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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
244527 | modular_modexp_compute_v1_1520064083_6971 | Let $a = 7$. Let $e$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14288400$. Let $m = 84100$. Compute the remainder when $a^e$ is divided by $m$. | 17,401 | graphs = [
Graph(
let={
"a": Const(7),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T08:28:13.915720Z | {
"verified": true,
"answer": 17401,
"timestamp": "2026-02-08T08:28:13.916615Z"
} | 559823 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 4203
},
"timestamp": "2026-02-13T20:50:49.039Z",
"answer": 17401
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7e7800 | nt_count_digit_sum_v1_1918700295_107 | Let $S$ be the set of all integers $t$ such that $15 \leq t \leq 93$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 5$, and $t = 9a + 6b$. Let $N$ be the number of elements in $S$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 89401$ and the sum of the de... | 4,983 | graphs = [
Graph(
let={
"upper": Const(89401),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"ONE_PHI_2"
] | 9858be | nt_count_digit_sum_v1 | null | 6 | 0 | [
"LIN_FORM",
"ONE_PHI_2"
] | 2 | 3.142 | 2026-02-08T03:00:21.365191Z | {
"verified": true,
"answer": 4983,
"timestamp": "2026-02-08T03:00:24.507656Z"
} | dbc885 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 5367
},
"timestamp": "2026-02-08T22:47:18.152Z",
"answer": 4983
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_P... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
9335c6_n | algebra_vieta_sum_v1_601307018_10499 | An architect designs a series of square tiles where the difference in area between two types is modeled by $32a^2 - 64ab + 32b^2 = 5408$ for dimensions $a \le b \le 30$. The number of valid tile pairs is $M$. Separately, a timing mechanism adjusts based on factor pairs of $43806$, minimizing the difference in their val... | 29,113 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(32), Pow... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/B3_DIFF"
] | 158001 | algebra_vieta_sum_v1 | null | 7 | null | [
"B3_DIFF",
"QF_PSD_ORBIT"
] | 2 | 0.011 | 2026-03-10T10:57:50.892638Z | null | 249a6d | 9335c6 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1025
},
"timestamp": "2026-04-23T14:38:36.886Z",
"answer": 29113
}
] | 2 | [
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
3c18b8 | sequence_lucas_compute_v1_48377204_1131 | Let $n = \sum_{k=1}^{6} k$. Define $L_n$ to be the $n$th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $21071 \cdot L_n$ is divided by $68795$. | 46,476 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"_c": Const(21071),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(68795)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T15:54:36.991236Z | {
"verified": true,
"answer": 46476,
"timestamp": "2026-02-08T15:54:36.992464Z"
} | b2f5d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1495
},
"timestamp": "2026-02-16T16:20:19.426Z",
"answer": 46476
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6ca97 | lin_form_endings_v1_798873815_198 | Let $ a = 9 $, $ b = 12 $, and $ k = 123 $. Let $ d = \gcd(a, b) $ and let $ e = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor $. Define $ x = (16932 \cdot e) \mod 51451 $. Compute $ x $. | 25,349 | graphs = [
Graph(
let={
"a_coeff": Const(9),
"b_coeff": Const(12),
"k_val": Const(123),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(16... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T02:31:08.168733Z | {
"verified": true,
"answer": 25349,
"timestamp": "2026-02-08T02:31:08.169060Z"
} | 7d4f48 | 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": 474
},
"timestamp": "2026-02-08T19:11:01.265Z",
"answer": 25349
},
{
"i... | 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_SUM",
"status": "no"
... | {
"lo": -3.81,
"mid": -1.88,
"hi": 0.06
} | ||
9a5e05 | comb_count_derangements_v1_898971024_389 | Let $m = 6$. Let $p$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = m$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i, j \leq 9$ such that $i + j = p$. Compute the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B1 | [
"B1/COUNT_SUM_EQUALS"
] | 2a6014 | comb_count_derangements_v1 | null | 5 | 0 | [
"B1",
"COUNT_SUM_EQUALS"
] | 2 | 0.017 | 2026-02-08T15:26:01.124809Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T15:26:01.141523Z"
} | e5bc2e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1506
},
"timestamp": "2026-02-24T20:50:46.161Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V8",
"st... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
9c3e76 | nt_num_divisors_compute_v1_784195855_8684 | Let $m = 3$. Define
$$
n_0 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $n$ be the largest prime number satisfying $2 \leq n \leq n_0$. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k"))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")),... | NT | null | COMPUTE | sympy | K2 | [
"K2/MAX_PRIME_BELOW"
] | f058da | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T16:16:43.293337Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:16:43.295466Z"
} | 20a513 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 433
},
"timestamp": "2026-02-16T07:13:20.994Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
f88d66 | comb_count_permutations_fixed_v1_717093673_1348 | Let $n$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $k = 5$. Define $$
result = \binom{n}{k} \cdot !(n - k),
$$ where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remainder when $20861 \cdot result$ is divided by $52080$. Comput... | 12,054 | graphs = [
Graph(
let={
"_n": Const(6),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T16:01:41.172539Z | {
"verified": true,
"answer": 12054,
"timestamp": "2026-02-08T16:01:41.175622Z"
} | 30506b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1068
},
"timestamp": "2026-02-24T19:29:35.064Z",
"answer": 12054
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
0f3526 | comb_binomial_compute_v1_1978505735_7032 | Let $m = 49$ and $n = 2$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $a$ be the minimum value in $T$.
Let $P$ be the set of all prime integers $n_1$ such that $2 \leq n_1 \leq 9$. Let $b$ be the maximum... | 3,432 | graphs = [
Graph(
let={
"_m": Const(49),
"_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")), Ref("_m")))), expr=Su... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T20:01:38.512474Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T20:01:38.515024Z"
} | 5ecc05 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 401
},
"timestamp": "2026-02-16T18:47:24.040Z",
"answer": 3432
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
0872bc | v7_endings_v1_168721529_295 | Let $n = 2969$. Compute the remainder when the sum of all nonnegative integers $k \leq n$ for which $\binom{n}{k}$ is odd is divided by $100000$. | 90,016 | graphs = [
Graph(
let={
"_n": Const(2969),
"_inner_result": SumOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Ref("_n")), Not(Divides(divisor=Const(2), dividend=Binom(n=Const(2969), k=Var("k"))))))),
"_mod_M": Const(100000),
... | NT | COMB | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.002 | 2026-02-08T12:56:56.714169Z | {
"verified": true,
"answer": 90016,
"timestamp": "2026-02-08T12:56:56.716314Z"
} | a1b3da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 991
},
"timestamp": "2026-02-09T03:23:23.169Z",
"answer": 90016
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
4f8c80 | comb_factorial_compute_v1_124444284_5003 | Let $h = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $f = \sum_{k=0}^{9} (-1)^k \binom{9}{k}$. Let $s$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 8$, $1 \leq j \leq 9$, and $i + j = 10$. Define $n = s \cdot h + f$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(10),
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(9),
"f": Summation(var="k", start=Const(0), end=Ref("n1... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_factorial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T06:20:38.011227Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T06:20:38.022883Z"
} | 303e06 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 596
},
"timestamp": "2026-02-24T06:02:12.947Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lem... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
4cf1d9 | geo_count_lattice_rect_v1_1353956133_177 | Let $a = 55$ and $b = 26$. Define the rectangle $R$ as the set of all lattice points $(x, y)$ such that $0 \le x \le a$ and $0 \le y \le b$. Compute the number of lattice points in $R$. | 1,512 | graphs = [
Graph(
let={
"a": Const(55),
"b": Const(26),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T11:20:20.366857Z | {
"verified": true,
"answer": 1512,
"timestamp": "2026-02-08T11:20:20.369361Z"
} | 7520fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 285
},
"timestamp": "2026-02-24T13:21:09.654Z",
"answer": 1512
},
{
"id... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
497cd0_l | nt_min_coprime_above_v1_1520064083_1895 | Let $S$ be the set of all integers $t$ such that $9 \leq t \leq 315$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 55$, $1 \leq b \leq 19$, and $t = 4a + 5b$. Let $m$ be the number of elements in $S$. Determine the value of the smallest integer $n$ such that $12544 < n \leq 12849$ and $\gcd(n, m) = ... | 12,545 | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.05 | 2026-02-08T04:21:40.609973Z | {
"verified": false,
"answer": 12546,
"timestamp": "2026-02-08T04:21:40.659587Z"
} | e05590 | 497cd0 | legacy_text | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 4387
},
"timestamp": "2026-02-10T16:21:04.318Z",
"answer": 12545
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | |
ab6ccf | algebra_quadratic_discriminant_v1_655260480_3479 | Let $m = 2695$. Let $d$ be the smallest divisor of $m$ that is at least $2$. Let $a$ be the largest prime number $n$ such that $2 \leq n \leq d$. Let $b = 5$ and $c = -5$. Compute $b^2 - 4ac$. | 125 | graphs = [
Graph(
let={
"_m": Const(2695),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Va... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.026 | 2026-02-08T17:24:00.137153Z | {
"verified": true,
"answer": 125,
"timestamp": "2026-02-08T17:24:00.163522Z"
} | 6312d6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 409
},
"timestamp": "2026-02-16T09:41:51.774Z",
"answer": 125
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "PO... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
10f69a | antilemma_k2_v1_1918700295_740 | Compute
$$
\sum_{k=1}^{371} \phi(k) \left\lfloor \frac{371}{k} \right\rfloor + \left( 2^{\left( \sum_{k=1}^{371} \phi(k) \left\lfloor \frac{371}{k} \right\rfloor \right) \bmod 15} \bmod 58059 \right).
