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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6e2da4 | nt_max_prime_below_v1_458359167_1002 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $S$. Find the largest prime number $n$ such that $c \leq n \leq 27225$. | 27,211 | graphs = [
Graph(
let={
"upper": Const(27225),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.616 | 2026-02-08T04:13:11.072621Z | {
"verified": true,
"answer": 27211,
"timestamp": "2026-02-08T04:13:11.688137Z"
} | 50dc09 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 4524
},
"timestamp": "2026-02-10T15:53:05.806Z",
"answer": 27211
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
81e96d | nt_lcm_compute_v1_349078426_1903 | Let $a = 2533$ and $b$ be the largest prime number less than or equal to 2959. Let $L = \mathrm{lcm}(a, b)$. Compute the remainder when $L + \left(2^{L \bmod 15}\right) \bmod 52868$ is divided by 52868. | 37,741 | graphs = [
Graph(
let={
"a": Const(2533),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(2959)), IsPrime(Var("n"))))),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Ref("result"), Mod(value... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_lcm_compute_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:59:40.815735Z | {
"verified": true,
"answer": 37741,
"timestamp": "2026-02-08T13:59:40.818167Z"
} | c1fd25 | 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": 1672
},
"timestamp": "2026-02-15T22:47:30.202Z",
"answer": 37741
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
62ca5f | nt_min_coprime_above_v1_1918700295_1745 | Let $n_0 = 21$ and $\text{start} = 4356$. Let $\text{upper}$ be the number of positive integers $j$ such that $1 \leq j \leq 4811$ and $j^4 \leq 535724400609841$. Let $\text{modulus} = 445$. Consider the set of integers $n$ such that $n > \text{start}$, $n \leq \text{upper}$, and $\gcd(n, \text{modulus}) = 1$. Compute ... | 139 | graphs = [
Graph(
let={
"_n": Const(21),
"start": Const(4356),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(4811)), Leq(Pow(Var("j"), Const(4)), Const(535724400609841))), domain='positive_integers')),
... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | 8a214c | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C3"
] | 1 | 0.04 | 2026-02-08T05:59:20.371065Z | {
"verified": true,
"answer": 139,
"timestamp": "2026-02-08T05:59:20.410778Z"
} | c69548 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 2605
},
"timestamp": "2026-02-12T17:49:37.945Z",
"answer": 139
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
165a42 | nt_sum_divisors_mod_v1_784195855_1839 | Let $n = 20160$ and let $\sigma(n)$ denote the sum of the positive divisors of $n$. Let $M = 10301$, and define
\[
r \equiv \sigma(n) \pmod{M}, \qquad 0 \le r < M.
\]
Let $F(m)$ denote the Fibonacci sequence defined by $F_1 = 1$, $F_2 = 1$, and $F_{m+2} = F_{m+1} + F_m$ for all positive integers $m$. Let $Q$ be the sm... | 2,380 | graphs = [
Graph(
let={
"n": Const(20160),
"M": Const(10301),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
... | NT | null | COMPUTE | sympy | C3 | [
"C3/C5/OMEGA_ONE",
"WILSON"
] | f635ce | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"C3",
"C5",
"OMEGA_ONE",
"WILSON"
] | 4 | 0.025 | 2026-02-08T05:21:04.991354Z | {
"verified": true,
"answer": 2380,
"timestamp": "2026-02-08T05:21:05.016499Z"
} | 2e8e76 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 4464
},
"timestamp": "2026-02-12T06:52:49.030Z",
"answer": 2380
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemm... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
98b43f | nt_count_intersection_v1_1439011603_1291 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 25000000$. Let $a = 11$ and $b = 14$. Define $S$ as the set of all integers $n$ with $1 \leq n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. Let $r = |S|$. Compute $ (78409 \cdot r) \bmod 97070 ... | 2,460 | 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(25000000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(11)... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.462 | 2026-02-08T16:01:10.510974Z | {
"verified": true,
"answer": 2460,
"timestamp": "2026-02-08T16:01:10.972991Z"
} | 061f4e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1979
},
"timestamp": "2026-02-16T18:38:53.760Z",
"answer": 2460
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
16fda5 | nt_count_gcd_equals_v1_798873815_516 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 34225$. Define $k$ to be the minimum value of $x + y$ over all such pairs.
Let $A$ be the set of all positive integers $n$ such that $1 \le n \le 15129$ and $\gcd(n, k) = 10$.
Compute the number of elements in $A$. | 1,472 | graphs = [
Graph(
let={
"upper": Const(15129),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(34225)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B3"
] | 1 | 1.069 | 2026-02-08T02:40:25.542178Z | {
"verified": true,
"answer": 1472,
"timestamp": "2026-02-08T02:40:26.611536Z"
} | ca0fc9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2699
},
"timestamp": "2026-02-08T19:38:42.937Z",
"answer": 1472
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -0.84,
"mid": 1,
"hi": 2.64
} | ||
aa7b93 | nt_lcm_compute_v1_397696148_265 | Let $S_1$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 331776$, and let $A$ be the minimum value of $x + y$ over all such pairs. Let $S_2$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 210681$, and let $B$ be the minimum value of $x + y$ over all such pai... | 58,752 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(331776)))), expr=Sum(Var("x"), Var("y")))),
"b": MinOverSet(... | NT | null | COMPUTE | sympy | K3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3",
"K3"
] | 2 | 0.009 | 2026-02-08T11:24:10.605656Z | {
"verified": true,
"answer": 58752,
"timestamp": "2026-02-08T11:24:10.614708Z"
} | c5c257 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1270
},
"timestamp": "2026-02-14T13:34:17.871Z",
"answer": 58752
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
17160b | comb_sum_binomial_row_v1_1742523217_729 | Let $n = \sum_{k=1}^{4} k$. Compute $2^n$. | 1,024 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T03:11:51.732447Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T03:11:51.733104Z"
} | 016584 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 72
},
"timestamp": "2026-02-09T21:50:21.477Z",
"answer": 1024
},
{
"id"... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHME... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
b70a67 | comb_count_permutations_fixed_v1_655260480_1877 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 4500$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $\binom{7}{k} \cdot !(7 - k)$, where $!n$ denotes the number of derangements of $n$ elements. | 70 | graphs = [
Graph(
let={
"n": Const(7),
"k": 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=4500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T16:27:19.985277Z | {
"verified": true,
"answer": 70,
"timestamp": "2026-02-08T16:27:19.989047Z"
} | dcbe57 | 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": 1481
},
"timestamp": "2026-02-17T03:18:48.577Z",
"answer": 70
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e0009a | diophantine_product_count_v1_1440796553_152 | Let $k = 360$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 30276$. Define $T$ as the set of all values $x + y$ where $(x, y) \in S$. Let $u$ be the minimum value in $T$. Compute the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \... | 22 | graphs = [
Graph(
let={
"k": Const(360),
"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(30276)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.096 | 2026-02-08T11:37:05.878243Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T11:37:05.973926Z"
} | 348ecf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1627
},
"timestamp": "2026-02-14T16:45:50.704Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7d7878 | nt_count_coprime_and_v1_124444284_1612 | Let $n = 29$. Define $k_2$ to be the number of positive integers $m$ such that $1 \le m \le 29$ and $m \equiv \left\lfloor \frac{m}{2} \right\rfloor \pmod{3}$. Let $S$ be the set of all positive integers $k$ such that $1 \le k \le 74760$, $\gcd(k, 4) = 1$, and $\gcd(k, k_2) = 1$. Compute the remainder when $43627$ time... | 24,080 | graphs = [
Graph(
let={
"_n": Const(29),
"upper": Const(74760),
"k1": Const(4),
"k2": 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'), ri... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 8.204 | 2026-02-08T04:02:27.186991Z | {
"verified": true,
"answer": 24080,
"timestamp": "2026-02-08T04:02:35.390821Z"
} | 08c0d4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 3848
},
"timestamp": "2026-02-11T16:11:18.348Z",
"answer": 32420
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
86c6f2 | nt_count_divisible_v1_677425708_1688 | Let $m_1$ be the value of $\sum_{d\mid 1} \mu(d)$, where $\mu$ denotes the Möbius function. Let $N=7\cdot 3\cdot 71$. Let $t$ be the remainder when $\tau(N)$ is divided by $2m_1$, where $\tau(N)$ is the number of positive divisors of $N$.
Let $D=26+t$. Let $R$ be the number of integers $n$ with $1\le n\le 32768$ such ... | 59,382 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": Const(2),
"n1": Const(1),
"m": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"p": Const(7),
"q": Const(3),
"r": Const(71),
"n": Mul(Re... | NT | null | COUNT | sympy | B1 | [
"B1/C4/B1",
"DIVISOR_PARITY",
"MOBIUS_SUM"
] | 674777 | nt_count_divisible_v1 | negation_mod | 7 | 2 | [
"B1",
"C4",
"DIVISOR_PARITY",
"MOBIUS_SUM"
] | 4 | 4.4 | 2026-02-08T04:22:34.300032Z | {
"verified": true,
"answer": 59382,
"timestamp": "2026-02-08T04:22:38.700242Z"
} | 044e14 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 453,
"completion_tokens": 1102
},
"timestamp": "2026-02-09T23:25:12.815Z",
"answer": 59382
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma":... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
81181a | comb_count_partitions_v1_1520064083_7025 | Let
\[n_1 = \sum_{d\mid 38} \varphi(d),\]
where $\varphi$ denotes Euler's totient function. Next, let
\[n = \sum_{d\mid n_1} \varphi(d).\]
Let $p(n)$ denote the number of integer partitions of $n$, and let $P = p(n)$.
