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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
55bc19 | algebra_quadratic_discriminant_v1_1978505735_2028 | Let $m$ be the number of integers $j$ with $0 \leq j \leq 1536$ such that $\binom{1536}{j}$ is odd. Let $p$ be a positive integer, and define $n$ to be the number of such $p$ for which there exists a positive integer $q$ satisfying $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $s$ be the set of all ordered pairs... | 0 | graphs = [
Graph(
let={
"_c": Const(1536),
"_m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(1536)), Eq(Mod(value=Binom(n=Ref("_c"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"_n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3",
"V8/COPRIME_PAIRS"
] | aecd9c | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"V8"
] | 3 | 0.008 | 2026-02-08T16:37:17.831717Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:37:17.839282Z"
} | 228a38 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 2446
},
"timestamp": "2026-02-17T08:51:36.009Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ae2bbe | nt_min_crt_v1_397696148_1572 | Let $m = 4$ and $k = 5$. Let $a = 3$ and $b = 4$. Define $S$ as the set of all integers $n$ such that $1 \leq n \leq 20$, $n \equiv 3 \pmod{4}$, and $n \equiv 4 \pmod{5}$. Let $r$ be the minimum element of $S$. Compute $r + \phi(|r| + 1) + \tau(|r| + 1)$, where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ d... | 33 | graphs = [
Graph(
let={
"m": Const(4),
"k": Const(5),
"a": Const(3),
"b": Const(4),
"upper": Const(20),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | nt_min_crt_v1 | null | 4 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.206 | 2026-02-08T12:38:57.903373Z | {
"verified": true,
"answer": 33,
"timestamp": "2026-02-08T12:38:58.108934Z"
} | 7adedf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 939
},
"timestamp": "2026-02-15T03:09:41.448Z",
"answer": 33
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "V... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
eeb685 | nt_min_coprime_above_v1_1978505735_5675 | Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1 \leq a \leq 19$, $1 \leq b \leq 15$, $8 \leq t \leq 140$, and $t = 5a + 3b$. Let $n$ be the number of elements in $S$. Let $M$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 123$, $j \leq 123$, and ... | 12,273 | 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=19)), Geq(left=Var(name='b'), right=Const(value... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | nt_min_coprime_above_v1 | null | 7 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.022 | 2026-02-08T19:09:38.805857Z | {
"verified": true,
"answer": 12273,
"timestamp": "2026-02-08T19:09:38.828051Z"
} | 4ca08d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 5255
},
"timestamp": "2026-02-18T21:32:08.977Z",
"answer": 12273
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab43ad | nt_count_divisors_in_range_v1_784195855_6740 | Let $n = 45360$. Let $a$ be the number of integers $t$ such that $25 \leq t \leq 101$ and there exist integers $a$ and $b$ with $1 \leq a \leq 17$, $1 \leq b \leq 5$, and $t = 3a + 7b + 15$. Let $b = 3788$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 59 | graphs = [
Graph(
let={
"n": Const(45360),
"a": 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=17)), Geq(left=Va... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 17.492 | 2026-02-08T08:50:08.797074Z | {
"verified": true,
"answer": 59,
"timestamp": "2026-02-08T08:50:26.288884Z"
} | c620b5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 6695
},
"timestamp": "2026-02-13T22:02:41.972Z",
"answer": 59
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a9793c | nt_sum_phi_v1_548369836_61 | Let $a = 54$ and $b = 35$. Define $m = \sum_{d \mid \gcd(a,b)} \mu(d)$, where $\mu$ is the M\"obius function. Let $e = \lambda(29) + 1$, where $\lambda$ is the Liouville function. Let $S$ be the set of positive integers $n$ such that $1 \le n \le 443m$. Compute the remainder when $48467$ times the sum of $\phi(n)$ over... | 53,216 | graphs = [
Graph(
let={
"a": Const(54),
"b": Const(35),
"m": SumOverDivisors(n=GCD(a=Ref(name='a'), b=Ref(name='b')), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Const(29),
"e": Sum(LiouvilleLambda(n=Ref(name='n')), Const(1)),
"uppe... | NT | null | SUM | sympy | LIOUVILLE_MINUS_ONE | [
"LIOUVILLE_MINUS_ONE",
"MOBIUS_COPRIME"
] | add503 | nt_sum_phi_v1 | null | 6 | 2 | [
"LIOUVILLE_MINUS_ONE",
"MOBIUS_COPRIME"
] | 2 | 0.024 | 2026-02-08T02:44:46.123245Z | {
"verified": true,
"answer": 53216,
"timestamp": "2026-02-08T02:44:46.147415Z"
} | 66ab70 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 617
},
"timestamp": "2026-02-09T01:57:26.615Z",
"answer": 48467
},... | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"statu... | {
"lo": 2.6,
"mid": 6.26,
"hi": 10
} | ||
0e1c45 | modular_sum_quadratic_residues_v1_601307018_4557 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 30$ such that $97a^4 - 292a^3b + 510a^2b^2 - 316ab^3 + 82b^4 = 5780241$. Let $p$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 184200$. Let $R = \frac{p(p-1)}{M}$. Find the rem... | 23,861 | graphs = [
Graph(
let={
"_m": Const(4),
"_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(82), Pow(Var("b"), Const(4))), Mu... | NT | null | SUM | sympy | POLY4_COUNT | [
"POLY4_COUNT/B3_DIFF"
] | 7522fe | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"B3_DIFF",
"POLY4_COUNT"
] | 2 | 0.005 | 2026-03-10T05:12:47.891610Z | {
"verified": true,
"answer": 23861,
"timestamp": "2026-03-10T05:12:47.896867Z"
} | 2c4520 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:44:22.724Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
4892c1 | comb_count_permutations_fixed_v1_153355830_1726 | Let $m = 9$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $n$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. Let $k$ be the number of positive integers $p$ for which there exists a positive ... | 5,544 | graphs = [
Graph(
let={
"_m": Const(9),
"_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 | COMB | COUNT | sympy | LIN_FORM | [
"COPRIME_PAIRS",
"B3/B1"
] | 62f112 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"B1",
"B3",
"COPRIME_PAIRS",
"LIN_FORM"
] | 4 | 0.018 | 2026-02-08T06:35:24.810346Z | {
"verified": true,
"answer": 5544,
"timestamp": "2026-02-08T06:35:24.828429Z"
} | 5fc799 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1893
},
"timestamp": "2026-02-13T02:26:34.584Z",
"answer": 5544
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f425b9 | nt_sum_totient_over_divisors_v1_677425708_1161 | Let $n = 85239$. Define $S$ to be the set of all positive integers $t$ such that $7 \leq t \leq 317$ and there exist positive integers $a \leq 21$ and $b \leq 55$ satisfying $t = 2a + 5b$. Let $\varphi$ denote Euler's totient function, and define
$$
r = \sum_{d \mid n} \varphi(d).
$$
Let $m = |S|$, the number of elemen... | 6,595 | graphs = [
Graph(
let={
"n": Const(85239),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Ex... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | d6c893 | nt_sum_totient_over_divisors_v1 | two_moduli | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T04:01:24.635756Z | {
"verified": true,
"answer": 6595,
"timestamp": "2026-02-08T04:01:24.638916Z"
} | 2b8c5b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 279,
"completion_tokens": 2885
},
"timestamp": "2026-02-10T15:02:20.533Z",
"answer": 6659
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
7af2d9 | diophantine_product_count_v1_2051736721_743 | Let $k$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 15$ and $1 \leq j \leq 16$. Let $\text{upper} = 38$.
Let $T$ be the set of all positive integers $x$ such that $1 \leq x \leq 38$, $x$ divides $k$, and $\frac{k}{x} \leq 38$. Let $r$ be the number of elements in $T$.