$$ | 69,070 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(371), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(371), Var("k"))))),
"Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(15))), modulus=Const(58059))),
},
goal=Ref("... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T03:24:26.135307Z | {
"verified": true,
"answer": 69070,
"timestamp": "2026-02-08T03:24:26.135721Z"
} | a325e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 529
},
"timestamp": "2026-02-10T14:14:34.783Z",
"answer": 69070
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
d57f9d | nt_count_intersection_v1_1116507919_412 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $s$ be the minimum value of $x + y$ over all such pairs in $P$. Let $N$ be the largest positive integer $d$ such that $d \le s$ and $d$ divides $25015000$. Let $a = 11$ and $b = 10$. Let $T$ be the set of all positive in... | 183 | graphs = [
Graph(
let={
"N": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), 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(... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | nt_count_intersection_v1 | null | 5 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.152 | 2026-02-08T02:34:00.572825Z | {
"verified": true,
"answer": 183,
"timestamp": "2026-02-08T02:34:00.724970Z"
} | ced260 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 4289
},
"timestamp": "2026-02-09T17:19:34.267Z",
"answer": 183
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"... | {
"lo": -4.58,
"mid": 0.57,
"hi": 5.69
} | ||
a100d4 | nt_max_prime_below_v1_1915831931_258 | Let $n$ be a positive integer. Consider the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 54$, and $\gcd(p, q) = 1$. Let $L$ be the number of elements in this set. Determine the value of $Q$, where $Q$ is the remainder when $44121 \cdot r$ is divided by $69572$, and ... | 36,035 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(47089),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.168 | 2026-02-08T15:17:13.394089Z | {
"verified": true,
"answer": 36035,
"timestamp": "2026-02-08T15:17:14.562577Z"
} | 451197 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 2581
},
"timestamp": "2026-02-16T04:09:20.543Z",
"answer": 36035
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5364ad | algebra_poly_eval_v1_153355830_1922 | Let $k = 11$. Let $S$ be the set of all integers $t$ such that $28 \leq t \leq 1463$ and there exist positive integers $a \leq 196$ and $b \leq 15$ for which $t = 7a + 5b + 16$. Compute the value of
$$
\frac{4k^5 - 46k^4 - 760k^3 + |S| \cdot k^2 + 3880k - 2400}{-378}.
$$ | 2,195 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(11),
"result": Div(Sum(Mul(Const(4), Pow(Ref("k"), Const(5))), Mul(Const(-46), Pow(Ref("k"), Const(4))), Mul(Const(-760), Pow(Ref("k"), Const(3))), Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T06:47:33.631213Z | {
"verified": true,
"answer": 2195,
"timestamp": "2026-02-08T06:47:33.634116Z"
} | 6f010b | 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": 6289
},
"timestamp": "2026-02-13T04:38:14.259Z",
"answer": 2195
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
38618c | comb_count_derangements_v1_124444284_10372 | Let $p$ and $q$ be positive integers such that $pq = 132300$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such integers $p$. Define $Q$ to be the remainder when $49229 \cdot !n$ is divided by $61334$, where $!n$ denotes the number of derangements of $n$ elements. Compute $Q$. | 32,487 | 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=132300)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T13:01:46.878624Z | {
"verified": true,
"answer": 32487,
"timestamp": "2026-02-08T13:01:46.880004Z"
} | 6ea300 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1951
},
"timestamp": "2026-02-15T09:03:51.783Z",
"answer": 32487
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f5bd9a | nt_lcm_compute_v1_1080341949_282 | Let $a = 1258$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 2088025$. Compute $\operatorname{lcm}(a, b)$. Then, find the remainder when $12949$ times this least common multiple is divided by $65552$. | 47,226 | graphs = [
Graph(
let={
"a": Const(1258),
"b": 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(2088025)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:24:06.246974Z | {
"verified": true,
"answer": 47226,
"timestamp": "2026-02-08T13:24:06.250423Z"
} | ccc300 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 2606
},
"timestamp": "2026-02-15T14:47:54.085Z",
"answer": 47226
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
73734c | nt_count_divisible_v1_1526740231_37 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 63001$ and $n$ is divisible by $5$. Let $B$ be the smallest divisor of $1859$ that is at least $2$. Let $C$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 158$. Compute the remainder when $A^2 + B \cdot... | 41,837 | graphs = [
Graph(
let={
"_n": Const(158),
"upper": Const(63001),
"divisor": Const(5),
"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")), Cons... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B1"
] | 2f1a67 | nt_count_divisible_v1 | quadratic_mod | 5 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 4.012 | 2026-02-08T11:18:55.774245Z | {
"verified": true,
"answer": 41837,
"timestamp": "2026-02-08T11:18:59.785900Z"
} | ad05b2 | 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": 744
},
"timestamp": "2026-02-14T11:54:22.634Z",
"answer": 41837
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c299f7 | modular_modexp_compute_v1_784195855_570 | Let $n$ be an integer satisfying $2 \leq n \leq S$, where $S$ is the sum of all real solutions $x$ to the equation $x^2 - 17x - 138 = 0$. Suppose $n$ is prime. Let $a$ be the largest such prime $n$.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4380649$. Let $e$ be the minimum v... | 59,053 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-17), Var("x")), Const(-138)), Const(0))))), IsPr... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/MAX_PRIME_BELOW",
"B3"
] | da76e0 | modular_modexp_compute_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T04:28:14.478558Z | {
"verified": true,
"answer": 59053,
"timestamp": "2026-02-08T04:28:14.480935Z"
} | 782713 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 4729
},
"timestamp": "2026-02-10T16:51:01.155Z",
"answer": 59053
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
20ef0e | nt_lcm_compute_v1_151522320_376 | Let $a$ be the largest positive divisor of $7466484$ that does not exceed $2724$. Let $b = 2976$. Compute the remainder when $\operatorname{lcm}(a, b)$ is divided by $94380$. | 14,892 | graphs = [
Graph(
let={
"_n": Const(2724),
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(7466484))))),
"b": Const(2976),
"result": LCM(a=Ref("a"), b=Ref(... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_lcm_compute_v1 | null | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T03:12:42.371700Z | {
"verified": true,
"answer": 14892,
"timestamp": "2026-02-08T03:12:42.372907Z"
} | f8b474 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 7685
},
"timestamp": "2026-02-09T01:59:19.413Z",
"answer": 2976
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
1dd3df | antilemma_k2_v1_1915831931_1061 | Let $m = 73$ and $n = 44121$. Let $x = \sum_{k=1}^{73} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid \left( \sum_{d_1 \mid m} \phi(d_1) \right)} \phi(d) \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the remainder when $n \cdot x$ is divided by $70109$. | 55,630 | graphs = [
Graph(
let={
"_m": Const(73),
"_n": Const(44121),
"x": Summation(var="k", start=Const(1), end=Const(73), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=SumOverDivisors(n=Ref(name='_m'), var='d1', expr=EulerPhi(n=Var(name='d1'))), var='d', expr=Euler... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3/K2",
"K2"
] | d92398 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.003 | 2026-02-08T15:51:39.800424Z | {
"verified": true,
"answer": 55630,
"timestamp": "2026-02-08T15:51:39.802965Z"
} | 28780d | 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": 1849
},
"timestamp": "2026-02-16T14:30:15.516Z",
"answer": 55630
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
03471b | lin_form_endings_v1_865884756_4365 | Let $a = 6$, $b = 10$, $A = 44$, and $B = 29$. Let $g = \gcd(a, b)$. Define $$
N = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.
