \cdot F_n$ i... | 6,420 | graphs = [
Graph(
let={
"_n": Const(15011),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(100)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T09:03:34.747179Z | {
"verified": true,
"answer": 6420,
"timestamp": "2026-02-08T09:03:34.747938Z"
} | d73bf6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1396
},
"timestamp": "2026-02-13T23:59:32.428Z",
"answer": 6420
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7916d0 | antilemma_product_of_sums_v1_1440796553_353 | Let $S_1 = \sum_{k=1}^{9} k$.
Let $T$ be the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 4$ and $1 \leq j \leq 9$. Define $S_2$ to be the sum of $i \cdot j$ over all pairs $(i,j)$ in $T$.
Let $x = S_1 \cdot S_2$.
Compute the remainder when $20164 - x$ is divided by $95708$. | 95,622 | graphs = [
Graph(
let={
"_n": Const(9),
"S1": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"S2": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=C... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 2 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T11:45:05.007643Z | {
"verified": true,
"answer": 95622,
"timestamp": "2026-02-08T11:45:05.008384Z"
} | 013ac5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 534
},
"timestamp": "2026-02-22T00:44:31.006Z",
"answer": 95622
}
] | 2 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
855500 | nt_min_coprime_above_v1_1431428450_925 | Let $m$ be the sum of all positive integers $n \le 134$ such that $n \equiv 0 \pmod{134}$. Determine the value of the smallest integer $n$ satisfying $32768 < n \le 32912$ and $\gcd(n, m) = 1$. | 32,769 | graphs = [
Graph(
let={
"_n": Const(134),
"start": Const(32768),
"upper": Const(32912),
"modulus": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(134)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0)))... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC",
"SUM_DIVISIBLE"
] | 2 | 0.057 | 2026-02-08T13:47:09.246907Z | {
"verified": true,
"answer": 32769,
"timestamp": "2026-02-08T13:47:09.304406Z"
} | 80360a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 391
},
"timestamp": "2026-02-16T04:56:49.338Z",
"answer": 32769
},
{
"id": 11,
... | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} |
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