Let $Q = 26244 + \sum_{i=0}^... | 26,252 | graphs = [
Graph(
let={
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Const(16)))),
"upper": Const(38),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Cons... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.018 | 2026-02-08T15:39:12.142840Z | {
"verified": true,
"answer": 26252,
"timestamp": "2026-02-08T15:39:12.160476Z"
} | 7fd0cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 821
},
"timestamp": "2026-02-16T11:08:49.222Z",
"answer": 26252
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8bb078 | sequence_lucas_compute_v1_1915831931_2094 | Let $n$ be the largest positive divisor of 638 that does not exceed 22. Compute the $n$th Lucas number. | 39,603 | graphs = [
Graph(
let={
"_n": Const(22),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(638))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("res... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T16:36:36.131536Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T16:36:36.132399Z"
} | d4b434 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 765
},
"timestamp": "2026-02-17T07:42:05.146Z",
"answer": 39603
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5b4d17 | modular_inverse_v1_153355830_2192 | Let $a$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 224$. Let $n = 19044$ and $m = 277$. Define $u$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 19044$. Determine the value of the smallest positive integer $x$ suc... | 47 | graphs = [
Graph(
let={
"_n": Const(19044),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1",
"B3"
] | 44bb30 | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.017 | 2026-02-08T06:57:51.440682Z | {
"verified": true,
"answer": 47,
"timestamp": "2026-02-08T06:57:51.457284Z"
} | 729dc8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1455
},
"timestamp": "2026-02-13T06:42:09.486Z",
"answer": 47
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
048a6a | nt_count_coprime_v1_1520064083_1145 | Let $k$ be the largest prime number less than or equal to $36$. Determine the number of positive integers $n \leq 58564$ such that $\gcd(n, k) = 1$. | 56,675 | graphs = [
Graph(
let={
"upper": Const(58564),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(36)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 6.208 | 2026-02-08T03:48:36.827159Z | {
"verified": true,
"answer": 56675,
"timestamp": "2026-02-08T03:48:43.034867Z"
} | ac7afc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1297
},
"timestamp": "2026-02-10T15:46:29.512Z",
"answer": 56675
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
6dae95_l | comb_catalan_compute_v1_784195855_17 | Let $N$ be the number of ordered triples $(x_1,x_2,x_3)$ of positive integers such that each of $x_1,x_2,x_3$ is odd and
$$x_1+x_2+x_3=7.$$
Let $K=\binom{6}{N}$ and let
$$F=K!.$$
Let $C_{11}$ be the $11$th Catalan number, and let
$$S=\sum_{n=F}^{\lvert C_{11}\rvert} d(n),$$
where $d(n)$ denotes the number of positive d... | 0 | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/ZERO_BINOM_N/ONE_FACTORIAL_0"
] | b96107 | comb_catalan_compute_v1 | sum_divisor_count | 7 | 0 | [
"COMB1",
"ONE_FACTORIAL_0",
"ZERO_BINOM_N"
] | 3 | 0.003 | 2026-02-08T02:54:14.193493Z | {
"verified": false,
"answer": 62818,
"timestamp": "2026-02-08T02:54:14.196332Z"
} | c5d351 | 6dae95 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T19:52:51.246Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ON... | {
"lo": 6.44,
"mid": 8.24,
"hi": 10
} | |
21266c | modular_inverse_v1_458359167_5483 | Let $a = 124$ and $m = 199$. Let $N$ be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 199$ and $1 \le j \le 199$ such that $i + j = 199$. Compute the smallest positive integer $x$ such that $1 \le x \le N$ and $ax \equiv 1 \pmod{m}$. | 130 | graphs = [
Graph(
let={
"a": Const(124),
"m": Const(199),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(199)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(199)), right=I... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | modular_inverse_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.014 | 2026-02-08T12:33:00.729193Z | {
"verified": true,
"answer": 130,
"timestamp": "2026-02-08T12:33:00.743471Z"
} | 4cf307 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1178
},
"timestamp": "2026-02-15T02:02:10.961Z",
"answer": 130
},
{
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
a984b1 | comb_catalan_compute_v1_151522320_1332 | Let $t$ be an integer such that $21 \leq t \leq 45$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 4a + 6b + 11$. Let $n$ be the number of such integers $t$. Compute the $n$-th Catalan number. | 58,786 | 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=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:53:20.856606Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T03:53:20.858030Z"
} | e9597e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1368
},
"timestamp": "2026-02-10T16:19:39.602Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ce7de0 | modular_sum_quadratic_residues_v1_1978505735_5668 | Let $n = 437$ and let $p$ be the largest prime number less than or equal to $n$. Compute the value of $\frac{p(p-1)}{4}$. | 46,764 | graphs = [
Graph(
let={
"_n": Const(437),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T19:09:08.304442Z | {
"verified": true,
"answer": 46764,
"timestamp": "2026-02-08T19:09:08.305776Z"
} | 5688f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 85,
"completion_tokens": 2180
},
"timestamp": "2026-02-18T21:30:30.722Z",
"answer": 46764
},
{... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a8318d | nt_count_divisible_v1_677425708_426 | Let $A$ be the set of positive integers $n \leq 45796$ that are divisible by $6$. Let $N$ be the number of elements in $A$.
Let $B$ be the set of ordered pairs of positive integers $(x, y)$ such that $x + y = 78$, and let $c$ be the maximum value of $xy$ over all such pairs.
Compute the remainder when $N^2 + 11N + c$... | 45,985 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": Const(45796),
"divisor": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const... | NT | null | COUNT | sympy | B1 | [
"B1"
] | bf138c | nt_count_divisible_v1 | quadratic_mod | 5 | 0 | [
"B1"
] | 1 | 1.443 | 2026-02-08T03:32:42.393273Z | {
"verified": true,
"answer": 45985,
"timestamp": "2026-02-08T03:32:43.836292Z"
} | 382a95 | 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": 954
},
"timestamp": "2026-02-08T20:34:10.798Z",
"answer": 45985
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
778a2d | lin_form_endings_v1_1820931509_655 | Let $a = 24$, $b = 32$, $A = 43$, and $B = 18$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. The size of a certain set $T$ is given by $a'A + b'B - a'b'$. The total number of elements under consideration is $aA + bB - a - b + 1$. Compu... | 1,364 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(32),
"A_val": Const(43),
"B_val": Const(18),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:49:00.881168Z | {
"verified": true,
"answer": 1364,
"timestamp": "2026-02-08T11:49:00.883224Z"
} | 4ff86b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 595
},
"timestamp": "2026-02-14T18:50:39.625Z",
"answer": 1364
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d3d7c4 | comb_catalan_compute_v1_1116507919_256 | Let $n$ be the number of integers $t$ with $15 \leq t \leq 51$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 3$ and $1 \leq b \leq 4$, such that $t = 9a + 6b$. Compute the remainder when $64279 \cdot C_n$ is divided by $62305$, where $C_n$ denotes the $n$-th Catalan number. | 31,654 | graphs = [
Graph(
let={
"_n": Const(64279),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T02:30:05.374704Z | {
"verified": true,
"answer": 31654,
"timestamp": "2026-02-08T02:30:05.376477Z"
} | bc7c1c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2750
},
"timestamp": "2026-02-08T19:20:18.444Z",
"answer": 31654
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 1.06,
"mid": 2.45,
"hi": 3.73
} | ||
3fc908 | comb_bell_compute_v1_784195855_8311 | Let $m = 64$. Let $n_0$ 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 $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n_0$. Compute the Bell number $B_n$. | 4,140 | graphs = [
Graph(
let={
"_m": Const(64),
"_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")))),
... | COMB | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_bell_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:00:20.413123Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:00:20.414878Z"
} | 3e607c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 635
},
"timestamp": "2026-02-24T19:31:14.704Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
002b3a | geo_visible_lattice_v1_2051736721_701 | Let $n = 89$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $2000 - L$ is divided by $60874$. | 57,963 | graphs = [
Graph(
let={
"n": Const(89),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(2000),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(60874)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.352 | 2026-02-08T15:38:40.982207Z | {
"verified": true,
"answer": 57963,
"timestamp": "2026-02-08T15:38:41.334100Z"
} | 7ac1df | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 3757
},
"timestamp": "2026-02-24T18:09:20.262Z",
"answer": 57963
},
{
... | 1 | [] | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||||
a30d59 | antilemma_k3_v1_1470522791_1850 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $59269$, where $\phi$ denotes Euler's totient function. | 59,269 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=59269), 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 | 2026-02-08T14:00:47.609304Z | {
"verified": true,
"answer": 59269,
"timestamp": "2026-02-08T14:00:47.609762Z"
} | 33ddee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 2483
},
"timestamp": "2026-02-15T23:45:39.036Z",
"answer": 59269
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8ee0ad_l | diophantine_fbi2_count_v1_397696148_2320 | Let $d$ be a positive integer. Determine the number of values of $d$ such that $3 \leq d \leq 57$, $d$ divides $120$, and the quotient $\frac{120}{d}$ satisfies $3 \leq \frac{120}{d} \leq 57$. Compute this number. | 11 | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.007 | 2026-02-08T13:06:41.555968Z | {
"verified": false,
"answer": 12,
"timestamp": "2026-02-08T13:06:41.562664Z"
} | ed228e | 8ee0ad | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1176
},
"timestamp": "2026-02-15T09:19:46.280Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | |
3aba4d | nt_count_intersection_v1_1080341949_197 | Let $N$ be the number of positive integers $t$ such that $14 \leq t \leq 5015$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2413$, $1 \leq b \leq 60$, and $t = 2a + 3b + 9$. Let $a = \sum_{k=1}^{2} k$ and $b = 14$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides... | 714 | graphs = [
Graph(
let={
"_n": Const(2),
"N": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2413)), Geq(left=Var... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | nt_count_intersection_v1 | null | 6 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.421 | 2026-02-08T13:18:03.299801Z | {
"verified": true,
"answer": 714,
"timestamp": "2026-02-08T13:18:03.720743Z"
} | 86cbad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 4861
},
"timestamp": "2026-02-15T12:18:47.483Z",
"answer": 714
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"s... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
98bdae | antilemma_coprime_grid_v1_1742523217_743 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 6$ and $1 \leq j \leq 91$ such that $\gcd(i, j) = 1$. Find the remainder when $44121x$ is divided by $91054$. | 57,036 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(91))))),
"Q"... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"COUNT_COPRIME_GRID"
] | 2 | 0.01 | 2026-02-08T03:11:52.022560Z | {
"verified": true,
"answer": 57036,
"timestamp": "2026-02-08T03:11:52.033026Z"
} | 4584b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 3310
},
"timestamp": "2026-02-09T22:02:18.745Z",
"answer": 56236
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
2803d7 | sequence_lucas_compute_v1_397696148_2769 | Let $ n = \sum_{k=1}^{6} k $. Let $ L_n $ denote the $ n $-th Lucas number, where $ L_1 = 1 $, $ L_2 = 3 $, and $ L_k = L_{k-1} + L_{k-2} $ for $ k \geq 3 $. Compute the remainder when $ 82303 \cdot L_n $ is divided by $ 61861 $. | 6,624 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(82303), Ref("result")), modulus=Const(61861)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T13:32:49.947686Z | {
"verified": true,
"answer": 6624,
"timestamp": "2026-02-08T13:32:49.948579Z"
} | e4e6d4 | 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": 1500
},
"timestamp": "2026-02-16T00:04:06.397Z",
"answer": 6624
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3430c6 | nt_max_prime_below_v1_1915831931_1459 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $L = |A|$, the number of elements in $A$. Let $B$ be the set of all prime numbers $n$ such that $L \leq n \leq 25281$. Let $M$ be the maximum element of $B$. Define $Q = ... | 15,590 | graphs = [
Graph(
let={
"upper": Const(25281),
"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 | 0.8 | 2026-02-08T16:09:12.488725Z | {
"verified": true,
"answer": 15590,
"timestamp": "2026-02-08T16:09:13.288258Z"
} | 221483 | 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": 3952
},
"timestamp": "2026-02-16T21:49:40.362Z",
"answer": 15590
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
310ad3 | nt_sum_divisors_mod_v1_1520064083_1325 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. For each pair $(x, y)$ in $S$, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by $1... | 4,368 | 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(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10331... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:55:32.497302Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T03:55:32.499266Z"
} | a62470 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1107
},
"timestamp": "2026-02-10T16:11:08.147Z",
"answer": 4368
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
d976af | algebra_quadratic_discriminant_v1_865884756_1617 | Let $m = 2$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Let $n$ be the maximum value of $xy$ over all such pairs. Define $a = 3$, $b = 10$, and $c = -6$. Let $P$ be the set of all ordered pairs of positive integers $(p, q)$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p... | 2 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(4)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/COPRIME_PAIRS"
] | 219c61 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B1",
"COPRIME_PAIRS"
] | 2 | 0.007 | 2026-02-08T16:11:26.628632Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:11:26.635172Z"
} | dfedd6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 357
},
"timestamp": "2026-02-16T07:11:39.785Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": ... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
552334_n | comb_count_derangements_v1_1218484723_5419 | A game designer creates puzzles where players must unlock a sequence of $n$ switches, each labeled 1 through $n$, such that no switch is in its original position — a derangement. The value of $n$ is determined by counting how many distinct target scores $t$ between 16 and 25 inclusive can be formed as $t = 2a + 3b + 11... | 8,409 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T06:59:26.218696Z | null | ac472f | 552334 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 2580
},
"timestamp": "2026-03-30T23:25:39.631Z",
"answer": 8409
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
e3318d | nt_min_phi_inverse_v1_655260480_4916 | Let $T$ be the set of all integers $t$ with $42 \leq t \leq 291$ for which there exist positive integers $a \leq 5$ and $b \leq 12$ such that $t = 21a + 15b + 6$. Let $k = 18$. Let $n$ be the smallest positive integer at most $|T|$ such that $\phi(n) = k$. Compute the remainder when $98348 \cdot n$ is divided by $77183... | 16,220 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(val... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T18:12:51.344441Z | {
"verified": true,
"answer": 16220,
"timestamp": "2026-02-08T18:12:51.351310Z"
} | 1f379f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2996
},
"timestamp": "2026-02-18T15:04:27.187Z",
"answer": 16220
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c50422 | nt_min_phi_inverse_v1_1742523217_5162 | Let $k$ be the largest integer such that $2^k \leq 4531829$. Let $S$ be the set of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 50$ and $1 \leq j \leq 50$ such that $i + j = 51$. The number of elements in $S$ is denoted by $|S|$. Find the smallest positive integer $n \leq |S|$ such that $\phi(n) = k$, where $... | 64,135 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(51)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(50)), right=IntegerRange(start=Const(1), end=... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"MAX_VAL"
] | 18ab07 | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"COUNT_SUM_EQUALS",
"MAX_VAL"
] | 2 | 0.012 | 2026-02-08T10:50:31.114458Z | {
"verified": true,
"answer": 64135,
"timestamp": "2026-02-08T10:50:31.126762Z"
} | 3f4c50 | 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": 2545
},
"timestamp": "2026-02-14T09:00:26.215Z",
"answer": 64135
},
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ffb054 | alg_telescope_v1_601307018_1821 | Let $B_n$ denote the $n$-th Bell number. Let $S = \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 153,\ 1 \leq b \leq 1765 \text{ such that } t = 12a + 15b,\ 27 \leq t \leq 28311 \right\}\right|$. Define $M = \left( \sum_{k=0}^{106} (3k^2 + 3k + 1) \right) \bmod S$. Let $Q = B_{M \bmod 11}$. ... | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(106), expr=Sum(Mul(Const(3), Pow(Var("k"), Ref("_n"))), Mul(Const(3), Var("k")), Const(1))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a')... | COMB | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.266 | 2026-03-10T02:33:46.662391Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-03-10T02:33:46.928868Z"
} | a97995 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 25545
},
"timestamp": "2026-03-29T03:31:28.767Z",
"answer": 1
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": 0.86,
"mid": 3.78,
"hi": 5.89
} | ||
bb0be5 | algebra_quadratic_discriminant_v1_1978505735_705 | Let $a = -2$, $b = -8$, and $c = 10$. Define $\Delta = b^2 - 4ac$. Compute the value of $$\sum_{n=1}^{|\Delta|} \phi(n),$$ where $\phi(n)$ denotes Euler's totient function. Find the value of this sum. | 6,330 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(-8),
"c": Const(10),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='result')), expr=EulerPhi(n=Var("n"))),
... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.047 | 2026-02-08T15:33:09.809365Z | {
"verified": true,
"answer": 6330,
"timestamp": "2026-02-08T15:33:09.855956Z"
} | bf1c49 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 2549
},
"timestamp": "2026-02-16T08:19:14.669Z",
"answer": 6330
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ffba15 | antilemma_sum_equals_v1_1439011603_1222 | Let $n$ be the number of integers $t$ such that $11 \leq t \leq 95$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 8$, and $t = 7a + 4b$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 65$, $1 \leq j \leq 66$, and $i + j = n$. Compute ... | 65 | 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=9)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T15:58:46.700006Z | {
"verified": true,
"answer": 65,
"timestamp": "2026-02-08T15:58:46.707681Z"
} | f41bdd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 3574
},
"timestamp": "2026-02-24T19:27:02.729Z",
"answer": 65
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
eb5787 | modular_min_modexp_v1_124444284_9263 | Let $a = 13$, and let $b$ be the sum of all real solutions to the equation $x^2 - 682x + 52777 = 0$. Let $m = 709$. Define $u$ to be the number of positive integers $n$, where $1 \le n \le 1180$, such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Find the smallest positive integer $x$ such that $1 \l... | 158 | graphs = [
Graph(
let={
"a": Const(13),
"b": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-682), Var("x")), Const(52777)), Const(0)))),
"m": Const(709),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condi... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM",
"L3C"
] | e98a55 | modular_min_modexp_v1 | null | 7 | 0 | [
"L3C",
"VIETA_SUM"
] | 2 | 0.014 | 2026-02-08T12:20:31.207468Z | {
"verified": true,
"answer": 158,
"timestamp": "2026-02-08T12:20:31.221393Z"
} | 709b6e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 7962
},
"timestamp": "2026-02-15T00:18:07.555Z",
"answer": 158
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
33473a | nt_min_coprime_above_v1_124444284_5385 | Let $S$ be the set of all integers $t$ such that $10 \leq t \leq 4413$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 1415$, $1 \leq b \leq 24$, and $t = 3a + 7b$. Let $s = 4181$ and $m = 201$. Define $u = |S|$. Let $n_0$ be the smallest integer $n$ such that $n > s$, $n \leq u$, and $\gcd(n, m) = 1$... | 27,308 | graphs = [