$$ Let $x$ be the remainder when $6763 \cdot N$ is divided by 90607. Compute $x$. | 13,870 | graphs = [
Graph(
let={
"a_coeff": Const(6),
"b_coeff": Const(10),
"A_val": Const(44),
"B_val": Const(29),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), Re... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:54:33.675609Z | {
"verified": true,
"answer": 13870,
"timestamp": "2026-02-08T17:54:33.677050Z"
} | 07f856 | 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": 705
},
"timestamp": "2026-02-18T09:42:53.440Z",
"answer": 13870
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5dcdcf | lte_diff_endings_v1_1125832087_42 | Let $a = 17$, $b = 7$, $n = 60$, $m = 75$, and $p = 5$. Define $G = \gcd(a^n - b^n, a^m - b^m)$. Let $k$ be the largest integer such that $p^k$ divides $G$. Compute the remainder when $17260k$ is divided by $83969$. | 34,520 | graphs = [
Graph(
let={
"a_val": Const(17),
"b_val": Const(7),
"n_val": Const(60),
"m_val": Const(75),
"p_val": Const(5),
"a_pow_n": Pow(Ref("a_val"), Ref("n_val")),
"b_pow_n": Pow(Ref("b_val"), Ref("n_val")),
"d... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 7 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:50:48.164059Z | {
"verified": true,
"answer": 34520,
"timestamp": "2026-02-08T02:50:48.164722Z"
} | a80ada | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 871
},
"timestamp": "2026-02-17T14:50:54.324Z",
"answer": 17260
}
] | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
f6e699 | diophantine_fbi2_min_v1_1431428450_186 | Let $k = 27$ and let $\text{upper} = 37$. Consider the set of all integers $d$ such that $d \geq 2$, $d \leq 37$, $d$ divides $k$, and $\frac{k}{d} \geq m$, where $m$ is the minimum value of the set of all integers $d'$ such that $d' \geq 2$ and $d'$ divides 245. Determine the value of the smallest such $d$. | 3 | graphs = [
Graph(
let={
"k": Const(27),
"upper": Const(37),
"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")), MinOverSet(set=So... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.129 | 2026-02-08T13:17:21.509262Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T13:17:21.638633Z"
} | 4583fa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 581
},
"timestamp": "2026-02-16T04:30:09.080Z",
"answer": 3
},
{
"id": 11,
"... | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
0167e7 | lin_form_endings_v1_1918700295_3781 | Let $a = 6$ and $b = 4$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 27$ and $B = 43$. Compute the value of $x$, where $x$ is the remainder when $9347 \cdot (a' A + b' B - a' b')$ is divided by $7... | 48,127 | graphs = [
Graph(
let={
"a_coeff": Const(6),
"b_coeff": Const(4),
"A_val": Const(27),
"B_val": Const(43),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": Fl... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:55:56.255051Z | {
"verified": true,
"answer": 48127,
"timestamp": "2026-02-08T08:55:56.256060Z"
} | 0bb667 | 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": 552
},
"timestamp": "2026-02-13T22:43:55.106Z",
"answer": 48127
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b3d56d | nt_sum_over_divisible_v1_717093673_4148 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 174$. Let $M$ be the maximum value of $xy$ over all such pairs. Let $R$ be the sum of all positive integers $n$ such that $n \leq M$ and $n$ is divisible by $193$. Compute the remainder when $16129 - R$ is divided by $98953$. | 63,495 | graphs = [
Graph(
let={
"_n": Const(98953),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(174)))), expr=Mul(Var("x"), Var("y")... | NT | null | SUM | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"B1"
] | 1 | 2.931 | 2026-02-08T18:03:47.590057Z | {
"verified": true,
"answer": 63495,
"timestamp": "2026-02-08T18:03:50.520995Z"
} | 0b24df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1621
},
"timestamp": "2026-02-18T13:28:42.533Z",
"answer": 63495
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c8dced | diophantine_fbi2_count_v1_124444284_279 | Let $p_1 = 5$, and let $h$ be the remainder when $(4! + 1)$ is divided by $p_1$. Let $p = 7$ and $q = 71$, and define $n = p^2 \cdot q$. Let $t = (\mu(n))^2$, where $\mu$ denotes the M\"obius function. Let $k = 360 + h + t$. Let $S$ be the set of all integers $d$ such that $3 \leq d \leq 692$, $d$ divides $k$, and $5 \... | 29,323 | graphs = [
Graph(
let={
"p1": Const(5),
"h": Mod(value=Sum(Factorial(Sub(Ref("p1"), Const(1))), Const(1)), modulus=Ref("p1")),
"p": Const(7),
"q": Const(71),
"n": Mul(Pow(Ref("p"), Const(2)), Ref("q")),
"t": Pow(MoebiusMu(n=Ref(name='n'... | NT | null | COUNT | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE",
"WILSON",
"C5"
] | de8042 | diophantine_fbi2_count_v1 | null | 5 | 2 | [
"C5",
"MOBIUS_SQUAREFREE",
"WILSON"
] | 3 | 0.008 | 2026-02-08T03:08:41.124733Z | {
"verified": true,
"answer": 29323,
"timestamp": "2026-02-08T03:08:41.133096Z"
} | 249b6f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 308,
"completion_tokens": 7559
},
"timestamp": "2026-02-09T15:37:13.903Z",
"answer": 29323
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
79e6c7 | antilemma_cartesian_v1_1520064083_4050 | Compute the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 13$ and $1 \leq b \leq 33$. | 429 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Const(33)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T06:02:55.340516Z | {
"verified": true,
"answer": 429,
"timestamp": "2026-02-08T06:02:55.341032Z"
} | 6668ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 214
},
"timestamp": "2026-02-24T05:18:24.954Z",
"answer": 429
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
6bf289 | antilemma_k3_v1_865884756_209 | Compute the sum $$\sum_{d \mid 75002} \phi(d),$$ where $\phi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $75002$. | 75,002 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=75002), 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 | 2026-02-08T15:15:56.697707Z | {
"verified": true,
"answer": 75002,
"timestamp": "2026-02-08T15:15:56.698198Z"
} | 51ae20 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 2224
},
"timestamp": "2026-02-10T05:36:07.056Z",
"answer": 75002
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
a3eacc | comb_count_partitions_v1_124444284_246 | Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 415$ and $t = 3a + 5b$ for some positive integers $a \leq 85$ and $b \leq 32$. Let $n$ be the number of elements in $T$. Now consider the set of all pairs of positive integers $(x, y)$ such that $xy = n$. Let $s = x + y$ range over all such pairs. Determin... | 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=85)), Geq(left=Var(name='b'), right=Const(value... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | comb_count_partitions_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T03:06:13.307527Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T03:06:13.309263Z"
} | 682943 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 26947
},
"timestamp": "2026-02-23T21:49:52.905Z",
"answer": 37338
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
e12c3b | comb_count_surjections_v1_124444284_10236 | Let $n$ be the number of ordered pairs $(a,b)$ where $a$ and $b$ are integers with $1 \leq a \leq 2$ and $1 \leq b \leq 2$. Let $k = 2$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Let $c = 60631$. Compute the remainder when $c \cdot \text{result}$ is divide... | 26,978 | graphs = [
Graph(
let={
"_n": Const(58704),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(2)))),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'),... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T12:54:30.576179Z | {
"verified": true,
"answer": 26978,
"timestamp": "2026-02-08T12:54:30.577458Z"
} | c1e659 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1240
},
"timestamp": "2026-02-24T16:46:38.750Z",
"answer": 26978
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
8187e2 | comb_count_partitions_v1_1520064083_8031 | Let $n = 41$. Define $\sigma(n)$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Let $p(\sigma(n))$ denote the number of integer partitions of $\sigma(n)$. Compute $p(\sigma(n))$. | 44,583 | graphs = [
Graph(
let={
"_n": Const(41),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | K3 | [
"K3"
] | 54c41e | comb_count_partitions_v1 | null | 7 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T09:29:40.282904Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T09:29:40.283757Z"
} | 731abb | 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": 544
},
"timestamp": "2026-02-14T05:58:27.076Z",
"answer": 44583
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7277ee | nt_count_coprime_v1_153355830_2309 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 50$. Define $P$ to be the maximum value of $xy$ over all pairs in $S$. Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = P$. Define $k$ to be the minimum value of $x + y$ over all pairs in $T$. Let... | 35,284 | 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(50)))), expr=Mul(Var("x"), Var("y")))),
"upper": Const(8820... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_coprime_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 7.812 | 2026-02-08T07:02:54.238885Z | {
"verified": true,
"answer": 35284,
"timestamp": "2026-02-08T07:03:02.050432Z"
} | 6294da | 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": 1225
},
"timestamp": "2026-02-13T07:27:14.926Z",
"answer": 35284