Let $C=87809$, and define
\[Q \equiv C\cdot P \pmod{87445},\]
with $0\le Q<87445$.
Find the remainde... | 25,400 | graphs = [
Graph(
let={
"_n": SumOverDivisors(n=Const(value=38), var='d', expr=EulerPhi(n=Var(name='d'))),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Partition(arg=Ref(name='n')),
"_c": Const(87809),
... | NT | COMB | COUNT | sympy | K3 | [
"K3/K3"
] | 4ddc06 | comb_count_partitions_v1 | null | 8 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T08:43:08.931450Z | {
"verified": true,
"answer": 25400,
"timestamp": "2026-02-08T08:43:08.932916Z"
} | 9799e7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1249
},
"timestamp": "2026-02-13T20:55:34.965Z",
"answer": 25400
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
de741f | sequence_count_fib_divisible_v1_124444284_6938 | Let $\phi(n)$ denote the number of positive integers $n$ at most $2257$ that are relatively prime to $12$. Let $D$ be the number of positive integers $n$ at most $\phi(12)$ such that the $n$-th Fibonacci number is divisible by $4$. Compute the remainder when $81023 \cdot D$ is divided by $51802$. | 26,485 | graphs = [
Graph(
let={
"_n": Const(12),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2257)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"d": Const(4),
"result": CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.032 | 2026-02-08T08:43:28.399511Z | {
"verified": true,
"answer": 26485,
"timestamp": "2026-02-08T08:43:28.431817Z"
} | cb471e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 3080
},
"timestamp": "2026-02-13T21:18:45.536Z",
"answer": 26485
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8d5462 | comb_binomial_compute_v1_601307018_1489 | Let $n = \sum_{k=1}^{5} k$. Compute $\binom{n}{8}$. | 6,435 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Const(1), end=Const(5), expr=Var("k1")),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | COMB | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"POLY_ORBIT_LEGENDRE",
"SUM_ARITHMETIC"
] | 2 | 0.117 | 2026-03-10T02:12:54.859456Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-03-10T02:12:54.976560Z"
} | 54d9aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 344
},
"timestamp": "2026-03-29T02:21:21.104Z",
"answer": 6435
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -6.52,
"mid": -3.37,
"hi": -0.99
} | ||
4dc7d9 | diophantine_fbi2_count_v1_1520064083_4246 | Let $n = 84$ and $k = 480$. Define $S$ as the set of all positive integers $d$ such that $4 \leq d \leq \max\{ d' \mid 1 \leq d' \leq n \text{ and } d' \text{ divides } 8148 \}$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 82$. Let $Q = \sum_{m=1}^{|S|} \tau(m)$, where $\tau(m)$ denotes the number of positive divisor... | 41 | graphs = [
Graph(
let={
"_n": Const(84),
"k": Const(480),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), ... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.019 | 2026-02-08T06:10:27.128038Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T06:10:27.147301Z"
} | c51d0b | 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": 2032
},
"timestamp": "2026-02-12T20:21:54.418Z",
"answer": 41
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
adf894 | comb_binomial_compute_v1_717093673_1207 | Let $n = 13$ and $k = 5$. Let $c$ be the sum of all solutions $x$ to the equation $x^2 - 44x - 3485 = 0$. Compute the remainder when $c - \binom{n}{k}$ is divided by 80835. | 79,592 | graphs = [
Graph(
let={
"n": Const(13),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-44), Var("x")), Const(-3485)), Const(0)))),
"Q": Mo... | ALG | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 4b7103 | comb_binomial_compute_v1 | negation_mod | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T15:56:35.342594Z | {
"verified": true,
"answer": 79592,
"timestamp": "2026-02-08T15:56:35.345020Z"
} | 63cf09 | 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": 626
},
"timestamp": "2026-02-24T19:07:56.875Z",
"answer": 79592
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
3fca9a | nt_lcm_compute_v1_677425708_3238 | Let $S$ be the set of all real numbers $x$ such that $x^2 - 1695x + 133796 = 0$. Let $N$ be the sum of all elements in $S$. Let $a$ be the largest prime number $n$ such that $2 \leq n \leq N$. Let $b = 686$, and define $L = \operatorname{lcm}(a, b)$. Let $M = |L| + 1$. Compute the value of
$$
L + \phi(M) + \tau(M)
$$
m... | 60,293 | graphs = [
Graph(
let={
"_n": Const(64397),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-1695), Var("x")), Const(133796)), Const(0))))... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/MAX_PRIME_BELOW"
] | 438451 | nt_lcm_compute_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T05:33:23.426813Z | {
"verified": true,
"answer": 60293,
"timestamp": "2026-02-08T05:33:23.429220Z"
} | ce8fa8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 5042
},
"timestamp": "2026-02-12T11:31:27.602Z",
"answer": 60293
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cd5095 | comb_catalan_compute_v1_458359167_73 | Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 44$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $r$ be the $n$th Catalan number. Compute the Bell number $B_{|r| \bmod 11}$. Find the value of this Bell nu... | 2 | graphs = [
Graph(
let={
"_m": Const(11),
"_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")), C... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COMB1/COMB1"
] | b2c526 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.052 | 2026-02-08T02:59:16.203565Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T02:59:16.255777Z"
} | 2104af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1755
},
"timestamp": "2026-02-10T12:01:35.452Z",
"answer": 2
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
605117 | algebra_poly_eval_v1_349078426_837 | Let $z = 6$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $T$ be the set of all values of $x + y$ as $(x, y)$ ranges over $S$. Let $m$ be the minimum value in $T$. Let $D$ be the set of all integers $d \geq 2$ such that $d$ divides $3675$. Let $d_{\min}$ be the smallest... | 1,461 | graphs = [
Graph(
let={
"z": Const(6),
"result": Sum(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16)))), expr=Sum(Var("x"), Var("... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B3"
] | 6c6c26 | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3",
"MIN_PRIME_FACTOR"
] | 2 | 0.006 | 2026-02-08T13:18:27.282273Z | {
"verified": true,
"answer": 1461,
"timestamp": "2026-02-08T13:18:27.288261Z"
} | 648ca8 | 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": 1065
},
"timestamp": "2026-02-15T12:26:53.714Z",
"answer": 1461
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
3505ba | nt_min_phi_inverse_v1_124444284_6471 | Let $U = 10$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq U$ and $\phi(n) = 1$. Let $m$ be the smallest element in $A$.
Compute the value of $\sum_{n=1}^{m} \phi(n)$. | 1 | graphs = [
Graph(
let={
"upper": Const(10),
"k": Const(1),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Summation(var="n", start=Const(1), en... | NT | null | EXTREMUM | sympy | C4 | [
"K2"
] | 6897ab | nt_min_phi_inverse_v1 | null | 3 | 0 | [
"C4",
"K2"
] | 2 | 0.045 | 2026-02-08T08:28:43.686494Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T08:28:43.731228Z"
} | 2ef42c | 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": 781
},
"timestamp": "2026-02-13T18:56:17.308Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
133519 | geo_count_lattice_triangle_v1_1218484723_7370 | Let $R = \left|200 \cdot \max\{ xy \mid x > 0, y > 0, x + y = 20\} + 48 \cdot (-23)\right|$. Let $S = \gcd(200, 23) + \gcd(|48 - 200|, |100 - 23|) + \gcd(|48|, |100|)$. Compute $\frac{R + 2 - S}{2}$. | 9,446 | graphs = [
Graph(
let={
"_m": Const(200),
"_n": Const(48),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_m'), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')),... | GEOM | NT | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B1"
] | 7086d0 | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.009 | 2026-02-25T08:46:35.537353Z | {
"verified": true,
"answer": 9446,
"timestamp": "2026-02-25T08:46:35.545890Z"
} | 58dead | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 825
},
"timestamp": "2026-03-30T04:12:04.439Z",
"answer": 9446
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
e35aa5 | geo_count_lattice_rect_v1_458359167_3095 | Compute the number of lattice points in the rectangle $[0, 66] \times [0, 166]$, including the boundary. | 11,189 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(166),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T06:56:47.652203Z | {
"verified": true,
"answer": 11189,
"timestamp": "2026-02-08T06:56:47.652694Z"
} | 2f41cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 297
},
"timestamp": "2026-02-24T07:27:36.562Z",
"answer": 11189
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
8e1df9 | antilemma_cartesian_v1_2051736721_2730 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 15$ and $1 \leq b \leq 20$. Compute the value of $$x + \phi(|x| + 0!) + \tau(|x| + 1),$$ where $\phi(n)$ denotes the number of positive integers at most $n$ that are relatively prime to $n$, and $\tau(n)$ denotes the number of positive divisors of... | 556 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Const(20)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Factorial(Const(0)))), NumDivisors(n=Sum(Abs(arg=Ref(name='x... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | cb6f65 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 2 | 0.002 | 2026-02-08T16:52:00.977669Z | {
"verified": true,
"answer": 556,
"timestamp": "2026-02-08T16:52:00.979499Z"
} | 51745f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 523
},
"timestamp": "2026-02-17T14:43:06.392Z",
"answer": 556
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
d511a3 | nt_count_coprime_and_v1_124444284_2847 | Let $x$ and $y$ be positive integers such that $x + y = 6$. Define $k_1$ to be the maximum value of $xy$ over all such pairs $(x, y)$. Let $k_2 = 11$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 38166$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Compute the remainder when $32 - |S|$ is div... | 73,985 | graphs = [
Graph(
let={
"_n": Const(32),
"upper": Const(38166),
"k1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), ... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_coprime_and_v1 | null | 4 | 0 | [
"B1"