Graph(
let={
"start": Const(4181),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1415)), Ge... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.02 | 2026-02-08T06:34:12.343563Z | {
"verified": true,
"answer": 27308,
"timestamp": "2026-02-08T06:34:12.363328Z"
} | 998bab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 4304
},
"timestamp": "2026-02-13T01:28:29.860Z",
"answer": 27308
},
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4d36eb | geo_count_lattice_rect_v1_655260480_2146 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 333$ and $0 \leq y \leq 208$. Let this number be $L$. Find the value of $78961 - L$. | 9,155 | graphs = [
Graph(
let={
"a": Const(333),
"b": Const(208),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(78961),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T16:35:18.645189Z | {
"verified": true,
"answer": 9155,
"timestamp": "2026-02-08T16:35:18.646062Z"
} | b446cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 371
},
"timestamp": "2026-02-17T07:01:53.202Z",
"answer": 9155
},
{
... | 1 | [] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||||
b21ef9_n | geo_count_lattice_rect_v1_601307018_6303 | A city grid extends from avenue 0 to avenue 90 and from street 0 to street 80. Each intersection is a lattice point. How many intersections are there in this grid? | 7,371 | graphs = [
Graph(
let={
"a": Const(90),
"b": Const(80),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | null | null | null | 0.001 | 2026-03-10T06:54:49.642344Z | null | f4b07e | b21ef9 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 471
},
"timestamp": "2026-04-23T12:05:12.198Z",
"answer": 7371
}
] | 2 | [] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
43bcde | comb_count_derangements_v1_677425708_1681 | Let $a = 2$ and $b = 3$. Define $n_2 = a + b$. Let $$v = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.$$ Let $u = 4$, and define $n_1 = u + \binom{4}{4} + v$. Let $$t = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.$$ Let $n = 8$, and let $D_n$ denote the number of derangements of $n$ objects. Compute the remainder when $(66619 + t... | 44,047 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(3),
"n2": Sum(Ref("a"), Ref("b")),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(4),
"n1": Sum(Re... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 961fba | comb_count_derangements_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 2 | 0.001 | 2026-02-08T04:22:25.351484Z | {
"verified": true,
"answer": 44047,
"timestamp": "2026-02-08T04:22:25.352906Z"
} | 847f3b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 2096
},
"timestamp": "2026-02-09T23:16:25.080Z",
"answer": 44047
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"l... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ac2bb8 | nt_min_phi_inverse_v1_865884756_6372 | Let $k$ be the largest integer such that $2^k \leq 7026685$. Let $n$ be the smallest positive integer at most 50 for which $\phi(n) = k$. Compute $n$. | 23 | graphs = [
Graph(
let={
"upper": Const(50),
"k": MaxOverSet(set=SolutionsSet(var=Var("k1"), condition=Leq(Pow(Const(2), Var("k1")), Const(7026685)))),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), E... | NT | null | EXTREMUM | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"MAX_VAL"
] | 1 | 0.008 | 2026-02-08T19:10:07.162539Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T19:10:07.170765Z"
} | 8dbe82 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 1770
},
"timestamp": "2026-02-18T21:27:24.214Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cecf73 | geo_count_lattice_rect_v1_601307018_9123 | Find the number of lattice points $(x, y)$ with $0 \le x \le 360$ and $0 \le y \le 129$. | 46,930 | graphs = [
Graph(
let={
"a": Const(360),
"b": Const(129),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-03-10T09:30:03.075085Z | {
"verified": true,
"answer": 46930,
"timestamp": "2026-03-10T09:30:03.076314Z"
} | 6c4b18 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 318
},
"timestamp": "2026-04-19T10:41:35.658Z",
"answer": 46930
},
{
"... | 2 | [] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||||
40ea5d | alg_qf_psd_min_v1_601307018_5323 | Let $R$ be the largest positive integer $d$ such that $d^2 \le 17947$ and $d \mid 17947$. Let $S$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers with $x \le y$ and $xy = 394384$. Let $Q$ be the minimum value of $\min\{ |x_1 - y_1| : x_1, y_1 > 0,\ x_1 y_1 = 3166385 \} \cdot b^2 + S... | 2,512 | graphs = [
Graph(
let={
"_d": Const(2),
"_c": Const(2),
"_m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(17947)), Leq(Mul(Var("d"), Var("d")), Const(17947))))),
"_n": MinOverSet(set... | NT | null | COMPUTE | sympy | B3 | [
"B3/MIN_PRIME_FACTOR",
"B3_CLOSEST/B3",
"B3_DIFF"
] | 152dcf | alg_qf_psd_min_v1 | null | 7 | 0 | [
"B3",
"B3_CLOSEST",
"B3_DIFF",
"MIN_PRIME_FACTOR"
] | 4 | 0.094 | 2026-03-10T05:59:27.456590Z | {
"verified": true,
"answer": 2512,
"timestamp": "2026-03-10T05:59:27.550875Z"
} | 28c3ea | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 18438
},
"timestamp": "2026-04-19T01:50:25.080Z",
"answer": 2512
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
c01bf2 | diophantine_fbi2_min_v1_124444284_176 | Let $d$ be the smallest integer such that $2 \le d \le 20$, $d$ divides $10$, and $\frac{10}{d} \ge 3$. Let $p$ range over the positive integers for which there exists an integer $q > p$ such that $pq = 24$ and $\gcd(p, q) = 1$. Compute $d^{k} + 11d + 1225$, where $k$ is the number of such integers $p$. | 1,251 | graphs = [
Graph(
let={
"k": Const(10),
"upper": Const(20),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3))))),
... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 14fbb8 | diophantine_fbi2_min_v1 | quadratic_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.009 | 2026-02-08T03:02:18.009590Z | {
"verified": true,
"answer": 1251,
"timestamp": "2026-02-08T03:02:18.018638Z"
} | 21b2e7 | 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": 688
},
"timestamp": "2026-02-09T14:21:59.275Z",
"answer": 1251
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -5.92,
"mid": -3.15,
"hi": 0.24
} | ||
76908d | nt_sum_divisors_mod_v1_124444284_7973 | Let $n = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $\sigma$ be the sum of the positive divisors of $n$. Determine the value of $\sigma \bmod 10771$. | 360 | graphs = [
Graph(
let={
"_n": Const(15),
"n": Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"M": Const(10771),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"),... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T09:29:33.549087Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T09:29:33.551972Z"
} | 522406 | 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": 768
},
"timestamp": "2026-02-14T04:17:23.422Z",
"answer": 360
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
23144f | comb_count_permutations_fixed_v1_717093673_1616 | Let $n$ be the largest positive integer $d$ such that $1 \leq d \leq 11$ and $d$ divides $187$. Let $k = 6$. Define $R = \binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. Compute the remainder when $44121 \cdot R$ is divided by $83287$. | 57,272 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(11)), Divides(divisor=Var("d"), dividend=Const(187))))),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref(... | NT | COMB | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T16:12:35.461016Z | {
"verified": true,
"answer": 57272,
"timestamp": "2026-02-08T16:12:35.462665Z"
} | b2c893 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1974
},
"timestamp": "2026-02-16T23:14:58.382Z",
"answer": 57272
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d51b1c | comb_count_surjections_v1_1874849503_225 | Let $n = 8$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 6$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the value of this expression. | 5,796 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(8),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T12:53:12.154961Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T12:53:12.157366Z"
} | 993b4d | 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": 978
},
"timestamp": "2026-02-09T14:52:15.145Z",
"answer": 5796
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
b71730 | nt_count_intersection_v1_1520064083_9432 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 25000$ and $5$ divides the $n$-th Fibonacci number. Let $a = 3$, and let $b$ be the largest positive integer at most $20$ that divides $620$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) ... | 666 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(25000)), Divides(divisor=Const(5), dividend=Fibonacci(arg=Var(name='n')))))),
"a": Const(3),
"b": MaxOverSet(set=SolutionsSet(var=Var("d"), ... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"MAX_DIVISOR"
] | b4c662 | nt_count_intersection_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_DIVISOR"
] | 2 | 0.238 | 2026-02-08T10:45:26.028405Z | {
"verified": true,
"answer": 666,
"timestamp": "2026-02-08T10:45:26.266885Z"
} | 9559ca | 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": 2521
},
"timestamp": "2026-02-14T08:48:46.831Z",
"answer": 666
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4faef7 | comb_count_permutations_fixed_v1_601307018_10994 | Let $n = \sum_{k_1 = \binom{17}{0} - 1}^{2} 2^{k_1}$ and let $R = \binom{n}{1} \cdot D_{n-1}$, where $D_m$ denotes the number of derangements of $m$ elements. Find the remainder when $86263 \cdot R$ is divided by $53590$. | 51,715 | graphs = [
Graph(
let={
"_n": Const(53590),
"n": Summation(var="k1", start=Sub(Binom(n=Const(17), k=Const(0)), Const(1)), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(na... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 71c45c | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM",
"ZERO_BINOM_0"
] | 3 | 0.089 | 2026-03-10T11:25:28.325060Z | {
"verified": true,
"answer": 51715,
"timestamp": "2026-03-10T11:25:28.414020Z"
} | d2dd43 | 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": 1350
},
"timestamp": "2026-04-19T15:15:39.396Z",
"answer": 51715
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
8c5d3f | comb_sum_binomial_row_v1_124444284_3456 | Let $S$ be the set of integers $t$ such that $18 \leq t \leq 100$ and $t = 4a + 14b$ for some positive integers $a \leq 18$ and $b \leq 2$.
Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = |S|$.