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8607b4 | comb_factorial_compute_v1_1419126231_1472 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 35$ such that $25b^2 + 9a^2 + 30ab = 20449$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(9),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Eq(Sum(Mul(Const(25), Pow(Var("b"), Const(2))), Mul... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_factorial_compute_v1 | null | 4 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-02-25T10:56:06.713687Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T10:56:06.715228Z"
} | ef9978 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 904
},
"timestamp": "2026-03-30T12:41:31.263Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
4afa90 | sequence_count_fib_divisible_v1_1915831931_3671 | Let $ d $ be the number of positive integers $ j $ such that $ 1 \le j \le 13 $ and $ j^3 \le 2197 $. Determine the number of positive integers $ n $ such that $ 1 \le n \le 835 $ and $ d $ divides the $ n $-th Fibonacci number. | 119 | graphs = [
Graph(
let={
"upper": Const(835),
"d": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(13)), Leq(Pow(Var("j"), Const(3)), Const(2197))), domain='positive_integers')),
"result": CountOverSet(set=SolutionsSet... | NT | null | COUNT | sympy | K13 | [
"C3"
] | 8a214c | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"C3",
"K13"
] | 2 | 0.056 | 2026-02-08T17:48:14.360631Z | {
"verified": true,
"answer": 119,
"timestamp": "2026-02-08T17:48:14.416843Z"
} | 74569d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 2096
},
"timestamp": "2026-02-18T08:07:44.598Z",
"answer": 119
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
60557b | comb_factorial_compute_v1_1470522791_4 | Let $n_2$ be the number of ordered pairs $(i,j)$ of positive integers such that $i+j=6$, $1 \leq i \leq 4$, and $1 \leq j \leq 5$. Let
$$
e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 0$ and
$$
c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Define $n = 7 + e$. Compute the remainder when $44121 \cdot c \cdot... | 11,710 | graphs = [
Graph(
let={
"_n": Const(7),
"n2": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | a56205 | comb_factorial_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ZERO_BINOM_0"
] | 3 | 0.063 | 2026-02-08T12:47:17.165473Z | {
"verified": true,
"answer": 11710,
"timestamp": "2026-02-08T12:47:17.228779Z"
} | 53316c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 1687
},
"timestamp": "2026-02-24T16:19:40.056Z",
"answer": 11710
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lem... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
5c1f00 | nt_count_digit_sum_v1_2051736721_4246 | Let $n = 9999$. Let $\text{upper}$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $\text{result}$ be the number of positive integers $n$ with $1 \le n \le \text{upper}$ such that the sum of the decimal digits of $n$ is $14$. Determine the value of $\tex... | 540 | graphs = [
Graph(
let={
"_n": Const(9999),
"upper": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"target_sum": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), ... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_digit_sum_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.366 | 2026-02-08T17:51:07.693724Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T17:51:08.060006Z"
} | 341f22 | 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": 1161
},
"timestamp": "2026-02-18T08:36:10.889Z",
"answer": 540
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ae102e | nt_count_primes_v1_809748730_504 | Let $p$ be a positive integer. Suppose there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of such integers $p$. Let $S$ be the set of all prime numbers $n$ such that $L \leq n \leq 16384$. Determine the number of elements in $S$. | 1,900 | graphs = [
Graph(
let={
"upper": Const(16384),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.382 | 2026-02-08T11:33:12.806407Z | {
"verified": true,
"answer": 1900,
"timestamp": "2026-02-08T11:33:13.187917Z"
} | 12df9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1482
},
"timestamp": "2026-02-14T15:39:03.432Z",
"answer": 1900
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
aab443 | nt_count_coprime_and_v1_53965629_18 | Let $u = 5517$, $k_1 = 4$, and $k_2 = 9$. Let $r$ be the number of positive integers $n$ such that $1 \leq n \leq u$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. Let $s = \sum_{i=d}^{\lfloor \log_{10} |r| \rfloor} d_i(i+1)^2$, where $d_i$ is the $i$-th decimal digit of $|r|$ (starting from the units digit as the 0-th d... | 138 | graphs = [
Graph(
let={
"upper": Const(5517),
"k1": Const(4),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq(GCD(a=Var("n"... | COMB | NT | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.54 | 2026-02-08T11:12:53.015175Z | {
"verified": true,
"answer": 138,
"timestamp": "2026-02-08T11:12:53.555494Z"
} | 7b8897 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 291,
"completion_tokens": 854
},
"timestamp": "2026-02-09T10:56:02.091Z",
"answer": 138
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "C... | {
"lo": -5.15,
"mid": -0.06,
"hi": 5.13
} | ||
80a475 | alg_poly_orbit_hensel_v1_1218484723_303 | For a non-negative integer $a$, define the sequence $N = (a^3 + 2a) \bmod 961$, $M = (N^3 + 2N) \bmod 961$, $R = (M^3 + 2M) \bmod 961$, $S = (R^3 + 2R) \bmod 961$, $T = (S^3 + 2S) \bmod 961$. Find the number of integers $a$ with $0 \le a \le 1388644$ such that $T = a$ but $N \ne a$, $M \ne a$, $R \ne a$, and $S \ne a$. | 43,350 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(2), Var("a"))), modulus=Const(961)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(2), Ref("p1"))), modulus=Const(961)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(2), Re... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.034 | 2026-02-25T02:01:48.337289Z | {
"verified": true,
"answer": 43350,
"timestamp": "2026-02-25T02:01:48.371481Z"
} | f64bcb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 7780
},
"timestamp": "2026-03-10T09:30:22.281Z",
"answer": 43350
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
7ce60e | nt_count_divisible_and_v1_1742523217_208 | Find the number of positive integers $n \leq 12996$ such that $n$ is divisible by 6 and the remainder when $n$ is divided by 9 equals $$\sum_{k=0}^{6} (-1)^k \binom{6}{k}.$$ Express your answer as a single integer. | 722 | graphs = [
Graph(
let={
"upper": Const(12996),
"d1": Const(6),
"d2": Const(9),
"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("d1")), Const(0)), Eq(Mo... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.456 | 2026-02-08T02:55:58.976207Z | {
"verified": true,
"answer": 722,
"timestamp": "2026-02-08T02:55:59.432614Z"
} | fdace6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 563
},
"timestamp": "2026-02-09T14:45:21.400Z",
"answer": 722
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"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"
},
{
... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
66788a | sequence_lucas_compute_v1_1520064083_2922 | Let $m = 88691$. Define $S$ as the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$.
Now, let $T$ be the set of all positive divisors $d$ of 190969 such that $d \geq k$. Define $n$ to be the sma... | 74,079 | graphs = [
Graph(
let={
"_m": Const(88691),
"_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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T05:19:13.512993Z | {
"verified": true,
"answer": 74079,
"timestamp": "2026-02-08T05:19:13.516418Z"
} | be308f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 2887
},
"timestamp": "2026-02-12T07:06:11.520Z",
"answer": 74079
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ecbc76 | nt_max_prime_below_v1_1915831931_3399 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Let $t$ be the number of elements in $A$. Find the largest prime number $n$ such that $t \le n \le 17424$. | 17,419 | graphs = [
Graph(
let={
"upper": Const(17424),
"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 | 0.419 | 2026-02-08T17:37:59.363459Z | {
"verified": true,
"answer": 17419,
"timestamp": "2026-02-08T17:37:59.782086Z"
} | 03c6f3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 546
},
"timestamp": "2026-02-16T11:27:58.879Z",
"answer": 5
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
57db49 | antilemma_k3_v1_971394319_1477 | Let $x = \sum_{d \mid 60851} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $20021 \cdot x$ is divided by $98490$. | 75,061 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=60851), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(20021),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(98490)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:42:25.890961Z | {
"verified": true,
"answer": 75061,
"timestamp": "2026-02-08T13:42:25.891690Z"
} | 87ae61 | 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": 2520
},
"timestamp": "2026-02-15T19:41:39.304Z",
"answer": 75061
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b8de80 | modular_sum_quadratic_residues_v1_1440796553_886 | Let $m = 4$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 42849$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $p$ be the largest prime number less than or equal to $n$. Compute $\frac{p(p-1)}{m}$. | 41,718 | graphs = [
Graph(
let={
"_m": Const(4),
"_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(42849)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | C5 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"B3",
"C5",
"MAX_PRIME_BELOW"
] | 3 | 0.005 | 2026-02-08T12:02:11.243699Z | {
"verified": true,
"answer": 41718,
"timestamp": "2026-02-08T12:02:11.248522Z"
} | c3951d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1081
},
"timestamp": "2026-02-14T21:51:24.161Z",
"answer": 41718