] | 1 | 3.969 | 2026-02-08T05:02:35.860954Z | {
"verified": true,
"answer": 73985,
"timestamp": "2026-02-08T05:02:39.829863Z"
} | b11a2d | 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": 1219
},
"timestamp": "2026-02-11T22:47:22.551Z",
"answer": 73985
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
eee5ae | modular_count_residue_v1_865884756_3328 | Let $m = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the remainder when $44121$ times the number of positive integers $n$ less than or equal to 36864 such that $n \equiv 6 \pmod{m}$ is divided by 82373. | 46,550 | graphs = [
Graph(
let={
"upper": Const(36864),
"m": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"r": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | modular_count_residue_v1 | null | 4 | 0 | [
"K2"
] | 1 | 1.175 | 2026-02-08T17:18:21.583413Z | {
"verified": true,
"answer": 46550,
"timestamp": "2026-02-08T17:18:22.758482Z"
} | 74ea3d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1144
},
"timestamp": "2026-02-17T23:33:28.212Z",
"answer": 46550
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b42a00 | sequence_count_fib_divisible_v1_2051736721_4347 | Let $n = 29241$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $d = 17$. Define $A$ as the set of all positive integers $k$ such that $1 \leq k \leq s$ and $d$ divides the $k$-th Fibonacci number. Compute the numbe... | 43,938 | graphs = [
Graph(
let={
"_n": Const(29241),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.046 | 2026-02-08T17:55:31.464016Z | {
"verified": true,
"answer": 43938,
"timestamp": "2026-02-08T17:55:31.509688Z"
} | 884037 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2562
},
"timestamp": "2026-02-18T10:08:26.696Z",
"answer": 43938
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d9213e | comb_binomial_compute_v1_1520064083_9991 | Let $n = 12$. Define $k$ as follows: first, let $d_{\text{min}}$ be the smallest divisor of 847 that is at least 2. Then, let $k = \sum_{d \mid d_{\text{min}}} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute $\binom{12}{k}$. | 792 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"k": SumOverDivisors(n=MinOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(left=Var(name='d'), right=Ref(name='_n')), Divides(divisor=Var(name='d'), dividend=Const(value=847))))), var='d', expr=EulerPhi(... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K3"
] | 54b4a9 | comb_binomial_compute_v1 | null | 6 | 0 | [
"K3",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T11:08:53.155236Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T11:08:53.156612Z"
} | 994f01 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 376
},
"timestamp": "2026-02-15T21:08:46.503Z",
"answer": 792
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
020fc1 | antilemma_k2_v1_458359167_4062 | Let $c = 388$ and let $m = \sum_{d \mid c} \phi(d)$, where $\phi$ is Euler's totient function. Let $n = 388$. Compute $$ \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{\sum_{d \mid m} \phi(d)}{k} \right\rfloor. $$ | 75,466 | graphs = [
Graph(
let={
"_c": Const(388),
"_m": SumOverDivisors(n=Ref(name='_c'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_n": Const(388),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Ref(... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K3/K2",
"K2"
] | d92398 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.004 | 2026-02-08T11:29:46.346278Z | {
"verified": true,
"answer": 75466,
"timestamp": "2026-02-08T11:29:46.350695Z"
} | 31cee8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 979
},
"timestamp": "2026-02-14T15:23:16.913Z",
"answer": 75466
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_V... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
864908 | nt_count_intersection_v1_677425708_631 | Let $m = 35$ and $n = 9$. Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 65619$, $n$ divides $k$, and $\gcd(k, m) = 1$. Let $a = 9$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 100$. Determine the number of positive integers $k$ s... | 222 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(9),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Const(65619)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_m")), Const(... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2",
"C5",
"B3"
] | 80903e | nt_count_intersection_v1 | null | 6 | 0 | [
"B3",
"C5",
"ONE_PHI_2"
] | 3 | 2.422 | 2026-02-08T03:37:55.212290Z | {
"verified": true,
"answer": 222,
"timestamp": "2026-02-08T03:37:57.634549Z"
} | 2bc60e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 2862
},
"timestamp": "2026-02-08T20:51:54.849Z",
"answer": 222
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"le... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
ef025b | comb_binomial_compute_v1_124444284_10321 | Let $n$ be the largest positive divisor of $156$ that is at most $12$. Compute $\binom{n}{6}$. | 924 | graphs = [
Graph(
let={
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(12)), Divides(divisor=Var("d"), dividend=Const(156))))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | comb_binomial_compute_v1 | null | 2 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T12:58:29.813536Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T12:58:29.814391Z"
} | b474b5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 513
},
"timestamp": "2026-02-16T04:24:01.598Z",
"answer": 924
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
f388d1 | alg_poly_orbit_hensel_v1_1419126231_165 | Define the function $f(x) = (x^5 + 5x^4 - 2x^3 - 2x^2 - 4x + 4) \bmod 6859$. Let $N = f(a)$, $M = f(N)$, $R = f(M)$, and $S = f(R)$. Find the number of non-negative integers $a$ with $0 \le a \le 3628410$ such that $S = a$, $N \ne a$, $M \ne a$, and $R \ne a$. | 2,116 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(5)), Mul(Const(5), Pow(Var("a"), Const(4))), Mul(Const(-2), Pow(Var("a"), Const(3))), Mul(Const(-2), Pow(Var("a"), Const(2))), Mul(Const(-4), Var("a")), Const(4)), modulus=Const(6859)),
"p2": Mod(value=Sum(Pow(Ref("p1"),... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.104 | 2026-02-25T09:44:25.560323Z | {
"verified": true,
"answer": 2116,
"timestamp": "2026-02-25T09:44:25.664506Z"
} | 852ac0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T07:24:43.058Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
623535 | antilemma_sum_equals_v1_1520064083_3830 | Let $n = 94$. Define $S$ to be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 92$, $1 \leq j \leq 92$, and $i + j = n$. Let $x$ be the number of elements in $S$. Compute the value of $\sum_{k=1}^{x} \phi(k)$, where $\phi$ denotes Euler's totient function. | 2,552 | graphs = [
Graph(
let={
"_n": Const(94),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(92)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T05:55:31.010687Z | {
"verified": true,
"answer": 2552,
"timestamp": "2026-02-08T05:55:31.014810Z"
} | 6dcf14 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 4223
},
"timestamp": "2026-02-24T04:59:49.221Z",
"answer": 2552
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
27c40d | nt_count_phi_equals_v1_655260480_280 | Let $N = 24964$. Let $\text{upper}$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 68$. Let $k$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = N$. Let $r$ be the number of positive integers $n$ such that $1 \leq n \... | 88,242 | graphs = [
Graph(
let={
"_n": Const(24964),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(68)))), expr=Mul(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3",
"B1"
] | 655d51 | nt_count_phi_equals_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.214 | 2026-02-08T15:20:11.048551Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T15:20:11.262872Z"
} | 705e1a | 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": 1690
},
"timestamp": "2026-02-16T03:29:28.216Z",
"answer": 88242
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab7a76 | sequence_lucas_compute_v1_865884756_4410 | Let $m$ be the number of ordered pairs $(x, y)$ with $1 \leq x \leq 50$ and $1 \leq y \leq 50$. Let $n_1$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $n$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such tha... | 15,127 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(50)), right=IntegerRange(start=Const(1), end=Const(50)))),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/B3",
"B3/B3"
] | 2280fc | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 0.006 | 2026-02-08T17:55:12.426243Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T17:55:12.432276Z"
} | a4b020 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1056
},
"timestamp": "2026-02-18T09:47:12.560Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc2b0c | lin_form_endings_v1_971394319_122 | Let $a = 28$ and $b = 21$. Let $k = 37$. Define $d = \gcd(a, b)$, and let $g = \gcd(k, d)$. Let $m = \left\lfloor \frac{k}{g} \right\rfloor$. Define $s = 15369 \cdot m$, and let $M = 51633$. Compute the remainder when $s$ is divided by $M$. | 690 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(21),
"k_val": Const(37),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(15... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:50:53.235925Z | {
"verified": true,
"answer": 690,
"timestamp": "2026-02-08T12:50:53.236888Z"
} | 8efeb1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 622
},
"timestamp": "2026-02-15T06:48:51.248Z",
"answer": 690
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
25c2b5 | modular_mod_compute_v1_1439011603_2158 | Let $n = 108$ and $a = -2222$. Define $m = \sum_{k=1}^{108} k$. Compute the remainder when $a$ is divided by $m$. | 3,664 | graphs = [
Graph(
let={
"_n": Const(108),
"a": Const(-2222),
"m": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_mod_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T16:34:54.859437Z | {
"verified": true,
"answer": 3664,
"timestamp": "2026-02-08T16:34:54.861537Z"
} | 063142 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 217
},
"timestamp": "2026-02-16T07:33:55.415Z",
"answer": 3664
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"statu... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
612214 | nt_sum_over_divisible_v1_655260480_10 | Let $D$ be the number of integers $n$ such that $1 \leq n \leq 989$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 33670$ and $n_1$ is divisible by $D$. Let $\sigma$ be the sum of all elements in $S$.