Let $r = 2^n$. Determine the value of the smallest positive inte... | 684 | graphs = [
Graph(
let={
"_n": Const(2),
"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")), CountOverSet(set=SolutionsSet(var=Var("t"), condit... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T05:24:50.345628Z | {
"verified": true,
"answer": 684,
"timestamp": "2026-02-08T05:24:50.347509Z"
} | 24335e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 3261
},
"timestamp": "2026-02-12T08:28:47.190Z",
"answer": 684
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a56450 | diophantine_fbi2_min_v1_1248542787_774 | Let $x$ and $y$ be positive integers such that $xy = 324$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $A$ be the set of prime numbers $n$ such that $2 \leq n \leq 6$. Let $m$ be the maximum element of $A$. Find the smallest integer $d$ such that $m \leq d \leq s$, $d$ divides $26$, and $\frac{26}{... | 17,068 | graphs = [
Graph(
let={
"k": Const(26),
"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(324)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.006 | 2026-02-08T03:24:57.657036Z | {
"verified": true,
"answer": 17068,
"timestamp": "2026-02-08T03:24:57.662832Z"
} | 7be603 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 796
},
"timestamp": "2026-02-09T08:07:11.467Z",
"answer": 17068
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "VA... | {
"lo": -3.46,
"mid": 0.96,
"hi": 5.17
} | ||
73e320 | nt_min_coprime_above_v1_1470522791_925 | Let $a = 43925$, $s = 61504$, and $u = 61765$. Let $m$ be the largest prime number that is less than or equal to the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16384$. Let $r$ be the smallest integer $n$ such that $s < n \leq u$ and $\gcd(n, m) = 1$. Compute the remain... | 28,597 | graphs = [
Graph(
let={
"_n": Const(43925),
"start": Const(61504),
"upper": Const(61765),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[V... | NT | null | EXTREMUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.072 | 2026-02-08T13:18:45.908549Z | {
"verified": true,
"answer": 28597,
"timestamp": "2026-02-08T13:18:45.980222Z"
} | 4b2a79 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 3347
},
"timestamp": "2026-02-15T13:15:45.235Z",
"answer": 28597
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"st... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cc061d | antilemma_sum_equals_v1_1439011603_2502 | Let $n = 47$. Compute the number of ordered pairs $(i,j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 45$, and $1 \leq j \leq 46$. | 45 | graphs = [
Graph(
let={
"_n": Const(47),
"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(45)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.066 | 2026-02-08T16:50:18.972224Z | {
"verified": true,
"answer": 45,
"timestamp": "2026-02-08T16:50:19.038493Z"
} | 332f72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 1559
},
"timestamp": "2026-02-24T21:59:23.879Z",
"answer": 45
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
ca6272 | modular_mod_compute_v1_1915831931_1453 | Let $a = -144$ and $m = 46368$. Define $r = a \bmod m$, the unique integer such that $0 \leq r < m$ and $r \equiv a \pmod{m}$. Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 3481$. Let $s_{\min}$ be the minimum value of $x_1 + y_1$ as $(x_1, y_1)$ ranges over $S$. Let $T$... | 12,423 | graphs = [
Graph(
let={
"_n": Const(55166),
"a": Const(-144),
"m": Const(46368),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(ar... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 6cdf3d | modular_mod_compute_v1 | negation_mod | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T16:08:55.935817Z | {
"verified": true,
"answer": 12423,
"timestamp": "2026-02-08T16:08:55.938673Z"
} | a6d8f5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 926
},
"timestamp": "2026-02-16T21:47:50.364Z",
"answer": 12423
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
91b053 | nt_count_coprime_and_v1_168721529_653 | Let $k_1 = 5$ and let $k_2$ be the largest integer $k$ such that $2^k$ divides $7^{128} - 5^{128}$. Determine the number of positive integers $n$ such that $1 \leq n \leq 34972$, $\gcd(n, k_1) = \phi(1)$, and $\gcd(n, k_2) = 1$. Let $r$ denote this number. Compute $r + \phi(|r| + 1) + \tau(|r| + \phi(2))$, where $\phi$... | 36,476 | graphs = [
Graph(
let={
"upper": Const(34972),
"k1": Const(5),
"k2": MaxKDivides(target=Sub(Pow(Const(7), Const(128)), Pow(Const(5), Const(128))), base=Const(2)),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(... | NT | null | COUNT | sympy | LTE_DIFF_P2 | [
"LTE_DIFF_P2",
"ONE_PHI_2",
"ONE_PHI_1"
] | 84a372 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"LTE_DIFF_P2",
"ONE_PHI_1",
"ONE_PHI_2"
] | 3 | 5.262 | 2026-02-08T13:10:40.810342Z | {
"verified": true,
"answer": 36476,
"timestamp": "2026-02-08T13:10:46.072009Z"
} | 4e4f8e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 2707
},
"timestamp": "2026-02-09T07:31:47.201Z",
"answer": 36476
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
5ce84b | nt_count_divisible_and_v1_677425708_2676 | Let $N$ be the number of positive integers $n$ at most $32256$ that are divisible by both $12$ and $18$. Let $c$ be the smallest prime divisor of $1035044771$. Compute the remainder when $$353702 \cdot (|N| \mod 97) + 329703 \cdot \left((N^2 + 1) \mod 101\right) + 215534 \cdot \left(|N| + c \mod 103\right)$$ is divided... | 26,573 | graphs = [
Graph(
let={
"_n": Const(101),
"upper": Const(32256),
"d1": Const(12),
"d2": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modu... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | b5b91a | nt_count_divisible_and_v1 | crt_mix_3 | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.912 | 2026-02-08T05:11:13.765770Z | {
"verified": true,
"answer": 26573,
"timestamp": "2026-02-08T05:11:15.677750Z"
} | b5d6bf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 6541
},
"timestamp": "2026-02-11T23:05:23.277Z",
"answer": 26573
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
4ab6b0 | sequence_fibonacci_compute_v1_124444284_10388 | Let $m = 233$. Let $k$ range over the positive integers from 1 to 28193 inclusive that are divisible by $m$. Define $n$ to be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy$ equals the number of such $k$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by... | 17,711 | graphs = [
Graph(
let={
"_m": Const(233),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(28193)), Divides(divisor=Ref("_m"), dividend=Var("k"))), domain='positive_integers')),
"n": MinOverSet(set=MapOverSet(set... | NT | null | COMPUTE | sympy | C2 | [
"C2/B3"
] | 7c8509 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B3",
"C2"
] | 2 | 0.003 | 2026-02-08T13:03:00.456866Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T13:03:00.459512Z"
} | 41099f | 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": 862
},
"timestamp": "2026-02-15T09:04:11.848Z",
"answer": 17711
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d1f928 | comb_count_derangements_v1_124444284_9879 | Let $m=2$ and $N=1408$. Consider all ordered pairs $(x,y)$ of positive integers such that $xy=495616$. For each such pair, compute the sum $x+y$. Let $S$ be the set of all values of $x+y$ obtained in this way, and let $r$ be the minimum element of $S$.
For each integer $j$ with $0\le j\le N$, consider the binomial coe... | 14,833 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(1408),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("... | COMB | null | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | comb_count_derangements_v1 | null | 8 | 0 | [
"B3",
"V8"
] | 2 | 0.003 | 2026-02-08T12:42:30.194944Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T12:42:30.197697Z"
} | 7b66d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 1899
},
"timestamp": "2026-02-24T16:12:58.636Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
b8e361 | nt_count_divisible_v1_1353956133_460 | Let $p$ be the number of prime numbers $q$ such that $2 \leq q \leq 71$. Compute the number of positive integers $n \leq 65025$ that are divisible by $p$. | 3,251 | graphs = [
Graph(
let={
"_n": Const(71),
"upper": Const(65025),
"divisor": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), ... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 2.393 | 2026-02-08T11:27:46.324971Z | {
"verified": true,
"answer": 3251,
"timestamp": "2026-02-08T11:27:48.717979Z"
} | c7c663 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 347
},
"timestamp": "2026-02-14T14:45:10.320Z",
"answer": 3250
},
... | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d82fe6 | alg_poly_preperiod_count_v1_1419126231_931 | For a non-negative integer $a$, define the sequence $N = (a^4 + 2a^3 + a^2 + 5a - 3) \bmod 37$, $M = (N^4 + 2N^3 + N^2 + 5N - 3) \bmod 37$, $R = (M^4 + 2M^3 + M^2 + 5M - 3) \bmod 37$, and $S = (R^4 + 2R^3 + R^2 + 5R - 3) \bmod 37$. Find the number of integers $a$ with $0 \leq a \leq 28970$ such that $S = N$, $M \neq N$... | 4,698 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(2), Pow(Var("a"), Const(3))), Pow(Var("a"), Const(2)), Mul(Const(5), Var("a")), Const(-3)), modulus=Const(37)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(2), Pow(Ref("p1"), Const(3))), Pow(Re... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.074 | 2026-02-25T10:27:04.123759Z | {
"verified": true,
"answer": 4698,
"timestamp": "2026-02-25T10:27:04.197810Z"
} | 7d79df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 8379
},
"timestamp": "2026-03-30T10:43:02.194Z",
"answer": 4698
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
3b7e2d | sequence_fibonacci_compute_v1_397696148_855 | Let $n$ be the number of integers $k$ with $1 \leq k \leq 241$ such that $k \equiv \left\lfloor \frac{k}{2} \right\rfloor \pmod{11}$. Let $F_n$ denote the $n$-th Fibonacci number. Compute the remainder when $22621 \cdot F_n$ is divided by $67819$. | 2,297 | graphs = [
Graph(
let={
"_n": Const(241),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T11:46:51.063132Z | {
"verified": true,
"answer": 2297,
"timestamp": "2026-02-08T11:46:51.064278Z"
} | 6c1f0e | 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": 1313
},
"timestamp": "2026-02-14T20:57:12.337Z",
"answer": 2297
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a389be | modular_sum_quadratic_residues_v1_1440796553_1461 | Let $p = 181$. Define $r = \frac{p(p-1)}{4}$. Let $c$ be the largest prime number less than or equal to $1600$ that is at least $2$. Compute the remainder when $c - r$ is divided by $63187$. | 56,639 | graphs = [
Graph(
let={
"_n": Const(2),
"p": Const(181),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(1600)), IsPrime(Var("n"))))),
... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | modular_sum_quadratic_residues_v1 | negation_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T14:00:59.877368Z | {
"verified": true,
"answer": 56639,
"timestamp": "2026-02-08T14:00:59.880289Z"
} | 74813d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 950
},
"timestamp": "2026-02-15T22:59:57.365Z",
"answer": 56639
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8ea7e6 | comb_count_partitions_v1_1742523217_737 | Let $N$ be the number of integers $t$ such that $50\le t\le1301$ and there exist integers $a$ and $b$ with $1\le a\le86$ and $1\le b\le12$ satisfying
$$t=12a+21b+17.$$
Let $n$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy=N$.
