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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
66d3e5 | modular_mod_compute_v1_655260480_5765 | Let $a$ be the number of positive integers $n$ at most $34560$ such that $1 + 2 + 3 + 4$ divides the $n$-th Fibonacci number. Compute the remainder when $a$ is divided by $33333$. | 2,304 | graphs = [
Graph(
let={
"_n": Const(4),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(34560)), Divides(divisor=Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), dividend=Fibonacci(arg=Var(name='n')))))),
... | ALG | NT | COMPUTE | sympy | LIN_FORM | [
"SUM_ARITHMETIC/COUNT_FIB_DIVISIBLE"
] | a53b1f | modular_mod_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 3 | 0.022 | 2026-02-08T18:39:13.616500Z | {
"verified": true,
"answer": 2304,
"timestamp": "2026-02-08T18:39:13.638366Z"
} | b2b37b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1064
},
"timestamp": "2026-02-18T18:26:24.685Z",
"answer": 2304
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c0ec74_l | comb_sum_binomial_mod_v1_1742523217_177 | Let $S$ be the sum
$$
\sum_{k = A}^{B} \binom{285}{k},
$$
where
$$
A = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor
\quad\text{and}\quad
B = \sum_{k=1}^{21} \phi(k) \left\lfloor \frac{21}{k} \right\rfloor.
$$
Compute the remainder when $S$ is divided by $10597$. | 0 | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.039 | 2026-02-08T02:54:54.464057Z | {
"verified": false,
"answer": 857,
"timestamp": "2026-02-08T02:54:54.502708Z"
} | 0a020d | c0ec74 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T18:25:30.271Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
... | {
"lo": 4.56,
"mid": 6.51,
"hi": 9.5
} | |
e00736 | diophantine_fbi2_count_v1_971394319_2040 | Determine the number of positive integers $d$ such that $3 \leq d \leq 102$, $d$ divides $180$, and the quotient $\frac{180}{d}$ satisfies $5 \leq \frac{180}{d} \leq 104$.
Compute this number. | 12 | graphs = [
Graph(
let={
"k": Const(180),
"a": Const(2),
"b": Const(4),
"upper": Const(100),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(102)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | K14 | [
"K14/B3"
] | 646d8f | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"K14"
] | 2 | 0.044 | 2026-02-08T14:05:41.952925Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T14:05:41.996536Z"
} | 1d8fb4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1407
},
"timestamp": "2026-02-16T00:12:08.478Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c798c8 | nt_sum_totient_over_divisors_v1_1978505735_2153 | Let $n$ be the number of integers $t \in [9, 2307]$ for which there exist positive integers $a \in [1, 331]$ and $b \in [1, 235]$ such that $t = 2a + 7b$.
Compute
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function. | 2,293 | 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=331)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.007 | 2026-02-08T16:41:06.506443Z | {
"verified": true,
"answer": 2293,
"timestamp": "2026-02-08T16:41:06.513401Z"
} | f9018d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 4906
},
"timestamp": "2026-02-17T11:12:48.741Z",
"answer": 2293
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
896caa | nt_min_crt_v1_1742523217_4098 | Let $u = \sum_{k=1}^{8} k$. Find the minimum positive integer $n$ such that $n \leq u$, $n \equiv 2 \pmod{4}$, and $n \equiv 5 \pmod{9}$. | 14 | graphs = [
Graph(
let={
"m": Const(4),
"k": Const(9),
"a": Const(2),
"b": Const(5),
"upper": Summation(var="k", start=Const(1), end=Const(8), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n")... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_min_crt_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 2 | 0.152 | 2026-02-08T06:59:54.295297Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T06:59:54.447557Z"
} | d74e6d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 301
},
"timestamp": "2026-02-15T18:48:44.757Z",
"answer": 14
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -10,
"mid": -7.3,
"hi": -4.61
} | ||
a6ee1a | nt_sum_divisors_mod_v1_1520064083_3950 | Let $n$ be the number of positive integers $t$ such that $24 \leq t \leq 1750$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 168$, $1 \leq b \leq 5$, and $t = 10a + 14b$. Let $\sigma$ be the sum of all positive divisors of $n$. Let $r$ be the remainder when $\sigma$ is divided by $11489$. Define $m ... | 390 | 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=168)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T05:59:32.598675Z | {
"verified": true,
"answer": 390,
"timestamp": "2026-02-08T05:59:32.601317Z"
} | a7420a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 4453
},
"timestamp": "2026-02-12T17:59:24.544Z",
"answer": 390
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
35cb4c | nt_count_digit_sum_v1_151522320_70 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 30$ and there exist positive integers $a \leq 3$ and $b \leq 8$ for which $t = 2a + 3b$. Let $s$ be the number of elements in $T$. Let $U$ be the set of all positive integers $n$ such that $1 \leq n \leq 39204$ and the sum of the decimal digits of $n$ is e... | 1,969 | graphs = [