Let $C$ be the number of... | 23,330 | graphs = [
Graph(
let={
"_m": Const(12000),
"_n": Const(2),
"upper": Const(33670),
"divisor": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(989)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM",
"COMB1",
"L3C"
] | e8b700 | nt_sum_over_divisible_v1 | quadratic_mod | 7 | 0 | [
"COMB1",
"L3C",
"LIN_FORM"
] | 3 | 1.052 | 2026-02-08T15:08:03.579036Z | {
"verified": true,
"answer": 23330,
"timestamp": "2026-02-08T15:08:04.631033Z"
} | f4726e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 3306
},
"timestamp": "2026-02-16T00:24:51.622Z",
"answer": 23330
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c6bf5f | alg_poly4_sum_v1_601307018_8098 | Find the remainder when $$\sum_{a=1}^{381} \sum_{b=1}^{381} \left( \min_{\substack{a1=1..17 \\ b1=1..17}} \left\{ 256b1^4 + 256a1^4 \right\} \cdot a^3b + 128ab^3 + 256a^4 + \min_{\substack{x>0 \\ y>0 \\ xy=36864}} \{x+y\} \cdot a^2b^2 + 17b^4 \right)$$ is divided by $62353$. | 9,866 | graphs = [
Graph(
let={
"_m": Const(128),
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(381)), Geq(Var("b"), Const(1)), Leq(Var("b"), Cons... | ALG | null | COMPUTE | sympy | POLY4_MIN | [
"POLY4_MIN",
"B3"
] | a2070e | alg_poly4_sum_v1 | null | 7 | 0 | [
"B3",
"POLY4_MIN"
] | 2 | 0.361 | 2026-03-10T08:35:23.624890Z | {
"verified": true,
"answer": 9866,
"timestamp": "2026-03-10T08:35:23.986292Z"
} | b3a032 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 8952
},
"timestamp": "2026-04-19T08:17:32.640Z",
"answer": 9866
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY4_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f64f38 | antilemma_cartesian_v1_655260480_68 | Let $A$ be the set of all ordered pairs $(i, j)$ such that $1 \le i \le 26$ and $1 \le j \le 49$. Define $x = |A|$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $x + 2$. | 210 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(26)), right=IntegerRange(start=Const(1), end=Const(49)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.006 | 2026-02-08T15:09:50.232076Z | {
"verified": true,
"answer": 210,
"timestamp": "2026-02-08T15:09:50.237737Z"
} | 5054f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 3807
},
"timestamp": "2026-02-24T19:54:49.560Z",
"answer": 210
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
4fc051 | nt_count_divisible_v1_1439011603_2572 | Let $d$ be the largest prime number between 2 and 5, inclusive. Compute the number of positive integers $n$ such that $1 \leq n \leq 43681$ and $n$ is divisible by $d$. | 8,736 | graphs = [
Graph(
let={
"upper": Const(43681),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Co... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_divisible_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.517 | 2026-02-08T16:52:14.227586Z | {
"verified": true,
"answer": 8736,
"timestamp": "2026-02-08T16:52:15.744375Z"
} | e25f78 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 368
},
"timestamp": "2026-02-16T07:55:37.518Z",
"answer": 8736
},
{
"id": 11,
... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
993f1b | diophantine_sum_product_min_v1_124444284_7866 | Let $S = 36$ and $P = 203$. Let $A$ be the set of all real solutions $x$ to the equation $x^2 - 35x - 246 = 0$. Let $T$ be the set of all integers $x$ such that $1 \leq x \leq \sum A$ and $x(S - x) = P$, where $\sum A$ denotes the sum of all elements in $A$. Compute the smallest element of $T$. | 7 | graphs = [
Graph(
let={
"_n": Const(2),
"S": Const(36),
"P": Const(203),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")... | NT | null | EXTREMUM | sympy | K14 | [
"VIETA_SUM"
] | b33a7a | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"K14",
"VIETA_SUM"
] | 2 | 0.033 | 2026-02-08T09:24:06.970702Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T09:24:07.004168Z"
} | 7117a9 | 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": 528
},
"timestamp": "2026-02-14T03:42:00.783Z",
"answer": 7
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
df2f4d | diophantine_fbi2_count_v1_124444284_9447 | Let $k = 120$. Determine the number of positive integers $d$ such that $4 \leq d \leq 69$, $d$ divides $k$, and the quotient $k/d$ satisfies $3 \leq k/d \leq 68$. Compute this count. | 11 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(69)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(R... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"K2"
] | 6897ab | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.034 | 2026-02-08T12:27:46.464447Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T12:27:46.498771Z"
} | e2965f | 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": 893
},
"timestamp": "2026-02-15T01:41:57.402Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
77b582 | comb_count_derangements_v1_655260480_2384 | Let $n$ be the largest prime number that is at least $2$ and at most the smallest divisor of $77$ that is greater than $1$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77)))))), IsPrime(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.014 | 2026-02-08T16:41:50.018139Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T16:41:50.032421Z"
} | 16bd95 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 530
},
"timestamp": "2026-02-17T09:31:56.517Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
991972 | comb_binomial_compute_v1_458359167_2798 | Let $n = 14$ and let $k = \sum_{i=1}^{3} i$. Compute $\binom{n}{k}$. Let $Q$ be the remainder when $44121$ times this binomial coefficient is divided by $78475$. Find the value of $Q$. | 29,563 | graphs = [
Graph(
let={
"n": Const(14),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(78475)),
},
goal=Ref("Q"),
... | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T06:46:25.248207Z | {
"verified": true,
"answer": 29563,
"timestamp": "2026-02-08T06:46:25.249036Z"
} | 2ae2c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1237
},
"timestamp": "2026-02-24T07:04:53.104Z",
"answer": 29563
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
a3fc76 | sequence_count_fib_divisible_v1_717093673_3983 | Let $n = 50$. Define $P$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 50$. Let $\text{upper}$ be the maximum value of $xy$ as $(x, y)$ ranges over $P$. Let $d = 20$. Determine the number of positive integers $n$ with $1 \leq n \leq \text{upper}$ such that $F_n$ is divisible by $d$... | 30 | graphs = [
Graph(
let={
"_n": Const(50),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | C3 | [
"B1"
] | 5b950e | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B1",
"C3"
] | 2 | 2.676 | 2026-02-08T17:59:00.704682Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T17:59:03.380514Z"
} | 52df25 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1770
},
"timestamp": "2026-02-18T10:58:19.934Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8687f1 | sequence_fibonacci_compute_v1_677425708_2354 | Let $k$ be a nonnegative integer. Determine the largest integer $k$ such that $2^k \le 4582237$. Let $n$ be this value. Compute the $n$th Fibonacci number, where $F_0 = 0$, $F_1 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \ge 2$. | 17,711 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(4582237)))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T05:00:50.720471Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T05:00:50.721745Z"
} | 2f8407 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 560
},
"timestamp": "2026-02-11T22:44:29.901Z",
"answer": 17711
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"statu... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
b283d4 | nt_num_divisors_compute_v1_971394319_1554 | Let $n$ be the number of positive integers at most 45 that are divisible by 3 and relatively prime to 14. Compute $15459$ times the number of positive divisors of $n$. | 30,918 | graphs = [
Graph(
let={
"_n": Const(45),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(3), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"result": NumDivisors(n=... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.003 | 2026-02-08T13:43:36.237182Z | {
"verified": true,
"answer": 30918,
"timestamp": "2026-02-08T13:43:36.239779Z"
} | f846cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 580
},
"timestamp": "2026-02-15T20:21:22.492Z",
"answer": 30918
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
2fe9f2 | nt_num_divisors_compute_v1_717093673_2920 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq N$, where $N$ is the number of integers $t$ with $14 \leq t \leq 120$ for which there exist positive integers $a \leq 10$ and $b \leq 5$ such that $t = 10a + 4b$. Suppose $\binom{50}{j}$ is odd. Let $n$ be the sum of all such $j$ in $S$ for whi... | 12 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V8"
] | 654a7e | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.004 | 2026-02-08T17:17:23.681312Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T17:17:23.684822Z"
} | b62cab | 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": 3240
},
"timestamp": "2026-02-17T23:08:32.026Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2f007d | algebra_quadratic_discriminant_v1_1520064083_784 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the smallest positive integer $n$ such that $2^3$ divides $n!$. Compute $(-6)^2 - m \cdot a \cdot (-9)$. | 108 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)), Eq(left=GCD(a=Va... | NT | null | COMPUTE | sympy | K3 | [
"COPRIME_PAIRS",
"V5"
] | 4f48e4 | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"K3",
"V5"
] | 3 | 0.005 | 2026-02-08T03:35:33.530126Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T03:35:33.534688Z"
} | bb6efd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 265
},
"timestamp": "2026-02-18T03:27:53.768Z",
"answer": 108
}
] | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
c800f6 | antilemma_k2_v1_1520064083_3471 | Let $c=674$ and
$$m=\sum_{d\mid c} \varphi(d),$$
where the sum is taken over all positive divisors $d$ of $c$, and $\varphi$ is Euler's totient function.