Let $P(n)$ denote the number of integer part... | 37,338 | 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=86)), Geq(left=Var(name='b'), right=Const(value... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_count_partitions_v1 | null | 8 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T03:11:51.869712Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T03:11:51.872150Z"
} | 613a39 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:54:08.341Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": 3.17,
"mid": 4.49,
"hi": 5.75
} | ||
a22397 | nt_euler_phi_compute_v1_677425708_3870 | Let $n = 76176$ and define $\varphi(n)$ to be Euler's totient function of $n$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $|S|$ denote the number of elements in $S$. Compute the remainder when $|S| - \varphi(n)$ i... | 41,167 | graphs = [
Graph(
let={
"n": Const(76176),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Sub(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=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | nt_euler_phi_compute_v1 | negation_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:59:08.405352Z | {
"verified": true,
"answer": 41167,
"timestamp": "2026-02-08T05:59:08.406303Z"
} | 256002 | 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": 1054
},
"timestamp": "2026-02-12T18:26:24.540Z",
"answer": 41167
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
826c2c | modular_sum_quadratic_residues_v1_809748730_1101 | Let $p$ be the largest prime number less than or equal to $137$. Define $r = \frac{p(p-1)}{4}$. Let $m = |r| + 2$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $m$. | 390 | graphs = [
Graph(
let={
"_n": Const(137),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": FibonacciEntry... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T12:10:46.735545Z | {
"verified": true,
"answer": 390,
"timestamp": "2026-02-08T12:10:46.737008Z"
} | f8e17c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 2824
},
"timestamp": "2026-02-14T22:48:32.797Z",
"answer": 390
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
171253 | nt_min_phi_inverse_v1_2051736721_5469 | Let $t$ be an integer satisfying $7 \le t \le 42$. Suppose there exist positive integers $a$ and $b$ with $1 \le a \le 3$ and $1 \le b \le 10$ such that $t = 4a + 3b$. Let $u$ be the number of such integers $t$. Let $k = 10$. Determine the smallest positive integer $n$ such that $1 \le n \le u$ and $\phi(n) = k$. | 11 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(val... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_1"
] | 2 | 0.116 | 2026-02-08T18:36:54.667696Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T18:36:54.784044Z"
} | 3906ff | 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": 2322
},
"timestamp": "2026-02-18T18:23:34.980Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c328cf | comb_sum_binomial_row_v1_1353956133_489 | Let $m = 2$ and let $S$ be the set of all integers $x$ such that $x^2 - 2x - 4355 = 0$. Define $s$ to be the sum of all elements in $S$. Let $n$ be the smallest divisor of $224939$ that is at least $s$. Let $r = 2^n$. Find the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|r| + 2$... | 300 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-2), Var("x")), Const(-4355)), Const(0)))),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), ... | NT | null | SUM | sympy | VIETA_SUM | [
"VIETA_SUM/MIN_PRIME_FACTOR"
] | b1c8ca | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T11:28:19.057588Z | {
"verified": true,
"answer": 300,
"timestamp": "2026-02-08T11:28:19.059554Z"
} | 1b92bd | 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": 1963
},
"timestamp": "2026-02-14T14:50:10.200Z",
"answer": 300
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
445ab4 | antilemma_k2_v1_1742523217_1056 | Let $ r_1 $ and $ r_2 $ be the roots of the quadratic equation $ x^2 - 181x - 4242 = 0 $. Define $ k_{\text{max}} $ to be the sum of these roots. For each integer $ k $ from $ 1 $ to $ k_{\text{max}} $, let $ a_k = \phi(k) \left\lfloor \frac{s}{k} \right\rfloor $, where $ \phi(k) $ is the number of positive integers at... | 16,471 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-181), Var("x")), Const(-4242)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=Sol... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T03:24:03.296273Z | {
"verified": true,
"answer": 16471,
"timestamp": "2026-02-08T03:24:03.298524Z"
} | 1448d7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 1260
},
"timestamp": "2026-02-10T02:37:37.465Z",
"answer": 16471
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
de1c59 | alg_sym_quad_system_v1_1218484723_5184 | Let $N$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 134$. Define
$$R = \sum_{(a,b,c)} \bigl(a^{5} + b^{5} + c^{5}\bigr) \bmod 7461,$$
where the sum is taken over all ordered triples $(a,b,c)$ of positive integers satisfying
$$a^{2} + b^{2} + c^{2} = ab + bc + ca ... | 64,890 | graphs = [
Graph(
let={
"_n": Const(5),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul... | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"B1"
] | d2b6e1 | alg_sym_quad_system_v1 | negation_mod | 7 | 0 | [
"B1",
"SUM_GEOM"
] | 2 | 0.114 | 2026-02-25T06:49:11.490664Z | {
"verified": true,
"answer": 64890,
"timestamp": "2026-02-25T06:49:11.605047Z"
} | 628ced | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 2252
},
"timestamp": "2026-03-29T19:49:36.039Z",
"answer": 64890
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
54291d | nt_count_coprime_v1_784195855_532 | Let $n = 3$ and $U = 73984$. Let $$
k = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$ Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq U$ and $\gcd(n, k) = 1$. Compute $\text{result}$. | 24,661 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(73984),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_coprime_v1 | null | 7 | 0 | [
"K2"
] | 1 | 5.807 | 2026-02-08T04:25:46.037140Z | {
"verified": true,
"answer": 24661,
"timestamp": "2026-02-08T04:25:51.844201Z"
} | 1ce692 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1119
},
"timestamp": "2026-02-10T16:30:41.719Z",
"answer": 24661
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
bce0ce | comb_count_permutations_fixed_v1_784195855_8292 | Let $n = 10$ and $k = 5$. Define $a = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $S = \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Compute the remainder when $S - a$ is divided by 97816. | 86,848 | graphs = [
Graph(
let={
"n": Const(10),
"k": Const(5),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Mod(value=Sub(Summation(var="k", start=Const(1), end=Const(15), expr=Mul(EulerPhi(n=Var("k... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 9468ae | comb_count_permutations_fixed_v1 | negation_mod | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T15:59:57.253671Z | {
"verified": true,
"answer": 86848,
"timestamp": "2026-02-08T15:59:57.256248Z"
} | bf2d05 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1079
},
"timestamp": "2026-02-16T19:00:21.683Z",
"answer": 86848
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
27b3af | algebra_quadratic_discriminant_v1_458359167_5204 | Let $n = 4$, $a = 2$, $b = -28$, and $c = 98$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Define $D = b^k - 4ac$. Let $\alpha = \begin{cases} 2 & \text{if } D > 0, \\ ... | 1 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(2),
"b": Const(-28),
"c": Const(98),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.1 | 2026-02-08T12:20:42.840444Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T12:20:42.940757Z"
} | a4288d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 846
},
"timestamp": "2026-02-15T00:35:08.107Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_E... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
aa2ec0 | nt_sum_divisors_mod_v1_1248542787_565 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Let $M = 11161$, and let $r$ be the remainder when $\sigma(n)$ is divided by $M$. Compute $43264 - ... | 35,081 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1116... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:13:11.533321Z | {
"verified": true,
"answer": 35081,
"timestamp": "2026-02-08T03:13:11.535305Z"
} | 475a5c | 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": 1783
},
"timestamp": "2026-02-09T05:36:42.277Z",
"answer": 35081
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
a27a76 | alg_poly3_sum_v1_601307018_1922 | Find the remainder when
$$
\sum_{\substack{1 \le a \le 300 \\ 1 \le b \le 300}} \left( 72a^3 + 91b^3 + 192a^2b + \left| \left\{ (a_1, b_1) : \begin{array}{c} 1 \le a_1 \le 30, \\ 1 \le b_1 \le 30, \\ 13a_1^2 - 2a_1b_1 + 2b_1^2 \le 1252 \end{array} \right\} \right| \cdot a b^2 \right)
$$
is divided by $83147$. | 23,736 | graphs = [
Graph(
let={
"_n": Const(300),
"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"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(300)))), expr=Sum(Mul(Const... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.197 | 2026-03-10T02:42:01.236203Z | {
"verified": true,
"answer": 23736,
"timestamp": "2026-03-10T02:42:01.432899Z"
} | 9b4f47 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 11829
},