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f46061 | nt_lcm_compute_v1_865884756_1434 | Let $a$ be the number of integers $t$ with $5 \leq t \leq 2661$ for which there exist positive integers $a'$ and $b'$ such that $t = 3a' + 2b'$, $1 \leq a' \leq 487$, and $1 \leq b' \leq 600$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 348100$. Compute $... | 10,620 | graphs = [
Graph(
let={
"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=487)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T16:04:16.017428Z | {
"verified": true,
"answer": 10620,
"timestamp": "2026-02-08T16:04:16.021756Z"
} | 13e41e | 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": 4169
},
"timestamp": "2026-02-16T20:06:38.833Z",
"answer": 10620
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c251a | antilemma_k2_v1_717093673_3324 | Let $n = 180$. Compute $$ \sum_{k=1}^{\sum_{d \mid 180} \phi(d)} \phi(k) \left\lfloor \frac{180}{k} \right\rfloor, $$ where the inner sum is over all positive divisors $d$ of $180$, and $\phi$ denotes Euler's totient function. | 16,290 | graphs = [
Graph(
let={
"_n": Const(180),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=180), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T17:29:41.406077Z | {
"verified": true,
"answer": 16290,
"timestamp": "2026-02-08T17:29:41.408943Z"
} | d338e7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 519
},
"timestamp": "2026-02-18T03:50:23.256Z",
"answer": 16290
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
19d916 | comb_sum_binomial_row_v1_1742523217_5573 | Let $n$ be the largest prime number less than or equal to $12$. Compute the remainder when $44121 \cdot 2^n$ is divided by $55144$. | 33,936 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"result": Pow(Ref("_n"), Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), m... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T11:04:53.593269Z | {
"verified": true,
"answer": 33936,
"timestamp": "2026-02-08T11:04:53.594132Z"
} | 670846 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 2587
},
"timestamp": "2026-02-14T10:20:17.799Z",
"answer": 33936
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2090aa | alg_telescope_v1_1218484723_2376 | Let $A$ be the number of integers $t$ for which there exist integers $a, b$ with $1 \le a \le 232$, $1 \le b \le 218$, such that $t = 10a + 6b$ and $16 \le t \le 3628$. Let $B$ be the number of pairs $(a, b)$ of integers with $1 \le a \le 35$, $1 \le b \le 35$, $a \le b$, and $$2a^{2} + 2b^{2} - 4ab = 2178.$$ Define $$... | 49,876 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=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'), ri... | ALG | null | COMPUTE | sympy | HALFPLANE_COUNT | [
"QF_PSD_ORBIT",
"LIN_FORM",
"B3"
] | 057f4c | alg_telescope_v1 | null | 7 | 0 | [
"B3",
"HALFPLANE_COUNT",
"LIN_FORM",
"QF_PSD_ORBIT"
] | 4 | 0.226 | 2026-02-25T04:11:21.156557Z | {
"verified": true,
"answer": 49876,
"timestamp": "2026-02-25T04:11:21.382595Z"
} | 726922 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 318,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T04:26:46.874Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
8f9f7f | modular_sum_quadratic_residues_v1_784195855_7522 | Let $p$ be the largest prime number less than or equal to 569. Compute the remainder when $\frac{p(p-1)}{4}$ is multiplied by 44121 and then divided by 86323. | 7,627 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(44121),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(569)), IsPr... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T09:22:26.508752Z | {
"verified": true,
"answer": 7627,
"timestamp": "2026-02-08T09:22:26.511433Z"
} | d6697f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 2079
},
"timestamp": "2026-02-14T03:27:59.249Z",
"answer": 7627
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cd154e | diophantine_fbi2_min_v1_2051736721_2239 | Let $m = 875$. Let $n$ be the smallest divisor of $m$ that is at least $2$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 8$, and let $k$ be the maximum value of $xy$ over all such pairs. Determine the value of the smallest integer $d$ such that $n \leq d \leq 26$, $d$ divides ... | 8 | graphs = [
Graph(
let={
"_m": Const(875),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"k": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), con... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/B1"
] | 2a25ab | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.009 | 2026-02-08T16:32:47.270472Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T16:32:47.279562Z"
} | 6fb10c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 241
},
"timestamp": "2026-02-16T07:29:58.192Z",
"answer": 8
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
3dc794 | alg_sum_powers_v1_1419126231_1845 | Find the remainder when $\sum_{k=1}^{1083} k^{3}$ is divided by $\left|\left\{ k1 : k1 \geq 1,\, k1 \leq 3363200,\, 400 \mid k1 \right\}\right|$. | 5,524 | graphs = [
Graph(
let={
"_n": Const(1083),
"result": Mod(value=Summation(var="k", start=Const(1), end=Ref("_n"), expr=Pow(Var("k"), Const(3))), modulus=CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k1"), Const(1)), Leq(Var("k1"), Const(3363200)), Divides(divisor... | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | alg_sum_powers_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.05 | 2026-02-25T11:24:13.370265Z | {
"verified": true,
"answer": 5524,
"timestamp": "2026-02-25T11:24:13.419924Z"
} | 026ac3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 2054
},
"timestamp": "2026-03-30T14:18:34.236Z",
"answer": 5524
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
05b1bc | alg_qf_psd_sum_v1_1218484723_6572 | Let $B = \left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 30,\ 13a_1^2 - 2a_1b_1 + 2b_1^2 \leq 1602 \right\}\right|$. Compute the remainder when
$$
\sum_{\substack{a=1}}^{266} \sum_{b=1}^{B} (13a^2 - 12ab + 9b^2)
$$
is divided by $52810$. | 41,600 | graphs = [
Graph(
let={
"_n": Const(1602),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(266)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(v... | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_sum_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ",
"SUM_GEOM"
] | 2 | 0.532 | 2026-02-25T08:07:25.188388Z | {
"verified": true,
"answer": 41600,
"timestamp": "2026-02-25T08:07:25.720786Z"
} | cd2b39 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 12610
},
"timestamp": "2026-03-30T02:15:15.702Z",
"answer": 41600
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
fb8f0e | sequence_lucas_compute_v1_655260480_4184 | Let $ n $ be the number of integers $ t $ with $ 8 \leq t \leq 38 $ such that there exist integers $ a $ and $ b $ satisfying $ 1 \leq a \leq 4 $, $ 1 \leq b \leq 6 $, and $ t = 5a + 3b $. Define $ L_n $ to be the $ n $-th Lucas number. Compute $ L_n + \phi(|L_n| + 1) + \tau(|L_n| + 1) $, where $ \phi $ denotes Euler's... | 81,035 | 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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T17:47:19.957433Z | {
"verified": true,
"answer": 81035,
"timestamp": "2026-02-08T17:47:19.961058Z"
} | 2a2d63 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 2464
},
"timestamp": "2026-02-18T07:50:37.306Z",
"answer": 81035
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
36d4e5 | nt_count_coprime_v1_124444284_8742 | Let $k = \sum_{i=1}^{9} i$. Determine the number of positive integers $n \le 65536$ such that $\gcd(n, k) = 1$. Compute this number. | 34,953 | graphs = [
Graph(
let={
"upper": Const(65536),
"k": Summation(var="k", start=Const(1), end=Const(9), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), C... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_coprime_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 7.079 | 2026-02-08T11:53:16.619601Z | {
"verified": true,
"answer": 34953,
"timestamp": "2026-02-08T11:53:23.698172Z"
} | 8c8737 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 1559
},
"timestamp": "2026-02-14T20:15:57.827Z",
"answer": 34953
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5816fc | nt_count_intersection_v1_798873815_147 | Let $N = 100000$ and $a = 11$. Let $b$ be the number of integers $t$ with $7 \leq t \leq 24$ such that there exist integers $a'$ and $b'$ satisfying $1 \leq a' \leq 2$, $1 \leq b' \leq 7$, and $t = 5a' + 2b'$. Determine the number of positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. | 3,896 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(11),
"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=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 2.992 | 2026-02-08T02:29:37.238193Z | {
"verified": true,
"answer": 3896,
"timestamp": "2026-02-08T02:29:40.230105Z"
} | 56996e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1485
},
"timestamp": "2026-02-08T19:04:37.051Z",
"answer": 3896
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -1.85,
"mid": 0.05,
"hi": 1.74
} | ||
af7fb3 | nt_count_gcd_equals_v1_865884756_1637 | Let $A$ be the set of all positive integers $t$ such that $21 \leq t \leq 624$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 94$, and $t = 15a + 6b$. Let $B$ be the set of all positive integers $t_1$ such that $14 \leq t_1 \leq 56$ and there exist positive integers $a$ and $b$ wit... | 553 | graphs = [
Graph(
let={
"upper": Const(10946),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 1.125 | 2026-02-08T16:12:07.596528Z | {
"verified": true,
"answer": 553,
"timestamp": "2026-02-08T16:12:08.721782Z"
} | 0444dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 2841
},
"timestamp": "2026-02-16T23:05:25.546Z",
"answer": 553
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5136b2 | nt_count_phi_equals_v1_1742523217_4254 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 76$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $M$ be the maximum value in $P$.