Let $n=339$. Consider the quadratic polynomial
$$f(x)=x^2-339x+m.$$
Let $S$ be the set of all integers $x$ such that $f(x)+m=0$, and assume this set is nonempty. Let... | 57,630 | graphs = [
Graph(
let={
"_c": Const(674),
"_m": SumOverDivisors(n=Ref(name='_c'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_n": Const(339),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=Solutio... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K3/VIETA_SUM/K2",
"K2"
] | 2b6013 | antilemma_k2_v1 | null | 8 | 0 | [
"K13",
"K2",
"K3",
"VIETA_SUM"
] | 4 | 0.003 | 2026-02-08T05:41:50.646196Z | {
"verified": true,
"answer": 57630,
"timestamp": "2026-02-08T05:41:50.649398Z"
} | 350955 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 4283
},
"timestamp": "2026-02-12T12:49:10.894Z",
"answer": 57630
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e6dfac | comb_sum_binomial_mod_v1_458359167_313 | Let $s = \sum_{k=21}^{T} \binom{141}{k}$, where $T = \sum_{k=1}^{15} k$. Compute the remainder when $s$ is divided by 10657. | 6,840 | graphs = [
Graph(
let={
"_n": Const(10657),
"sum": Summation(var="k", start=Const(21), end=Summation(var="k", start=Const(1), end=Const(15), expr=Var("k")), expr=Binom(n=Const(141), k=Var("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("_n")),
},
goal=... | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_sum_binomial_mod_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.009 | 2026-02-08T03:11:33.894298Z | {
"verified": true,
"answer": 6840,
"timestamp": "2026-02-08T03:11:33.903367Z"
} | 2661ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:01:00.831Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
fc1c52 | nt_sum_gcd_range_mod_v1_48377204_1555 | Let $N = 1296$ and $M = 11239$. Define $k$ to be the number of positive integers $n$ with $1 \leq n \leq 2016$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remainder when $\text{sum}$ is divided by $M$. | 10,512 | graphs = [
Graph(
let={
"N": Const(1296),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2016)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.071 | 2026-02-08T16:10:13.823117Z | {
"verified": true,
"answer": 10512,
"timestamp": "2026-02-08T16:10:13.894477Z"
} | 53025a | 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": 2853
},
"timestamp": "2026-02-16T23:23:12.634Z",
"answer": 10512
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cbb785 | modular_min_modexp_v1_1918700295_2932 | Let $m$ be the largest prime number less than or equal to $195$. Let $a = 11$, $b = 14$, and let $p$ be the largest prime number less than or equal to $m$. Determine the smallest positive integer $x \leq 64$ such that $$11^x \equiv 14 \pmod{p}.$$ Compute the remainder when $45751$ times this value of $x$ is divided by ... | 48,657 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(195)), IsPrime(Var("n"))))),
"a": Const(11),
"b": Const(14),
"m": MaxOverSet(set=SolutionsSet(var=Va... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | modular_min_modexp_v1 | null | 7 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.008 | 2026-02-08T08:19:17.981290Z | {
"verified": true,
"answer": 48657,
"timestamp": "2026-02-08T08:19:17.988909Z"
} | 1b58fd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 800
},
"timestamp": "2026-02-13T17:18:17.737Z",
"answer": 48657
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b34e6c | comb_count_permutations_fixed_v1_153355830_2782 | Let $n = 10$ and let $k = \sum_{i=1}^{3} i$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. Compute $39204 - r$. | 37,314 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(10),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Sub(Co... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T07:21:39.605278Z | {
"verified": true,
"answer": 37314,
"timestamp": "2026-02-08T07:21:39.607264Z"
} | 660037 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 661
},
"timestamp": "2026-02-24T08:01:15.652Z",
"answer": 37314
},
{
"i... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM"... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
ca5f1d | nt_sum_gcd_range_mod_v1_548369836_0 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 4999$ and the sum of the digits of $n$ is odd. Let $k = 480$ and $M = 10357$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Compute the remainder when $\text{sum}$ is divided by $M$. | 5,368 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4999)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"k": Const(480),
"M": Const(10357),
"sum": Summation(v... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | nt_sum_gcd_range_mod_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.507 | 2026-02-08T02:42:19.113631Z | {
"verified": true,
"answer": 5368,
"timestamp": "2026-02-08T02:42:19.621068Z"
} | ee694a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:53:00.296Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": 2.8,
"mid": 4.67,
"hi": 6.48
} | ||
e006d9 | diophantine_fbi2_count_v1_677425708_3834 | Let $k = \sum_{d \mid 480} \phi(d)$, where $\phi$ denotes Euler's totient function.
Determine the number of positive integers $d$ such that $2 \leq d \leq 65$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 68$. | 12 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(65),
"k": SumOverDivisors(n=Const(value=480), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("_n")), D... | NT | null | COUNT | sympy | B1 | [
"B1",
"K3"
] | 9ff3cb | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B1",
"K3"
] | 2 | 0.014 | 2026-02-08T05:57:19.449654Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T05:57:19.463915Z"
} | b2a567 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1106
},
"timestamp": "2026-02-12T18:24:13.954Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lem... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
a38aa8 | antilemma_k3_v1_1742523217_2458 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $33980$, where $\phi$ denotes Euler's totient function. Compute the remainder when $8 - x$ is divided by $51510$. | 17,538 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=33980), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(8), Ref("x")), modulus=Const(51510)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:47:15.444518Z | {
"verified": true,
"answer": 17538,
"timestamp": "2026-02-08T04:47:15.444811Z"
} | e2fcb9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 401
},
"timestamp": "2026-02-11T22:03:48.994Z",
"answer": 17538
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
17ad48 | nt_min_coprime_above_v1_898971024_2681 | Let $M$ be the number of integers $n$ with $1 \le n \le 1218$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $r$ be the smallest integer greater than 1600 and at most 1784 that is relatively prime to $M$. Compute the remainder when $44121 \cdot r$ is divided by 94214. | 71,435 | graphs = [
Graph(
let={
"_n": Const(94214),
"start": Const(1600),
"upper": Const(1784),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1218)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Va... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.02 | 2026-02-08T16:54:32.700379Z | {
"verified": true,
"answer": 71435,
"timestamp": "2026-02-08T16:54:32.719929Z"
} | f84552 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1338
},
"timestamp": "2026-02-17T14:17:33.895Z",
"answer": 71435
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
80931d | comb_sum_binomial_row_v1_1439011603_625 | Let $n$ be the value of the sum
$$
\sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $2^n \times 44121$ is divided by $68212$. Compute $Q$. | 23,560 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(68... | NT | null | SUM | sympy | K2 | [
"K2"
] | 6897ab | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T15:37:43.279474Z | {
"verified": true,
"answer": 23560,
"timestamp": "2026-02-08T15:37:43.281218Z"
} | 509ec2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1106
},
"timestamp": "2026-02-16T10:13:20.056Z",
"answer": 23560
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0ba355 | antilemma_sum_equals_v1_1918700295_2897 | Let $t_0$ be the number of integers $t$ with $17 \leq t \leq 112$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 46$, and $t = 5a + 2b + 10$. Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = t_0$. Let $x$ be the number of ordered... | 473 | graphs = [
Graph(
let={
"_m": Const(90226),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2"))... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b14821 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.012 | 2026-02-08T08:18:30.991222Z | {
"verified": true,
"answer": 473,
"timestamp": "2026-02-08T08:18:31.002980Z"
} | fd4c04 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 962
},
"timestamp": "2026-02-24T09:19:04.055Z",
"answer": 473
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
c59a4e | geo_visible_lattice_v1_601307018_884 | For each integer $a$ with $0 \le a \le 960$, define the sequence $M = (2a^3 + 4a) \bmod 961$, $R = (2M^3 + 4M) \bmod 961$, $S = (2R^3 + 4R) \bmod 961$, $T = (2S^3 + 4S) \bmod 961$, $K = (2T^3 + 4T) \bmod 961$, and $L = (2K^3 + 4K) \bmod 961$. Let $n$ be the number of such $a$ for which $L = a$, but $M \ne a$, $R \ne a$... | 2,203 | graphs = [
Graph(
let={
"_n": Const(960),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Ref("_n")), Eq(Ref("_po_p6"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a")), Neq(Ref("... | GEOM | GEOM | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | geo_visible_lattice_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL"
] | 1 | 0.211 | 2026-03-10T01:30:09.319423Z | {
"verified": true,
"answer": 2203,
"timestamp": "2026-03-10T01:30:09.530271Z"