"timestamp": "2026-03-29T03:52:37.874Z",
"answer": 23736
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 2.78,
"mid": 4.94,
"hi": 7.11
} | ||
5bb991 | sequence_fibonacci_compute_v1_1116507919_97 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 30$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 10$, and $t = 5a + 2b$. Let $n$ be the number of elements in $T$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}... | 12,921 | graphs = [
Graph(
let={
"_n": Const(75404),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:25:32.824921Z | {
"verified": true,
"answer": 12921,
"timestamp": "2026-02-08T02:25:32.826064Z"
} | 2c4d58 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 2968
},
"timestamp": "2026-02-08T19:02:48.175Z",
"answer": 12921
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -0.95,
"mid": 0.8,
"hi": 2.3
} | ||
55b1f9 | antilemma_sum_factor_cartesian_v1_1874849503_265 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 6$ and $1 \leq j \leq 18$. Define $x$ to be the sum of $i \cdot j$ over all pairs $(i, j)$ in $S$. Let $c = 82819$. Compute the remainder when $c \cdot x$ is divided by $91342$. Determine the value of this remainder. | 84,819 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(18)))), expr=Mul(Var("i"), Var("... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"ONE_PHI_1"
] | 1cb432 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"ONE_PHI_1",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T12:53:59.729686Z | {
"verified": true,
"answer": 84819,
"timestamp": "2026-02-08T12:53:59.730913Z"
} | 31ff2e | 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": 2405
},
"timestamp": "2026-02-09T15:07:34.138Z",
"answer": 84819
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
17fd4c | algebra_quadratic_discriminant_v1_2051736721_2000 | Let $N$ be the number of elements in the Cartesian product $\{1,2\} \times \{1,2\}$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = N$. Define $b$ to be the maximum value of $xy$ as $(x,y)$ ranges over $S$. Let $P$ be the set of all positive integers $p$ for which there exists a... | 0 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(2)))),
"a": Const(2),
"b": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), co... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/B1",
"COPRIME_PAIRS"
] | a2ff45 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B1",
"COPRIME_PAIRS",
"COUNT_CARTESIAN"
] | 3 | 0.008 | 2026-02-08T16:24:51.206071Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:24:51.214028Z"
} | 7ccd61 | 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": 1600
},
"timestamp": "2026-02-17T04:06:41.969Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
825e61 | alg_linear_system_2x2_v1_1218484723_5876 | Let $\text{det} = -14 \cdot (-9)$. Let $M = -604043 \cdot (-9) + 747 \cdot \left|\left\{ (a, b) : 1 \leq a, b \leq 35,\ 17a^4 + 102a^2b^2 + 68a^3b + 68ab^3 + 17b^4 = 653072 \right\}\right|$, and let $R = -14 \cdot (-747)$. Compute $\frac{M}{\text{det}} + \frac{R}{\text{det}}$. | 43,306 | graphs = [
Graph(
let={
"_n": Const(4),
"num_x": Sub(Mul(Const(-604043), Const(-9)), Mul(Const(-747), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_linear_system_2x2_v1 | null | 4 | 0 | [
"POLY4_COUNT"
] | 1 | 0.004 | 2026-02-25T07:26:38.182322Z | {
"verified": true,
"answer": 43306,
"timestamp": "2026-02-25T07:26:38.186114Z"
} | 48ecb3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 2281
},
"timestamp": "2026-03-29T23:10:52.259Z",
"answer": 43306
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
472a32 | comb_count_permutations_fixed_v1_601307018_152 | Let $D_n$ denote the number of derangements of $n$ elements. Let $n$ be the largest integer such that $3^n$ divides $2187 \cdot 81$. Compute $\binom{n}{7} \cdot D_{n - 7}$. | 2,970 | graphs = [
Graph(
let={
"n": MaxKDivides(target=Mul(Const(2187), Const(81)), base=Const(3)),
"k": Const(7),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
)
] | COMB | NT | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"K13"
] | 8d970a | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"K13",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.063 | 2026-03-10T00:46:04.756604Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-03-10T00:46:04.819552Z"
} | 454807 | CC BY 4.0 | null | null | [
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
f8ab12 | algebra_quadratic_discriminant_v1_601307018_3903 | Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6400$. Compute $4^{2} - 4(-2) \cdot c$. | 1,296 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(4),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.004 | 2026-03-10T04:30:51.733135Z | {
"verified": true,
"answer": 1296,
"timestamp": "2026-03-10T04:30:51.737361Z"
} | e61186 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 682
},
"timestamp": "2026-03-29T10:18:12.574Z",
"answer": 1296
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
e1487b | comb_binomial_compute_v1_124444284_2443 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x,y)$ such that $xy = 49$. Compute $\binom{n}{6}$. | 3,003 | graphs = [
Graph(
let={
"_n": Const(49),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_binomial_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:40:41.456322Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T04:40:41.457954Z"
} | a18488 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 452
},
"timestamp": "2026-02-24T01:25:34.674Z",
"answer": 3003
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
cc6da7 | nt_count_divisors_in_range_v1_1520064083_1326 | Let $n = 221760$. Determine the number of positive divisors $d$ of $n$ such that $65 \leq d \leq 18483$. Let this count be $C$. Now compute the value of
$$
\left( \sum_{k=1}^{10} \phi(k) \left\lfloor \frac{1 + 2 + 3 + 4}{k} \right\rfloor \right) - C,
$$
and find the remainder when this result is divided by $94179$. | 94,113 | graphs = [
Graph(
let={
"_n": Const(10),
"n": Const(221760),
"a": Const(65),
"b": Const(18483),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"),... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 18f523 | nt_count_divisors_in_range_v1 | negation_mod | 6 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.159 | 2026-02-08T03:55:32.504537Z | {
"verified": true,
"answer": 94113,
"timestamp": "2026-02-08T03:55:32.663524Z"
} | 3529a6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 5208
},
"timestamp": "2026-02-10T14:45:27.754Z",
"answer": 94113
},
{
... | 1 | [
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0f5845 | comb_count_surjections_v1_601307018_4162 | Let $k = 3$. For each integer $a$ with $0 \leq a \leq 3720$, define the sequence $M = a^2 + a + 1104 \bmod 3721$, $R = M^2 + M + 1104 \bmod 3721$, $S = R^2 + R + 1104 \bmod 3721$, and $T = S^2 + S + 1104 \bmod 3721$. Let $n$ be the number of values of $a$ for which $T = a$, but $M \ne a$, $R \ne a$, and $S \ne a$. Comp... | 5,796 | graphs = [
Graph(
let={
"_n": Const(1104),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(3720)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a"))))),
... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_HENSEL"
] | 53b6eb | comb_count_surjections_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.077 | 2026-03-10T04:47:26.927165Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-03-10T04:47:27.003842Z"
} | 5429ec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T11:17:26.583Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": 1.19,
"mid": 4.27,
"hi": 6.7
} | ||
b49cab | nt_count_divisible_and_v1_1742523217_1399 | Let $d_1 = 4$ and let $d_2 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$. Let $N$ be the number of positive integers $n$ such that $1 \le n \le 45852$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute $\sum_{n=1}^{N} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors o... | 32,103 | graphs = [
Graph(
let={
"upper": Const(45852),
"d1": Const(4),
"d2": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 6 | 0 | [
"K2"
] | 1 | 1.645 | 2026-02-08T03:42:18.475876Z | {
"verified": true,
"answer": 32103,
"timestamp": "2026-02-08T03:42:20.121018Z"
} | 457fe4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 7829
},
"timestamp": "2026-02-10T16:26:45.185Z",
"answer": 32103
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e66608 | nt_sum_divisors_mod_v1_865884756_1856 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1587600$. Let $n$ be the minimum value of $x + y$ over all pairs in $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $44262 \cdot \sigma$ is divided by $71129$. | 37,024 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1587600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1032... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:19:40.528643Z | {
"verified": true,
"answer": 37024,
"timestamp": "2026-02-08T16:19:40.530754Z"
} | bbe78c | 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": 2173
},
"timestamp": "2026-02-17T01:53:12.225Z",
"answer": 37024
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad7264 | nt_count_divisors_in_range_v1_971394319_84 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. Define $T$ to be the set of all values $x + y$ where $(x, y) \in S$. Let $n$ be the minimum element of $T$.