Let $r$ be the number of positive integers $n \leq M$ such that $\phi(n) = 378$, where $\phi$ denotes Euler's totient function... | 2 | graphs = [
Graph(
let={
"_n": Const(76),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_phi_equals_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.301 | 2026-02-08T07:09:00.010859Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T07:09:00.312224Z"
} | 3be73c | 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": 6839
},
"timestamp": "2026-02-13T08:11:41.598Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b1e5c1 | antilemma_sum_equals_v1_349078426_1700 | Let $n$ be the number of ordered pairs $(i, j)$ where $i$ and $j$ are integers with $1 \leq i \leq 7$ and $1 \leq j \leq 7$. Determine the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1 \leq i \leq 47$, $1 \leq j \leq 47$. Compute this value. | 46 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(7)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.12 | 2026-02-08T13:51:14.570364Z | {
"verified": true,
"answer": 46,
"timestamp": "2026-02-08T13:51:14.690128Z"
} | cc51cd | 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": 861
},
"timestamp": "2026-02-24T19:06:52.606Z",
"answer": 46
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
7f16a7 | modular_min_linear_v1_784195855_5593 | Let $ a $ be the number of ordered pairs of positive odd integers $ (x_1, x_2) $ such that $ x_1 + x_2 = 13224 $. Let $ m = 17899 $ and $ b = 9162 $. Let $ x $ be the smallest positive integer such that $ 1 \le x \le m $ and $ ax \equiv b \pmod{m} $. Find the value of $ x $. | 9,763 | graphs = [
Graph(
let={
"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")), Const(13224))))),
"... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_min_linear_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 5.526 | 2026-02-08T07:59:16.134891Z | {
"verified": true,
"answer": 9763,
"timestamp": "2026-02-08T07:59:21.661311Z"
} | 6eda62 | 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": 2577
},
"timestamp": "2026-02-13T14:03:10.806Z",
"answer": 9763
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
80c653 | lin_form_endings_v1_784195855_6804 | Let $a = 15$, $b = 35$, $A = 29$, and $B = 14$. Let $g = \gcd(a, b)$. Define $\text{numerator} = aA + bB - a - b$. Let $\text{inner\_result} = \left\lfloor \frac{\text{numerator}}{g} \right\rfloor + 1$. Then define $\text{scaled} = 18852 \cdot \text{inner\_result}$. Let $x$ be the remainder when $\text{scaled}$ is divi... | 24,944 | graphs = [
Graph(
let={
"a_coeff": Const(15),
"b_coeff": Const(35),
"A_val": Const(29),
"B_val": Const(14),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:52:50.647721Z | {
"verified": true,
"answer": 24944,
"timestamp": "2026-02-08T08:52:50.648270Z"
} | 407167 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 722
},
"timestamp": "2026-02-13T22:14:53.484Z",
"answer": 24944
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e5e2dc | comb_count_surjections_v1_349078426_736 | Let $n$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = 7$. Let $k = 2$. Define $S$ to be the number of ways to partition a set of $n$ distinct elements into $k$ nonempty unlabeled subsets, multiplied by $k!$. Let $N = 44121 \cdot S$. Find the remainder wh... | 16,526 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.063 | 2026-02-08T13:15:59.221666Z | {
"verified": true,
"answer": 16526,
"timestamp": "2026-02-08T13:15:59.284503Z"
} | 132b14 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1312
},
"timestamp": "2026-02-24T17:36:21.907Z",
"answer": 16526
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
454ed1 | comb_count_derangements_v1_1218484723_2042 | Let $T = 6$, $L = 9$, and $S = 0$. Define $t = \sum_{k=0}^{T} (-1)^k \binom{T}{k}$, $s = \sum_{k=0}^{L} (-1)^k \binom{L}{k}$, and $w = \sum_{k=0}^{S} (-1)^k \binom{S}{k}$. Let $n = 7w + s$. Let $K = \left|\{ t_1 : 9 \leq t_1 \leq 1389,\ \exists\, c,d \in \mathbb{Z}^+ \text{ with } 1 \leq c \leq 141,\ 1 \leq d \leq 165 ... | 77,935 | graphs = [
Graph(
let={
"_n": Const(7),
"a": Const(4),
"b": Const(2),
"n3": Sum(Ref("a"), Ref("b")),
"t": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n2": Const... | COMB | null | COUNT | sympy | HALFPLANE_COUNT | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | de7e70 | comb_count_derangements_v1 | negation_mod | 5 | 3 | [
"BINOMIAL_ALTERNATING",
"HALFPLANE_COUNT",
"LIN_FORM"
] | 3 | 0.097 | 2026-02-25T03:44:53.102424Z | {
"verified": true,
"answer": 77935,
"timestamp": "2026-02-25T03:44:53.199209Z"
} | a3d354 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 346,
"completion_tokens": 28421
},
"timestamp": "2026-03-29T02:44:54.429Z",
"answer": 77935
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemm... | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
207693 | nt_euler_phi_compute_v1_677425708_1952 | Consider all ordered pairs $(x,y)$ of positive integers such that $xy=81$. Let $m$ be the minimum value of $x+y$ over all such pairs $(x,y)$.
Let $p$ be the largest prime number $n$ such that $2\le n\le m$.
Define
$$r\equiv (p-1)!+1 \pmod p, \quad 0\le r<p,$$
and let $n_1=1+r$.
Let
$$c=\sum_{d\mid n_1} \mu(d),$$
whe... | 37,620 | graphs = [
Graph(
let={
"_m": 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")), Const(81)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW/WILSON",
"MOBIUS_SUM"
] | ca1395 | nt_euler_phi_compute_v1 | null | 7 | 2 | [
"B3",
"MAX_PRIME_BELOW",
"MOBIUS_SUM",
"WILSON"
] | 4 | 0.006 | 2026-02-08T04:40:00.184377Z | {
"verified": true,
"answer": 37620,
"timestamp": "2026-02-08T04:40:00.190118Z"
} | 18adfc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 1252
},
"timestamp": "2026-02-10T03:34:29.700Z",
"answer": 37620
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
95f2b8 | modular_inverse_v1_1820931509_67 | Let $a = 546$ and $m = 1103$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 303601$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $x_0$ be the smallest positive integer $x$ with $1 \leq x \leq s$ such that $546x \equiv 1 \pmod{1103}$. Compute the remainder when ... | 66,238 | graphs = [
Graph(
let={
"a": Const(546),
"m": Const(1103),
"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(303601)))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.071 | 2026-02-08T11:19:36.809135Z | {
"verified": true,
"answer": 66238,
"timestamp": "2026-02-08T11:19:36.880024Z"
} | 249730 | 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": 1639
},
"timestamp": "2026-02-14T12:13:21.319Z",
"answer": 66238
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
70f0b2 | modular_mod_compute_v1_655260480_121 | Let $a = -720$ and $m = 66564$. Define $r$ to be the remainder when $a$ is divided by $m$. Let $k$ be the smallest positive integer such that the $k$th Fibonacci number is divisible by $|r| + 2$. Compute the value of $k$. | 2,220 | graphs = [
Graph(
let={
"a": Const(-720),
"m": Const(66564),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_mod_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.012 | 2026-02-08T15:13:26.562668Z | {
"verified": true,
"answer": 2220,
"timestamp": "2026-02-08T15:13:26.574336Z"
} | a9b733 | 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": 2004
},
"timestamp": "2026-02-16T02:47:37.704Z",
"answer": 2220
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a97208 | nt_count_gcd_equals_v1_153355830_2988 | Let $n$ be a positive integer such that $1 \leq n \leq 13225$ and $\gcd(n, 490) = 5$. Compute the number of such integers $n$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 98$. Define $c$ to be the maximum value of $xy$ over all such pairs. Let $Q = c - N$, where $N$ is the n... | 1,267 | graphs = [
Graph(
let={
"upper": Const(13225),
"k": Const(490),
"d": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"... | NT | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | nt_count_gcd_equals_v1 | negation_mod | 5 | 0 | [
"B1"
] | 1 | 1.317 | 2026-02-08T07:31:09.040919Z | {
"verified": true,
"answer": 1267,
"timestamp": "2026-02-08T07:31:10.358324Z"
} | e4d683 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1360
},
"timestamp": "2026-02-13T10:56:50.833Z",
"answer": 1267
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a6a3a8 | diophantine_fbi2_count_v1_153355830_230 | Let $k = 120$ and $n = 5$. Let $S$ be the set of positive integers $n$ such that $1 \le n \le 231$ and $\gcd(n, 20) = 1$, and let $m$ be the number of elements in $S$. Let $r$ be the number of positive integers $d$ such that $n \le d \le m$, $d$ divides $k$, and $2 \le k/d \le 90$. Compute the remainder when $48074 \cd... | 60,745 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(231)... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.007 | 2026-02-08T02:58:24.436995Z | {
"verified": true,
"answer": 60745,
"timestamp": "2026-02-08T02:58:24.444397Z"
} | 4290e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1471
},
"timestamp": "2026-02-10T12:25:08.641Z",
"answer": 60645
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
9e5510 | nt_min_coprime_above_v1_1125832087_1015 | Let $n = 203$. Let $m$ be the number of positive integers $j$ such that $1 \le j \le n$ and $j^5 \le 344730881243$. Let $I$ be the set of integers $n$ such that $19881 < n \le 20094$ and $\gcd(n, m) = 1$. Determine the smallest element of $I$. | 19,882 | graphs = [
Graph(
let={
"_n": Const(203),
"start": Const(19881),
"upper": Const(20094),
"modulus": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(5)), Const(344730881243))), ... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | 8a214c | nt_min_coprime_above_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.02 | 2026-02-08T03:26:20.290884Z | {
"verified": true,
"answer": 19882,
"timestamp": "2026-02-08T03:26:20.311117Z"
} | 27adc8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1477
},
"timestamp": "2026-02-10T14:29:52.687Z",
"answer": 19882
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
672050 | diophantine_fbi2_count_v1_458359167_3645 | Let $k = 180$ and $n = 58$. Let $r$ be the number of integers $d$ such that $4 \leq d \leq n$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 56$. Compute the remainder when $44311r$ is divided by $84236$. | 26,316 | graphs = [
Graph(
let={
"_n": Const(58),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(R... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.012 | 2026-02-08T11:13:18.857947Z | {
"verified": true,
"answer": 26316,
"timestamp": "2026-02-08T11:13:18.870120Z"
} | bcb615 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1384
},
"timestamp": "2026-02-14T11:14:49.623Z",
"answer": 26316
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1169a4 | comb_count_partitions_v1_784195855_9914 | Let $n$ be the number of integers $t$ such that $24 \leq t \leq 174$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 11$, $1 \leq b \leq 5$, and $t = 9a + 15b$. Let $p(n)$ denote the number of integer partitions of $n$. Compute $p(n)$. | 63,261 | 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=11)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:17:41.169790Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T17:17:41.172100Z"
} | d4090e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 3290
},
"timestamp": "2026-02-18T00:13:17.849Z",
"answer": 63261
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
1018b9_n | comb_count_derangements_v1_601307018_3630 | A magician has $n$ distinct cards, each labeled with a unique number from $1$ to $n$. She wants to shuffle them so that no card ends up in its original position—a perfect derangement. The value of $n$ is the number of possible totals $t$ between $5$ and $14$ inclusive that can be formed as $t = 3a + 2b$ using integers ... | 14,833 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-03-10T04:15:29.369229Z | null | cd86eb | 1018b9 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 841
},
"timestamp": "2026-03-29T17:49:40.119Z",
"answer": 14833
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
cb8aad | antilemma_k3_v1_1742523217_2840 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $15447$, where $\phi$ denotes Euler's totient function. | 15,447 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=15447), 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 | 2026-02-08T05:24:45.739988Z | {
"verified": true,
"answer": 15447,
"timestamp": "2026-02-08T05:24:45.740283Z"
} | e142d8 | 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": 586
},
"timestamp": "2026-02-12T08:22:41.158Z",
"answer": 15447
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
bdd094 | nt_num_divisors_compute_v1_717093673_2375 | Let $n=180$. Let $d(n)$ denote the number of positive divisors of $n$. Compute $d(180)$. | 18 | graphs = [
Graph(
let={
"n": Const(180),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"MAX_PRIME_BELOW/K14/COPRIME_PAIRS/MOBIUS_SQUAREFREE",
"MIN_PRIME_FACTOR/MOBIUS_SQUAREFREE"
] | 0829a1 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"K14",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR",
"MOBIUS_SQUAREFREE",
"SUM_ARITHMETIC"
] | 6 | 1.901 | 2026-02-08T16:47:31.974200Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T16:47:33.875054Z"
} | 8cc513 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 262
},
"timestamp": "2026-02-16T07:53:05.844Z",
"answer": 18
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
4dd0ca | nt_sum_totient_over_divisors_v1_1116507919_182 | Let $n = 68179$. Define $\phi(k)$ to be Euler's totient function, the number of positive integers less than or equal to $k$ that are relatively prime to $k$. Let
$$
\text{result} = \sum_{d \mid n} \phi(d).