} | 662c8c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 330,
"completion_tokens": 16778
},
"timestamp": "2026-03-29T00:29:38.204Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
65e9b8 | nt_min_coprime_above_v1_1915831931_616 | Let $n = 63167$. Define $\text{start}$ to be the number of integers $j$ with $0 \leq j \leq n$ such that $\binom{n}{j}$ is odd. Let $\text{upper} = 8621$ and $\text{modulus} = 419$. Consider the set of all integers $n$ such that $\text{start} < n \leq \text{upper}$ and $\gcd(n, 419) = 1$. Determine the value of the sma... | 8,193 | graphs = [
Graph(
let={
"_n": Const(63167),
"start": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(63167), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | EXTREMUM | sympy | V8 | [
"V8"
] | 86348e | nt_min_coprime_above_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.038 | 2026-02-08T15:35:19.627931Z | {
"verified": true,
"answer": 8193,
"timestamp": "2026-02-08T15:35:19.665803Z"
} | b566a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1668
},
"timestamp": "2026-02-16T08:57:09.443Z",
"answer": 8193
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3becfb_n | alg_poly3_count_v1_1218484723_177 | A video game tracks player progress using Fibonacci-based achievements: a milestone occurs at level $n$ if $16 \mid F_n$, and there are $C$ such milestones up to level $43500$. A side quest generates challenges $(a_1, b_1)$ with $1\le a_1,b_1\le30$ for which $13a_1^2 - 2a_1b_1 + 2b_1^2 \le C$; let $D$ be the number of ... | 475 | ALG | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/QF_PSD_COUNT_LEQ"
] | d3c528 | alg_poly3_count_v1 | null | 7 | null | [
"COUNT_FIB_DIVISIBLE",
"QF_PSD_COUNT_LEQ"
] | 2 | 1.672 | 2026-02-25T01:51:57.590673Z | null | 905d9c | 3becfb | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 7060
},
"timestamp": "2026-03-31T05:20:50.766Z",
"answer": 475
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
b504bd | antilemma_v8_lucas_50713871_96 | Let $n = 54265$. Let $s = \sum_{d \mid 42} \mu(d)$, where $\mu$ denotes the M\"obius function. Let $T$ be the set of all nonnegative integers $j$ such that $s \leq j \leq n$ and $$\binom{54265}{j} \equiv 1 \pmod{m},$$ where $m$ is the number of positive integers $p$ for which there exists an integer $q > p$ such that $... | 2,048 | graphs = [
Graph(
let={
"_n": Const(54265),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), SumOverDivisors(n=Const(value=42), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(54265), k=Var("j")), modulus=Co... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8",
"MOBIUS_SUM",
"V8"
] | 7ef9f1 | antilemma_v8_lucas | null | 7 | 0 | [
"COPRIME_PAIRS",
"MOBIUS_SUM",
"V8"
] | 3 | 0.002 | 2026-02-08T02:45:17.833163Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T02:45:17.835626Z"
} | 9eed03 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 2061
},
"timestamp": "2026-02-08T19:48:49.664Z",
"answer": 2048
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
7ad22b | comb_sum_binomial_row_v1_1978505735_1547 | Let $n = 15$. Compute the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 54$. Raise this count to the power $n$. Subtract this result from $47895$. Find the value of the resulting expression. | 15,127 | graphs = [
Graph(
let={
"_n": Const(47895),
"n": Const(15),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:15:08.218763Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T16:15:08.221041Z"
} | 5d8ce7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1268
},
"timestamp": "2026-02-16T23:46:53.336Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
008aa8 | comb_sum_binomial_row_v1_1419126231_796 | Let $A$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 30$ such that $16a^2 - 8ab + b^2 = N$, where $N = \left|\{(a_1,b_1) : 1 \leq a_1,b_1 \leq 30,\ 13a_1^2 - 2a_1b_1 + 2b_1^2 \leq 1217\}\right|$. Compute $2^A$. | 4,096 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"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(16), P... | COMB | null | SUM | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_COUNT"
] | 831c70 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.005 | 2026-02-25T10:17:11.909294Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-25T10:17:11.914225Z"
} | acf0aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 3134
},
"timestamp": "2026-03-30T10:02:18.194Z",
"answer": 4096
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
c98809 | diophantine_product_count_v1_1742523217_1193 | Let $k$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 129600$. Let $S$ be the set of all positive integers $x$ such that $x \leq 122$, $x$ divides $k$, and $\frac{k}{x} \leq 122$. Compute the number of elements in $S$. | 20 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(129600)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(1... | NT | null | COUNT | sympy | LIN_FORM | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"MOBIUS_COPRIME"
] | 3 | 0.035 | 2026-02-08T03:31:01.358924Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T03:31:01.394413Z"
} | ca87b2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2580
},
"timestamp": "2026-02-09T12:26:51.097Z",
"answer": 20
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
d30d08 | nt_sum_over_divisible_v1_1431428450_295 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 6375625$. Define $T$ to be the set of all values $x + y$ where $(x, y) \in S$. Let $a$ be the minimum value in $T$.
Let $U$ be the set of all positive integers $t$ such that $7 \leq t \leq 208$ and there exist integers $a$ and $b$ wit... | 64,350 | 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(6375625)))), expr=Sum(Var("x"), Var("y")))),
"divisor": ... | NT | null | SUM | sympy | B3 | [
"LIN_FORM",
"B3"
] | 688dbe | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 5.927 | 2026-02-08T13:23:18.080986Z | {
"verified": true,
"answer": 64350,
"timestamp": "2026-02-08T13:23:24.008191Z"
} | 08cd2a | 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": 2662
},
"timestamp": "2026-02-15T13:59:07.940Z",
"answer": 64350
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e13a2a | antilemma_sum_factor_cartesian_v1_168721529_1415 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 8$ and $1 \leq j \leq 22$. Let $T$ be the subset of $S$ consisting of all pairs $(i,j)$ for which
$$
\sum_{d \mid \gcd(7,11)} \mu(d) = 1.
$$
Compute the sum of $ij$ over all pairs $(i,j)$ in $T$. | 9,108 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=7), b=Const(value=11)), var='d', expr=MoebiusMu(n=Var(name='d'))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME"
] | 1428b5 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T13:41:29.352592Z | {
"verified": true,
"answer": 9108,
"timestamp": "2026-02-08T13:41:29.353514Z"
} | e744b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 2184
},
"timestamp": "2026-02-09T16:44:14.493Z",
"answer": 9108
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
831328 | modular_count_residue_v1_1742523217_1668 | Let $m$ be the largest prime number less than or equal to 28. Let $r$ be the number of integers $t$ in the range $13 \leq t \leq 20$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 3a + 2b + 8$. Compute the number of positive integers $n$ such that $1 \leq n \leq 4494... | 22,824 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(44944),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(28)), IsPrime(Var("n"))))),
"r": CountOverSet(set=SolutionsSet(var=Var("t"), condition=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | modular_count_residue_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 1.477 | 2026-02-08T04:06:00.052851Z | {
"verified": true,
"answer": 22824,
"timestamp": "2026-02-08T04:06:01.530123Z"
} | 3d0a3f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 1436
},
"timestamp": "2026-02-10T15:18:01.708Z",
"answer": 22824
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4f6f3a_n | alg_sym_quad_system_v1_1218484723_7263 | A shipping company numbers its containers from $1$ to $595800$. A container is called *bulk* if its number is divisible by $100$, and $M$ is the total count of such bulk containers. Three warehouses $A, B, C$ must share exactly $M$ bulk containers, with $a, b, c$ containers respectively, where $a, b, c$ are positive in... | 1,825 | ALG | null | COMPUTE | sympy | C2 | [
"C2/L3C"
] | 79d5db | alg_sym_quad_system_v1 | null | 7 | null | [
"C2",
"L3C"
] | 2 | 0.016 | 2026-02-25T08:42:13.428615Z | null | 0dcf33 | 4f6f3a | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 368,
"completion_tokens": 3408
},
"timestamp": "2026-03-31T02:06:31.012Z",
"answer": 1825
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
9e6c87 | comb_count_permutations_fixed_v1_655260480_4172 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 21000$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $P$.
Let $D_n$ denote the number of derangements of $n$ elements, defined as the number of permutations of $n$ elements with no fixed... | 80,807 | 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=21000)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.011 | 2026-02-08T17:46:57.368921Z | {
"verified": true,
"answer": 80807,
"timestamp": "2026-02-08T17:46:57.380047Z"
} | a3cc5b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 3181
},
"timestamp": "2026-02-18T07:48:19.271Z",
"answer": 80807
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
181a58 | algebra_poly_eval_v1_971394319_108 | Let $d$ be a positive integer divisor of $47027$ such that $d \geq 2$. Let $m$ be the smallest such $d$. Compute the number of positive integers $n$ such that $1 \leq n \leq m$ and $\gcd(n, 15) = 1$. Call this number $y$. Let $n = \sum_{k=1}^{8} k$. Compute
$$
\frac{20y^4 - 36y^3 + 12y^2 - 58y + n}{30}.