Determine the number of positive divisors $d$ of $n$ such that $7 \leq d \leq 724$. Find the value of this number. | 48 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(7),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.1 | 2026-02-08T12:49:54.918294Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T12:49:55.018280Z"
} | 50f87c | 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": 2267
},
"timestamp": "2026-02-15T05:42:54.941Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bf97e6 | diophantine_product_count_v1_784195855_8077 | Let $k = 120$ and let $u = 52$. Consider the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Compute the number of elements in this set. | 12 | graphs = [
Graph(
let={
"k": Const(120),
"upper": Const(52),
"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 | ONE_PHI_2 | [
"LIN_FORM",
"V1"
] | 489129 | diophantine_product_count_v1 | null | 4 | 0 | [
"LIN_FORM",
"ONE_PHI_2",
"V1"
] | 3 | 0.077 | 2026-02-08T10:47:34.181294Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T10:47:34.258712Z"
} | 6aecce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1439
},
"timestamp": "2026-02-14T08:34:48.458Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
38edd6 | comb_count_partitions_v1_898971024_1646 | Let $a$ be the largest prime number between $2$ and $8$, inclusive. For each $k$ from $1$ to $9$ and each $j$ from $1$ to $3$, compute $\phi(k) \left\lfloor \frac{9}{k} \right\rfloor$, and let $s$ be the sum of all these values. Let $n = \frac{a \cdot s}{21}$. Let $p(n)$ denote the number of integer partitions of $n$. ... | 1,236 | graphs = [
Graph(
let={
"_m": Const(21),
"_n": Const(9),
"n": Div(Mul(MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(8)), IsPrime(Var("n1"))))), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/SUM_INDEPENDENT",
"K2"
] | 262f95 | comb_count_partitions_v1 | null | 7 | 0 | [
"K2",
"MAX_PRIME_BELOW",
"SUM_INDEPENDENT"
] | 3 | 0.007 | 2026-02-08T16:13:00.819860Z | {
"verified": true,
"answer": 1236,
"timestamp": "2026-02-08T16:13:00.827235Z"
} | add748 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2692
},
"timestamp": "2026-02-16T23:35:58.480Z",
"answer": 1236
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
d1f5a7 | nt_count_divisors_in_range_v1_2051736721_4452 | Let $T$ be the set of all positive integers $t$ such that $36 \leq t \leq 1623$ and $t = 21a + 15b$ for some positive integers $a \leq 8$ and $b \leq 97$. Let $b = |T|$. Let $D$ be the number of positive divisors of $20160$ that are at least $1$ and at most $b$. Compute the smallest positive integer $k$ such that the $... | 24 | graphs = [
Graph(
let={
"n": Const(20160),
"a": Const(1),
"b": 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=Co... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-08T17:59:40.708145Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T17:59:40.724167Z"
} | 1ab1c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 5690
},
"timestamp": "2026-02-18T11:33:27.868Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b6b913 | comb_factorial_compute_v1_784195855_6385 | Let $n$ be the sum of all positive integers at most 7 that are divisible by 7. Determine the value of $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(7),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(7)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
"result": Factorial(Ref("n")),
},
goal=Ref("resu... | ALG | COMB | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_factorial_compute_v1 | null | 2 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T08:37:49.165931Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T08:37:49.167316Z"
} | eee5d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 366
},
"timestamp": "2026-02-24T09:43:17.142Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
4837eb | nt_min_phi_inverse_v1_784195855_8104 | Let $k$ be the number of integers $t$ such that $14 \leq t \leq 44$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 2$, and $t = 4a + 10b$. Let $n$ be the smallest positive integer such that $1 \leq n \leq 50$ and $\phi(n) = k$. Compute the remainder when $44121 \cdot n$ is divided ... | 44,837 | graphs = [
Graph(
let={
"_n": Const(66092),
"upper": Const(50),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), ri... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T10:49:33.749033Z | {
"verified": true,
"answer": 44837,
"timestamp": "2026-02-08T10:49:33.754200Z"
} | 7f3056 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1256
},
"timestamp": "2026-02-16T16:06:56.562Z",
"answer": 44837
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ebe99d | nt_count_intersection_v1_1520064083_5136 | Let $T$ be the set of all integers $t$ such that $22 \leq t \leq 15037$ and $t = 9a + 12b + 1$ for some positive integers $a$ and $b$ with $1 \leq a \leq 552$ and $1 \leq b \leq 839$. Let $N$ be the number of elements in $T$. Now, let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq N$, $11$ divides... | 15,067 | 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=552)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.164 | 2026-02-08T06:38:46.765870Z | {
"verified": true,
"answer": 15067,
"timestamp": "2026-02-08T06:38:46.930229Z"
} | 76d68c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 4222
},
"timestamp": "2026-02-13T03:00:38.648Z",
"answer": 15067
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
165846 | alg_telescope_v1_1218484723_1586 | Let $A$ be the number of ordered pairs $(a,b)$ of integers with $1 \le a \le 40$ and $1 \le b \le 40$ such that
$$17b^{2} + 17a^{2} - 34ab = 3332.$$
Define
$$R = \sum_{k=0}^{A} \bigl((k+1)^{2} - k^{2}\bigr) \bmod B,$$
where $B$ is the number of integers $t$ for which there exist integers $a,b$ with $1 \le a \le 424$ an... | 29,177 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": Const(62516),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), C... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT",
"LIN_FORM"
] | 1faef7 | alg_telescope_v1 | null | 8 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT"
] | 2 | 0.009 | 2026-02-25T03:19:06.157016Z | {
"verified": true,
"answer": 29177,
"timestamp": "2026-02-25T03:19:06.165611Z"
} | b026a0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 298,
"completion_tokens": 2315
},
"timestamp": "2026-03-10T07:12:19.115Z",
"answer": 29177
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
94c84c | nt_sum_gcd_range_mod_v1_458359167_1724 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 174$. Let $\text{sum} = \sum_{n=1}^{N} \gcd(n, 168)$. Compute the remainder when $\text{sum}$ is divided by $10639$. | 5,340 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(174)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(168),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.34 | 2026-02-08T04:49:20.539028Z | {
"verified": true,
"answer": 5340,
"timestamp": "2026-02-08T04:49:20.879357Z"
} | a0b51a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2812
},
"timestamp": "2026-02-11T22:10:55.650Z",
"answer": 5340
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
090e22 | diophantine_fbi2_min_v1_1439011603_1725 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $k = 8$ and let the upper bound be $18$. Define $d$ to be an integer satisfying $4 \le d \le 18$, $d$ divides $k$, and $\frac{k}{d} \ge n$. Determine the value of the smal... | 1,760 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=12)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"COPRIME_PAIRS/B3"
] | bfccae | diophantine_fbi2_min_v1 | negation_mod | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.017 | 2026-02-08T16:14:22.287894Z | {
"verified": true,
"answer": 1760,
"timestamp": "2026-02-08T16:14:22.304499Z"
} | 84b321 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1552
},
"timestamp": "2026-02-17T00:34:00.271Z",
"answer": 1760
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c67614 | comb_count_permutations_fixed_v1_677425708_2838 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 24$ and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $S$. Define
$$
n = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{\sum_{k=1}^{m} k}{k} \right\rfloor.
$$Compute the value of $\binom{n}{3} \cdot !(n... | 23,140 | graphs = [
Graph(
let={
"_n": Const(19729),
"n": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(na... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_ARITHMETIC/K2"
] | 5e07bd | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T05:19:44.735567Z | {
"verified": true,
"answer": 23140,
"timestamp": "2026-02-08T05:19:44.738320Z"
} | c9ed59 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 951
},
"timestamp": "2026-02-12T06:33:28.611Z",
"answer": 23140
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
416423 | antilemma_v7_kummer_798873815_26 | Let $m = 413$. Define $S$ to be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $n \equiv 0 \pmod{59}$. Let $N$ be the sum of all elements in $S$. Determine the value of $k$ such that $2^k$ divides $\binom{4130}{N}$, but $2^{k+1}$ does not. | 10 | graphs = [
Graph(
let={
"_m": Const(413),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(Mod(value=Var("n"), modulus=Const(59)), Const(0))))),
"x": MaxKDivides(target=Binom(n=Const(4130), k=Ref("_n")), b... | NT | null | COMPUTE | sympy | V7 | [
"SUM_DIVISIBLE/V7",
"V7"
] | 3b997e | antilemma_v7_kummer | null | 7 | 0 | [
"SUM_DIVISIBLE",
"V7"
] | 2 | 0.01 | 2026-02-08T02:24:24.184179Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T02:24:24.193935Z"
} | 661fc3 | 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": 3799
},
"timestamp": "2026-02-08T18:30:15.911Z",
"answer": 10
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -1.89,
"mid": 1.79,
"hi": 4.93
} | ||
7cf40f | algebra_poly_eval_v1_677425708_3762 | Let $T$ be the set of all integers $t$ such that $20 \leq t \leq 54$ and there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 5$, and $t = 3a + 4b + 13$. Define $r = \frac{6 \cdot 9^5 + 23 \cdot 9^4 - 65 \cdot 9^3 - 45 \cdot 9^2 + 55 \cdot 9}{|T|}$. Let $Q$ be the remainder when $84523 \cdot r$ is di... | 76,434 | graphs = [
Graph(
let={
"_n": Const(79608),
"k": Const(9),
"result": Div(Sum(Mul(Const(6), Pow(Ref("k"), Const(5))), Mul(Const(23), Pow(Ref("k"), Const(4))), Mul(Const(-65), Pow(Ref("k"), Const(3))), Mul(Const(-45), Pow(Ref("k"), Const(2))), Mul(Const(55), Ref("k"))), Cou... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T05:55:27.379395Z | {
"verified": true,
"answer": 76434,
"timestamp": "2026-02-08T05:55:27.384795Z"
} | c0ad8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 3403
},
"timestamp": "2026-02-12T16:50:05.491Z",
"answer": 76434
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
33d1a9 | nt_count_coprime_v1_153355830_49 | Let $ S $ be the set of all integers $ n $ such that $ 1 \leq n \leq 22500 $ and $ \gcd(n, 31) = 1 $. Compute the number of elements in $ S $. | 21,775 | graphs = [
Graph(
let={
"upper": Const(22500),
"k": Const(31),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=11), b=Const(value=13)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Ref("upp... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_coprime_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 1.676 | 2026-02-08T02:51:27.068818Z | {
"verified": true,
"answer": 21775,
"timestamp": "2026-02-08T02:51:28.745273Z"
} | 3a1e94 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 289
},
"timestamp": "2026-02-08T22:27:35.746Z",
"answer": 21775
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
782e08 | alg_poly_orbit_count_v1_1218484723_2230 | For a non-negative integer $a$, define a sequence by $N = (a^4 - 2a^3 + a^2 - 4a) \bmod 31$, $M = (N^4 - 2N^3 + N^2 - 4N) \bmod 31$, $R = (M^4 - 2M^3 + M^2 - 4M) \bmod 31$, $S = (R^4 - 2R^3 + R^2 - 4R) \bmod 31$, and $T = (S^4 - 2S^3 + S^2 - 4S) \bmod 31$. Find the number of integers $a$ with $0 \le a \le 38563$ such t... | 6,220 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(-2), Pow(Var("a"), Const(3))), Pow(Var("a"), Const(2)), Mul(Const(-4), Var("a"))), modulus=Const(31)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(-2), Pow(Ref("p1"), Const(3))), Pow(Ref("p1"),... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.081 | 2026-02-25T04:00:25.315939Z | {
"verified": true,
"answer": 6220,
"timestamp": "2026-02-25T04:00:25.397320Z"
} | a1c367 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 316,
"completion_tokens": 15130
},
"timestamp": "2026-03-29T03:40:35.544Z",
"answer": 5
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} |
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