$$
Let $A$ be the absolute value of $\text{result}$. Let $m$ be the number of digits in $A$, and let $a_i$ denot... | 8,516 | graphs = [
Graph(
let={
"n": Const(68179),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), EulerPhi(n=Const(2))), expr=Mul(Digit(x... | NT | null | COMPUTE | sympy | V8 | [
"V8",
"ONE_PHI_2"
] | 935b4a | nt_sum_totient_over_divisors_v1 | digits_weighted_mod | 7 | 0 | [
"ONE_PHI_2",
"V8"
] | 2 | 0.004 | 2026-02-08T02:27:18.796840Z | {
"verified": true,
"answer": 8516,
"timestamp": "2026-02-08T02:27:18.801242Z"
} | 172192 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 333,
"completion_tokens": 1455
},
"timestamp": "2026-02-09T14:08:59.745Z",
"answer": 8516
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
... | {
"lo": -4.58,
"mid": 0.57,
"hi": 5.69
} | ||
ecb76b | antilemma_sum_equals_v1_898971024_1375 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 73$ and $1 \leq i, j \leq 73$. Compute the value of
$$
Q = \sum_{n=1}^{x} \tau(n),
$$
where $\tau(n)$ denotes the number of positive divisors of $n$.\n | 326 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(73)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(73)), right=IntegerRange(start=Const(1), end=Const(73))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.006 | 2026-02-08T16:05:40.529211Z | {
"verified": true,
"answer": 326,
"timestamp": "2026-02-08T16:05:40.535649Z"
} | 14439d | 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": 1516
},
"timestamp": "2026-02-24T19:45:23.115Z",
"answer": 326
},
{
"i... | 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": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
c4ab61 | comb_sum_binomial_row_v1_1915831931_711 | Let $m = 20480$. Let $s$ be the number of nonnegative integers $j \leq m$ for which $\binom{m}{j}$ is odd. Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 270$, $\gcd(p, q) = 1$, and $p < q$. Let $t$ be the number of elements in $T$. Compute $\sum_{k=1}^{t} ... | 69,800 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(20480),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=Const(20480), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegativ... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2",
"V8/K2"
] | 1c64f9 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"K2",
"V8"
] | 3 | 0.006 | 2026-02-08T15:38:49.227025Z | {
"verified": true,
"answer": 69800,
"timestamp": "2026-02-08T15:38:49.233476Z"
} | 2f59f6 | 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": 2370
},
"timestamp": "2026-02-16T10:19:38.048Z",
"answer": 69800
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6ba3e2 | antilemma_cartesian_v1_784195855_4510 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i, j \leq 18$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $x + 2$. | 492 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(18)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T07:09:05.913957Z | {
"verified": true,
"answer": 492,
"timestamp": "2026-02-08T07:09:05.914428Z"
} | f47889 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 6941
},
"timestamp": "2026-02-24T07:38:22.608Z",
"answer": 492
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
d6c005 | nt_max_prime_below_v1_458359167_1592 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $n \geq k$ and $n \leq 60025$. Let $r$ be the largest element of $T$. Compute ... | 17,737 | graphs = [
Graph(
let={
"upper": Const(60025),
"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 | 1.451 | 2026-02-08T04:46:31.500404Z | {
"verified": true,
"answer": 17737,
"timestamp": "2026-02-08T04:46:32.951790Z"
} | ad4a1e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 7268
},
"timestamp": "2026-02-11T21:53:30.429Z",
"answer": 17737
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b36117 | nt_min_coprime_above_v1_1520064083_10226 | Let $m$ be the number of positive integers $n \leq 2853$ such that $3$ divides $n$ and $\gcd(n, 10) = 1$. Find the smallest integer $n$ such that $27889 < n \leq 28280$ and $\gcd(n, m) = 1$. Compute the remainder when $44121$ times this value of $n$ is divided by $89822$. | 63,112 | graphs = [
Graph(
let={
"_n": Const(10),
"start": Const(27889),
"upper": Const(28280),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2853)), Divides(divisor=Const(3), dividend=Var("n")), Eq(GC... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.035 | 2026-02-08T11:17:17.282738Z | {
"verified": true,
"answer": 63112,
"timestamp": "2026-02-08T11:17:17.317556Z"
} | 74a31a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2282
},
"timestamp": "2026-02-14T11:11:57.532Z",
"answer": 63112
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9006d | comb_count_permutations_fixed_v1_1248542787_875 | Let $n = 7$ and let $k$ be the smallest integer greater than or equal to $2$ that divides $15$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Multiply this result by $14666$, and then find the remainder when the product is divided by $65917$. | 5,600 | graphs = [
Graph(
let={
"_n": Const(65917),
"n": Const(7),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(15))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T03:28:10.527908Z | {
"verified": true,
"answer": 5600,
"timestamp": "2026-02-08T03:28:10.529222Z"
} | 82a2cf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 753
},
"timestamp": "2026-02-09T09:22:04.474Z",
"answer": 5600
},
{
"id... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 0.96,
"hi": 5.17
} | ||
ae6a6d_n | alg_sum_powers_v1_1419126231_143 | A robot walks along a number line from position 1 to 1999. At each point $x$, it checks whether $|2x - 1864| \le 1862$. For each such $x$, it adds $x^2$ to a total log. After finishing, it reports the sum modulo $3573$. What value does it report? | 2,403 | ALG | null | COMPUTE | sympy | ABS_INEQ | [
"ABS_INEQ"
] | 1c5bb8 | alg_sum_powers_v1 | null | 4 | null | [
"ABS_INEQ"
] | 1 | 0.078 | 2026-02-25T09:40:44.166395Z | null | 6b6583 | ae6a6d | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 8443
},
"timestamp": "2026-03-31T03:20:34.486Z",
"answer": 2403
},
{
"i... | 1 | [
{
"lemma": "ABS_INEQ",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
d499ae | comb_catalan_compute_v1_655260480_1370 | Let $ T $ be the set of all ordered pairs $ (i,j) $ of integers with $ 1 \leq i \leq 11 $ and $ 1 \leq j \leq 12 $. Let $ A $ be the set of all integers $ t $ such that $ 5 \leq t \leq 18 $ and there exist integers $ a $, $ b $ with $ 1 \leq a \leq 3 $, $ 1 \leq b \leq 4 $, and $ t = 2a + 3b $. Let $ m = |A| $. Let $ C... | 31,730 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), CountOverSet(set=Solutions... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 0a8c9f | comb_catalan_compute_v1 | bell_mod | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T16:05:05.041230Z | {
"verified": true,
"answer": 31730,
"timestamp": "2026-02-08T16:05:05.051799Z"
} | ecb217 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 1196
},
"timestamp": "2026-02-24T19:47:23.313Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
3d709c | nt_num_divisors_compute_v1_784195855_10329 | Let $n = 14400$. Compute the number of positive divisors of $n$. | 63 | graphs = [
Graph(
let={
"n": Const(14400),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.009 | 2026-02-08T17:34:25.474169Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T17:34:25.482679Z"
} | 430f86 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 529
},
"timestamp": "2026-02-18T07:37:39.144Z",
"answer": 63
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09b116 | comb_bell_compute_v1_458359167_4966 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 280$ and $\binom{280}{j}$ is odd. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of size $n$. Compute the remainder when $73069 \cdot B_n$ is divided by $72520$. | 24,740 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(280)), Eq(Mod(value=Binom(n=Const(280), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"resul... | COMB | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC",
"V8"
] | 2 | 0.014 | 2026-02-08T12:09:22.699612Z | {
"verified": true,
"answer": 24740,
"timestamp": "2026-02-08T12:09:22.713190Z"
} | 006bbb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1965
},
"timestamp": "2026-02-24T15:16:12.186Z",
"answer": 24740
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
5af608 | diophantine_product_count_v1_153355830_2698 | Let $k$ be the largest positive divisor of $239520$ that is at most $480$. Let $S$ be the set of all positive integers $x \leq 330$ such that $x$ divides $k$ and $\frac{k}{x} \leq 330$. Compute $57121$ minus the number of elements in $S$. | 57,099 | graphs = [
Graph(
let={
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(480)), Divides(divisor=Var("d"), dividend=Const(239520))))),