$$
Let $Q$ be t... | 49,413 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_c")), Divides(divisor=Var("d"), dividend=Const(47027))))),
"_n": Summation(var="k", start=Const(1), end=Const(8), expr=Var("k")),
"y": Cou... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/SUM_ARITHMETIC/C4"
] | 0f2bc6 | algebra_poly_eval_v1 | null | 5 | 0 | [
"C4",
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 3 | 0.007 | 2026-02-08T12:50:35.040228Z | {
"verified": true,
"answer": 49413,
"timestamp": "2026-02-08T12:50:35.047646Z"
} | cceb79 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1815
},
"timestamp": "2026-02-15T06:47:24.585Z",
"answer": 49413
},
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMET... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
695b38 | diophantine_sum_product_min_v1_1116507919_252 | Let $S = 34$. Let $P$ be the number of positive integers $j$ such that $1 \leq j \leq 289$ and $j^5 \leq 2015993900449$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 33$ and $x(S - x) = P$. | 17 | graphs = [
Graph(
let={
"S": Const(34),
"P": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(289)), Leq(Pow(Var("j"), Const(5)), Const(2015993900449))), domain='positive_integers')),
"result": MinOverSet(set=Solutions... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | 8a214c | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"C3"
] | 1 | 0.004 | 2026-02-08T02:29:53.728636Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T02:29:53.732851Z"
} | dca453 | 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": 1663
},
"timestamp": "2026-02-08T19:20:18.442Z",
"answer": 17
},
{
"id"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -2.86,
"mid": -0.89,
"hi": 0.97
} | ||
a12917 | diophantine_fbi2_min_v1_124444284_3887 | Let $s$ be the largest integer such that $5^s \leq 10217212752907$. Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = s$. Let $k$ be the maximum value of $xy$ over all such pairs $(x, y) \in P$. Let $d$ be the smallest integer $d$ with $6 \leq d \leq 91$ such that $d$ divides $k$ ... | 48,044 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(6),
"k": 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")), MaxOverSet(set=Solutio... | NT | null | EXTREMUM | sympy | MAX_VAL | [
"MAX_VAL/B1"
] | 9f2470 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B1",
"MAX_VAL"
] | 2 | 0.007 | 2026-02-08T05:39:34.250362Z | {
"verified": true,
"answer": 48044,
"timestamp": "2026-02-08T05:39:34.257378Z"
} | 315bf1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1667
},
"timestamp": "2026-02-12T11:57:29.106Z",
"answer": 48044
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
606016 | nt_lcm_compute_v1_717093673_614 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 866761$. Let $b = \sum_{k=1}^{76} \phi(k) \left\lfloor \frac{76}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $r = \mathrm{lcm}(a, b)$. Compute $r + 2^{r \bmod 16} \bmod 96991$. | 20,486 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(76),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(866761)))), exp... | NT | null | COMPUTE | sympy | K2 | [
"K2",
"B3"
] | f1ea07 | nt_lcm_compute_v1 | null | 7 | 0 | [
"B3",
"K2"
] | 2 | 0.003 | 2026-02-08T15:33:25.571356Z | {
"verified": true,
"answer": 20486,
"timestamp": "2026-02-08T15:33:25.573974Z"
} | 8b8bb6 | 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": 5464
},
"timestamp": "2026-02-16T08:29:34.089Z",
"answer": 20486
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b65834 | geo_count_lattice_rect_v1_865884756_6960 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 333$ and $0 \leq y \leq 254$. | 85,170 | graphs = [
Graph(
let={
"a": Const(333),
"b": Const(254),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T19:29:01.609241Z | {
"verified": true,
"answer": 85170,
"timestamp": "2026-02-08T19:29:01.610561Z"
} | 7f679d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 642
},
"timestamp": "2026-02-18T22:43:05.551Z",
"answer": 85170
},
{
... | 1 | [] | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||||
978deb | diophantine_fbi2_count_v1_1520064083_8678 | Let $k$ be the number of positive integers $j$ such that $1 \leq j \leq 840$ and $j^5 \leq 418211942400000$. Let $T$ be the set of all integers $d$ such that $5 \leq d \leq 103$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 101$. Compute the remainder when $56333 \cdot |T|$ is divided by $50574$. | 41,570 | graphs = [
Graph(
let={
"_n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(840)), Leq(Pow(Var("j"), Ref("_n")), Const(418211942400000))), domain='positive_integers')),
"result": CountOverSet(set=Solu... | NT | null | COUNT | sympy | C3 | [
"C3"
] | 8a214c | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"C3"
] | 1 | 0.02 | 2026-02-08T10:17:53.604367Z | {
"verified": true,
"answer": 41570,
"timestamp": "2026-02-08T10:17:53.624767Z"
} | 1904d1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1767
},
"timestamp": "2026-02-14T07:02:58.533Z",
"answer": 41570
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3aec9d | geo_count_lattice_rect_v1_865884756_2353 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 77$ and $0 \leq y \leq 25$. | 2,028 | graphs = [
Graph(
let={
"a": Const(77),
"b": Const(25),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T16:43:01.147762Z | {
"verified": true,
"answer": 2028,
"timestamp": "2026-02-08T16:43:01.148464Z"
} | ddb26b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 412
},
"timestamp": "2026-02-24T21:49:05.278Z",
"answer": 2028
},
{
... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
ccb9c3 | sequence_fibonacci_compute_v1_349078426_347 | Let $n$ be the number of integers $t$ with $16 \leq t \leq 52$ such that there exist integers $a$ and $b$, each between $1$ and $5$ inclusive, satisfying $t = 5a + 4b + 7$. Compute the $n$-th Fibonacci number. | 75,025 | 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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T12:56:56.381373Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T12:56:56.384494Z"
} | 0f315e | 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": 3228
},
"timestamp": "2026-02-15T08:32:10.288Z",
"answer": 75025
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
29e824 | algebra_quadratic_discriminant_v1_1218484723_2464 | Let $c$ be the minimum value of $41a_1^2 - 28a_1b_1 + 5b_1^2$ over all positive integers $a_1, b_1$ with $1 \leq a_1, b_1 \leq 29$. Compute $10^2 - 4(-10) \cdot c€. | 180 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-10),
"b": Const(10),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(29)), Geq(Var("b1"), Const(1)), Le... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.002 | 2026-02-25T04:13:56.891349Z | {
"verified": true,
"answer": 180,
"timestamp": "2026-02-25T04:13:56.893807Z"
} | cde124 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 6693
},
"timestamp": "2026-03-29T04:53:29.007Z",
"answer": 180
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
3c8240 | algebra_quadratic_discriminant_v1_601307018_1820 | Let $M$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1 \le 30$ and $1 \le b_1 \le 30$ such that
$$-18a_1 b_1 + \left|\left\{ (a_2, b_2) : a_2 \ge 1,\ a_2 \le 35,\ b_2 \ge 1,\ b_2 \le 35,\ a_2 \le b_2,\ 2b_2^{2} + 2a_2^{2} - 4a_2 b_2 = 1250 \right\}\right| a_1^{2} + 25 b_1^{2} \le \left... | 511 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Const(5),
"c": Const(15),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/QF_PSD_COUNT_LEQ",
"LIN_FORM/QF_PSD_COUNT_LEQ"
] | 8bce69 | algebra_quadratic_discriminant_v1 | negation_mod | 7 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 3 | 0.03 | 2026-03-10T02:33:46.575394Z | {
"verified": true,
"answer": 511,
"timestamp": "2026-03-10T02:33:46.604966Z"
} | ab673f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 433,
"completion_tokens": 6680
},
"timestamp": "2026-04-19T00:59:31.872Z",
"answer": 528
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 3.48,
"mid": 5.87,
"hi": 8.97
} | ||
17ac9f | nt_count_divisible_and_v1_1520064083_4692 | Let $d_1$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 9$. Let $d_2 = 8$. Determine the number of positive integers $n \leq 82032$ such that $n$ is divisible by both $d_1$ and $d_2$. Multiply this number by 58741 and find the remainder when the product is divided by 59065... | 14,803 | graphs = [
Graph(
let={
"upper": Const(82032),
"d1": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 4.714 | 2026-02-08T06:23:09.041613Z | {
"verified": true,
"answer": 14803,
"timestamp": "2026-02-08T06:23:13.755991Z"
} | 5cdab3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1765
},
"timestamp": "2026-02-12T23:30:41.189Z",
"answer": 14803
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
dd7326 | nt_sum_over_divisible_v1_151522320_146 | Let $d$ be the sum of $\phi(d)$ over all positive divisors $d$ of $156$. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 13225$ and $n$ is divisible by $d$. Define $r$ to be the sum of all elements in $S$. Compute the remainder when $22433 \cdot r$ is divided by $90826$. | 88,408 | graphs = [
Graph(
let={
"_n": Const(156),
"upper": Const(13225),
"divisor": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref... | NT | null | SUM | sympy | K3 | [
"K3"
] | 54c41e | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"K3"
] | 1 | 1.086 | 2026-02-08T03:00:19.788412Z | {
"verified": true,
"answer": 88408,
"timestamp": "2026-02-08T03:00:20.873928Z"
} | 964ec4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 2787
},
"timestamp": "2026-02-10T12:29:10.362Z",
"answer": 88408
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
1e05b3 | algebra_poly_eval_v1_601307018_3282 | Compute $2z^4 - 8z^3 - 9z^2 - 4z - 7$, where $z$ is the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 25$ satisfying $-4ab + 2b^2 + 2a^2 = 722€. | 509 | graphs = [
Graph(
let={
"_n": Const(2),
"z": 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)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(-4), Var(... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | algebra_poly_eval_v1 | null | 6 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.005 | 2026-03-10T03:50:15.518821Z | {
"verified": true,
"answer": 509,
"timestamp": "2026-03-10T03:50:15.523360Z"
} | c8d2c3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 745
},
"timestamp": "2026-03-29T08:04:52.352Z",
"answer": 509
},
{
"id"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.24
} | ||
2d0d2a | diophantine_fbi2_min_v1_260342960_8 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 2700$, and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $A$. Find the smallest divisor $d$ of $72$ such that $d \geq m$, and $\frac{72}{d} \geq 4$. Compute the value of $d$. | 4 | graphs = [
Graph(
let={
"k": Const(72),
"upper": Const(82),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(... | NT | null | EXTREMUM | sympy | C4 | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"C4",
"COPRIME_PAIRS"
] | 2 | 0.233 | 2026-02-08T11:10:53.379937Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T11:10:53.613185Z"
} | b959a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 2352
},
"timestamp": "2026-02-08T20:27:02.069Z",
"answer": 4
},
{
"id":... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.01,
"mid": 0.45,
"hi": 2.53
} | ||
f5f6e4 | antilemma_k3_v1_1915831931_1464 | Let $n = 37476$. Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $n$, where $\varphi$ denotes Euler's totient function. | 37,476 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=37476), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T16:09:36.655904Z | {
"verified": true,
"answer": 37476,
"timestamp": "2026-02-08T16:09:36.656387Z"
} | 0e7d24 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 518
},
"timestamp": "2026-02-16T21:48:17.095Z",
"answer": 37476
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d62526 | algebra_quadratic_discriminant_v1_1431428450_383 | Let $a = 1$, $b = 18$, and $n = 2$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = b$. Define $c$ to be the maximum value of $xy$ over all $(x, y) \in S$. Let
$$
\text{result} = b^n - 4ac.
$$
Compute $15376 - \text{result}$. | 15,376 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Const(18),
"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(Sum(Var("x"), Var("y... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.005 | 2026-02-08T13:26:24.214453Z | {
"verified": true,
"answer": 15376,
"timestamp": "2026-02-08T13:26:24.219851Z"
} | 163471 | 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": 525
},
"timestamp": "2026-02-15T15:04:14.910Z",
"answer": 15376
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
f053fe | comb_count_surjections_v1_397696148_962 | Let $ T $ be the set of all ordered pairs of positive odd integers $ (x_1, x_2) $ such that $ x_1 + x_2 = n $, where $ n $ is the number of integers $ t $ with $ 15 \leq t \leq 48 $ for which there exist positive integers $ a \leq 5 $ and $ b \leq 2 $ such that $ t = 6a + 9b $. Let $ k = 5 $. Compute $ k! \cdot S(|T|, ... | 120 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T11:58:18.885957Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T11:58:18.888319Z"
} | 1d80a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 799
},
"timestamp": "2026-02-24T15:30:07.010Z",
"answer": 120
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": ... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
88d4ec | nt_count_intersection_v1_1742523217_31 | Let $N = 20000$ and $a = 7$. Define $b = \sum_{k=1}^{3} k$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. Compute the remainder when $72469$ times the number of elements in $S$ is divided by $71802$. | 61,235 | graphs = [
Graph(
let={
"N": Const(20000),
"a": Const(7),
"b": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(diviso... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_intersection_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.662 | 2026-02-08T02:50:37.140534Z | {
"verified": true,
"answer": 61235,
"timestamp": "2026-02-08T02:50:37.802695Z"
} | de9983 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2048
},
"timestamp": "2026-02-09T12:33:43.676Z",
"answer": 61235
},
{
"... | 1 | [
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"stat... | {
"lo": -0.87,
"mid": 0.99,
"hi": 2.62
} | ||
9e722d | nt_count_gcd_equals_v1_784195855_7443 | Let $k = 445$ and $\text{upper} = 22500$. Let $d$ be the largest prime number $n$ such that $2 \leq n \leq 92$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $\gcd(n, k) = d$. | 202 | graphs = [
Graph(
let={
"upper": Const(22500),
"k": Const(445),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(92)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.79 | 2026-02-08T09:19:38.670886Z | {
"verified": true,
"answer": 202,
"timestamp": "2026-02-08T09:19:40.461085Z"
} | d26ce3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 923
},
"timestamp": "2026-02-14T02:38:09.872Z",
"answer": 202
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b1afd2 | nt_count_with_divisor_count_v1_151522320_2235 | Let $m = 6561$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = m$. Let $u$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = n$. Determine the value of $Q$, where $Q$ is the number of positive integers $n$ wit... | 10 | graphs = [
Graph(
let={
"_m": Const(6561),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3/B1"
] | 7f76f7 | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 1.066 | 2026-02-08T04:42:17.293187Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T04:42:18.358713Z"
} | 460b43 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 7050
},
"timestamp": "2026-02-11T21:49:08.452Z",
"answer": 20
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
762df0 | nt_sum_over_divisible_v1_1915831931_3782 | Let $n = \sum_{k=1}^{4} \varphi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\varphi$ denotes Euler's totient function. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Define $P$ to be the maximum value of $xy$ over all pairs $(x, y) \in S$. Let $T$ be the set of all p... | 53,599 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"upper": Const(46665),
"divisor": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=... | NT | null | SUM | sympy | K2 | [
"K2/B1"
] | 995da8 | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"B1",
"K2"
] | 2 | 1.546 | 2026-02-08T17:54:41.929686Z | {
"verified": true,
"answer": 53599,
"timestamp": "2026-02-08T17:54:43.475576Z"
} | 2c8243 | 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": 2712
},
"timestamp": "2026-02-18T09:28:56.955Z",
"answer": 53599
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
416491 | diophantine_product_count_v1_1918700295_2985 | Let $k = 240$ and let $r$ be the number of positive integers $x$ with $1 \leq x \leq 28$ such that $x$ divides $k$ and $\frac{k}{x} \leq 28$. Let $s$ be the number of integers $t$ with $9 \leq t \leq 276$ for which there exist positive integers $a \leq 20$ and $b \leq 44$ such that $t = 5a + 4b$. Define $Q = \left(2^{|... | 320 | graphs = [
Graph(
let={
"k": Const(240),
"upper": Const(28),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper")))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 8e3411 | diophantine_product_count_v1 | two_stage_modexp | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T08:20:44.830547Z | {
"verified": true,
"answer": 320,
"timestamp": "2026-02-08T08:20:44.835372Z"
} | b25eaf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 4542
},
"timestamp": "2026-02-13T17:23:46.476Z",
"answer": 320
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1b1bc7 | nt_sum_over_divisible_v1_1915831931_578 | Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 174$. Let $M$ be the maximum value of $xy$ over all such pairs. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le M$ and $n$ is divisible by $61$. Let $r$ be the sum of all elements in $S$. Let $c = 8281$. Compu... | 60,941 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(174)))), expr=Mul(Var("x"), Var("y")))),
"divisor": Cons... | NT | null | SUM | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.589 | 2026-02-08T15:32:50.529535Z | {
"verified": true,
"answer": 60941,
"timestamp": "2026-02-08T15:32:51.118656Z"
} | e736f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1687
},
"timestamp": "2026-02-16T08:56:29.092Z",
"answer": 60941
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8ebadf | modular_mod_compute_v1_2051736721_4568 | Let $a = 23104$. Let $m$ be the number of integers $t$ in the range $9 \leq t \leq 1457$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 176$, $1 \leq b \leq 367$, and $$
t = 2a + 3b + 4.
$$ Determine the value of the remainder when $a$ is divided by $m$. | 1,399 | graphs = [
Graph(
let={
"a": Const(23104),
"m": 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=176)), Geq(left=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:02:36.305559Z | {
"verified": true,
"answer": 1399,
"timestamp": "2026-02-08T18:02:36.307269Z"
} | 16e852 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 3696
},
"timestamp": "2026-02-18T12:14:43.719Z",
"answer": 1399
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d70c7d | comb_count_partitions_v1_1820931509_603 | Let $m = 44121$ and define $n$ to be the largest prime number $n$ such that $2 \le n \le d_{\text{min}}$, where $d_{\text{min}}$ is the smallest divisor of $107113$ that is at least $2$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $m \cdot p(n)$ is divided by $89072$. | 67,461 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), divi... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | comb_count_partitions_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T11:46:59.499168Z | {
"verified": true,
"answer": 67461,
"timestamp": "2026-02-08T11:46:59.500813Z"
} | 646ebe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 3041
},
"timestamp": "2026-02-14T18:46:50.210Z",
"answer": 67461
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
15846d | comb_factorial_compute_v1_1218484723_530 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 10$ satisfying
$$
17a^4 + 68a^3b + 68ab^3 + 17b^4 + s \cdot a^2b^2 = 111537,
$$
depending on the value of
$$
s = \left|\left\{ v : 40 \le v \le 4840 \text{ and } \exists\, a,b \in \mathbb{Z}^+,\ 1\le a,b\le 11,\ 8a^2 + 32b^2 = v \... | 40,320 | graphs = [
Graph(
let={
"_m": Const(68),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(10)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(10)), Eq(Sum(Mul(Const(68), ... | COMB | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"QF_PSD_DISTINCT/POLY4_COUNT"
] | a605ae | comb_factorial_compute_v1 | null | 5 | 0 | [
"POLY4_COUNT",
"POLY_ORBIT_HENSEL",
"QF_PSD_DISTINCT"
] | 3 | 0.072 | 2026-02-25T02:11:42.070678Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T02:11:42.142562Z"
} | 7d26d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T23:02:30.562Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": 4.77,
"mid": 6.8,
"hi": 9.83
} | ||
b50c30 | diophantine_sum_product_min_v1_1248542787_304 | Let $n = 38$, $S = 39$, and $P = 140$. Let $x_{\text{min}}$ be the smallest positive integer $x \le n$ such that $x(S - x) = P$. Let $q$ be the largest prime number at most $7011$. Compute the value of $(x_{\text{min}} \bmod 307) + q \cdot (x_{\text{min}} \bmod 317)$. | 28,008 | graphs = [
Graph(
let={
"_n": Const(38),
"S": Const(39),
"P": Const(140),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("_n")), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | diophantine_sum_product_min_v1 | two_moduli | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.006 | 2026-02-08T03:03:15.988054Z | {
"verified": true,
"answer": 28008,
"timestamp": "2026-02-08T03:03:15.993851Z"
} | 146d09 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 2379
},
"timestamp": "2026-02-09T02:35:10.022Z",
"answer": 28008
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -0.51,
"mid": 1.78,
"hi": 3.62
} |
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