"upper": Const(330),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condit... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_product_count_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.013 | 2026-02-08T07:17:36.183181Z | {
"verified": true,
"answer": 57099,
"timestamp": "2026-02-08T07:17:36.195803Z"
} | 9b09da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1337
},
"timestamp": "2026-02-13T09:25:38.122Z",
"answer": 57099
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e9e6e1 | algebra_poly_eval_v1_1440796553_1204 | Let $a$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = N$, where $N$ is the number of integers $t$ with $8 \leq t \leq 59$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 8$, $1 \leq b \leq 7$, and $t = 3a + 5b$. Let $\text{result} = 6a^3 + 2a^2 + a - 1$... | 44,488 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"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(Su... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | algebra_poly_eval_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T12:13:54.363689Z | {
"verified": true,
"answer": 44488,
"timestamp": "2026-02-08T12:13:54.367138Z"
} | eca795 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 3507
},
"timestamp": "2026-02-15T18:25:24.336Z",
"answer": 44488
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
0fd96b | comb_binomial_compute_v1_1431428450_272 | Let $n = 16$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 26460$. Compute $\binom{n}{k}$. | 12,870 | graphs = [
Graph(
let={
"n": Const(16),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=26460)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_binomial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T13:22:16.868937Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-02-08T13:22:16.872052Z"
} | 0e9055 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 2580
},
"timestamp": "2026-02-15T13:56:32.623Z",
"answer": 12870
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6b58e8 | nt_count_gcd_equals_v1_1978505735_4057 | Let $k$ be the number of integers $t$ such that $26 \leq t \leq 498$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 48$, $1 \leq b \leq 55$, and $t = 2a + 7b + 17$. Compute the number of positive integers $n$ such that $1 \leq n \leq 40000$ and $\gcd(n, k) = 1$. Find the value of this count. | 39,915 | graphs = [
Graph(
let={
"upper": Const(40000),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=48)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 3.16 | 2026-02-08T17:59:34.601814Z | {
"verified": true,
"answer": 39915,
"timestamp": "2026-02-08T17:59:37.761956Z"
} | 13a9a1 | 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": 2700
},
"timestamp": "2026-02-18T10:48:54.148Z",
"answer": 39915
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f2aa88 | alg_poly4_count_v1_1419126231_1253 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 329$ such that $2a^4 + 24a^3b + 108a^2b^2 + 216ab^3 + 162b^4 = 453342420000$. | 109 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(329)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(329)), Eq(Sum(Mul(Const(24), Pow(Var("a"), Const(3)), Var("b")), Mul(Const(108)... | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_poly4_count_v1 | null | 5 | null | [
"QF_PSD_DISTINCT"
] | 1 | 2.376 | 2026-02-25T10:43:13.304162Z | {
"verified": true,
"answer": 109,
"timestamp": "2026-02-25T10:43:15.680178Z"
} | 3f4e6c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 3802
},
"timestamp": "2026-03-30T11:54:50.328Z",
"answer": 109
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
0bfb8f | comb_count_surjections_v1_601307018_4105 | Let $k = 6$ and $n = \sum_{i=0}^{2} 2^i$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 15,120 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Sub(Binom(n=Const(2), k=Const(2)), Const(1)), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_surjections_v1 | null | 3 | 0 | [
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM",
"ZERO_BINOM_N"
] | 3 | 0.013 | 2026-03-10T04:42:59.796934Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-03-10T04:42:59.809761Z"
} | abf21b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 453
},
"timestamp": "2026-03-29T10:59:23.720Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
4d2805 | antilemma_k3_v1_151522320_1825 | Compute the remainder when $841 - \sum_{d \mid 80077} \phi(d)$ is divided by $72117$, where $\phi$ denotes Euler's totient function. | 64,998 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=80077), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(Const(841), Ref("x")), modulus=Const(72117)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:23:52.359520Z | {
"verified": true,
"answer": 64998,
"timestamp": "2026-02-08T04:23:52.359816Z"
} | e113fe | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 661
},
"timestamp": "2026-02-10T16:33:43.579Z",
"answer": 64998
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
a95749 | nt_count_gcd_equals_v1_1742523217_265 | Let $T$ be the set of all positive integers $t$ such that $7 \le t \le 7570$ and $t = 5a + 2b$ for some positive integers $a \le 688$ and $b \le 2065$. Let $u$ be the number of elements in $T$. Let $d$ be the largest prime number between $2$ and $228$, inclusive. Let $k = 227$. Find the number of positive integers $n$ ... | 32,185 | graphs = [
Graph(
let={
"_m": Const(88988),
"_n": Const(44121),
"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')... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 2.695 | 2026-02-08T02:57:23.872766Z | {
"verified": true,
"answer": 32185,
"timestamp": "2026-02-08T02:57:26.567367Z"
} | 4e64d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 5822
},
"timestamp": "2026-02-09T15:45:51.155Z",
"answer": 32185
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "... | {
"lo": -1.77,
"mid": 0.99,
"hi": 3.5
} | ||
56887d | nt_sum_divisors_mod_v1_124444284_4286 | Let $n$ be the number of integers $t$ such that $11 \leq t \leq 2548$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 200$, $1 \leq b \leq 287$, and
$$
t = 7a + 4b.
$$
Let $\sigma$ be the sum of all positive divisors of $n$. Let $M = 10289$, and let $r$ be the remainder when $\sigma$ is divided by $M$... | 63,596 | graphs = [
Graph(
let={
"_n": Const(77419),
"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=200)), Geq(left=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T05:53:42.904981Z | {
"verified": true,
"answer": 63596,
"timestamp": "2026-02-08T05:53:42.908012Z"
} | 70daeb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 4099
},
"timestamp": "2026-02-12T16:39:40.037Z",
"answer": 63596
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ace5fb | nt_count_digit_sum_v1_1520064083_9414 | Let the target sum be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 100$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 58081$ and the sum of the digits of $n$ equals the target sum. Compute the remainder when $44121 \cdot N$ is divided by $80875$. | 57,332 | graphs = [
Graph(
let={
"upper": Const(58081),
"target_sum": 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(100)))), expr=Sum(Var("x"), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 5 | 0 | [
"B3"
] | 1 | 14.817 | 2026-02-08T10:43:45.590218Z | {
"verified": true,
"answer": 57332,
"timestamp": "2026-02-08T10:44:00.406829Z"
} | e445ac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 3825
},
"timestamp": "2026-02-14T08:46:45.385Z",
"answer": 57332
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9b408b | comb_sum_binomial_row_v1_601307018_2373 | Compute $\left|\left\{ (a, b) \mid 1 \leq a \leq 15,\ 1 \leq b \leq 15,\ 91a^3 - 96a^2b + 48ab^2 - 8b^3 = 120744 \right\}\right|^{13}$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(13),
"result": Pow(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Sum(Mul(Con... | COMB | null | SUM | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"POLY3_COUNT"
] | 1 | 0.003 | 2026-03-10T03:02:39.841525Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-03-10T03:02:39.844912Z"
} | 1143d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:11:43.689Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
f20edb | nt_num_divisors_compute_v1_809748730_1397 | Let $n = 10816$. Compute the number of positive divisors of $n$. | 21 | graphs = [
Graph(
let={
"n": Const(10816),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.016 | 2026-02-08T12:24:10.671881Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T12:24:10.687850Z"
} | 5f1390 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 343
},
"timestamp": "2026-02-16T03:46:59.360Z",
"answer": 40
},
{
"id": 11,
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} |
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