Graph(
let={
"upper": Const(39204),
"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=3)),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 19.099 | 2026-02-08T02:56:31.020220Z | {
"verified": true,
"answer": 1969,
"timestamp": "2026-02-08T02:56:50.119374Z"
} | b23667 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 16142
},
"timestamp": "2026-02-23T20:04:20.466Z",
"answer": 1949
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 2.8,
"mid": 4.67,
"hi": 6.48
} | ||
2bb2d3 | nt_num_divisors_compute_v1_784195855_9053 | Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 154$. Let $n$ be the maximum value of $xy$ over all such pairs. Let $d$ be the number of positive divisors of $n$. Let $S_1$ be the set of all ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 194$, and let... | 25,400 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(154)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COMB1",
"B1"
] | 627ae5 | nt_num_divisors_compute_v1 | crt_mix_3 | 7 | 0 | [
"B1",
"COMB1",
"MIN_PRIME_FACTOR"
] | 3 | 0.012 | 2026-02-08T16:30:00.004992Z | {
"verified": true,
"answer": 25400,
"timestamp": "2026-02-08T16:30:00.016602Z"
} | 07cc9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 2347
},
"timestamp": "2026-02-17T05:30:46.897Z",
"answer": 25400
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
435d14 | nt_sum_over_divisible_v1_601307018_284 | Let $S$ be the set of integers $v$ with $8 \le v \le 3530$ for which there exist integers $a, b$ satisfying $1 \le a, b \le 11$ and $10a^2 - 32ab + 32b^2 = v$. Let $N = |S|$. Let $T$ be the sum of all positive integers $n \le 1183$ such that $n \equiv 0 \pmod{N}$. Let $K$ be the sum of all positive integers $n_1 \le T$... | 21,436 | graphs = [
Graph(
let={
"_m": Const(3530),
"_n": Const(96416),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1183)), Eq(Mod(value=Var("n"), modulus=CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Ge... | NT | null | SUM | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/SUM_DIVISIBLE"
] | 61193f | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT",
"SUM_DIVISIBLE"
] | 2 | 0.01 | 2026-03-10T00:50:10.628222Z | {
"verified": true,
"answer": 21436,
"timestamp": "2026-03-10T00:50:10.638083Z"
} | 720e62 | CC BY 4.0 | null | null | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
{... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
ff1c8f | nt_sum_gcd_range_mod_v1_458359167_137 | Let $S$ be the set of positive divisors $d$ of $9292$ such that $1 \leq d \leq 92$. Define $N = \sum_{k=1}^{\max(S)} \phi(k) \left\lfloor \frac{92}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the sum $\sum_{n=1}^{N} \gcd(n, 168)$, and let $M = 10111$. Let $s$ be the remainder when this sum... | 71,944 | graphs = [
Graph(
let={
"_m": Const(71824),
"_n": Const(2),
"N": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(92)), Divides(divisor=Var("d"), dividend=Const(9292))))), expr=Mul(... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/K2"
] | 3a721e | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"K2",
"MAX_DIVISOR"
] | 2 | 0.36 | 2026-02-08T03:00:56.860959Z | {
"verified": true,
"answer": 71944,
"timestamp": "2026-02-08T03:00:57.221430Z"
} | 3137da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 319,
"completion_tokens": 7024
},
"timestamp": "2026-02-10T12:31:31.351Z",
"answer": 71944
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"st... | {
"lo": 1.66,
"mid": 3.8,
"hi": 5.62
} | ||
d108ea | nt_count_divisors_in_range_v1_809748730_400 | Let $x$ and $y$ be positive integers such that $xy = 14288400$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $b$ be the number of integers $t$ with $15 \leq t \leq 11385$ such that $t = 6a + 9b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 372$ and $1 \leq b \leq 1017$. Compute the remain... | 5,759 | graphs = [
Graph(
let={
"_n": Const(58741),
"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(14288400)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.073 | 2026-02-08T11:30:12.281692Z | {
"verified": true,
"answer": 5759,
"timestamp": "2026-02-08T11:30:12.354454Z"
} | aafa7b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4662
},
"timestamp": "2026-02-14T15:02:06.512Z",
"answer": 5759
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4df31b | comb_binomial_compute_v1_971394319_1203 | Let $n = 13$ and let $k$ be the largest prime number $p$ such that $2 \leq p \leq 7$. Define $r = \binom{n}{k}$. Compute the remainder when $20 - r$ is divided by 89651.
Find the value of this remainder. | 87,955 | graphs = [
Graph(
let={
"n": Const(13),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(20),
"Q": Mod(value=Su... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T13:31:45.419043Z | {
"verified": true,
"answer": 87955,
"timestamp": "2026-02-08T13:31:45.420510Z"
} | 93f45d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 808
},
"timestamp": "2026-02-16T04:50:29.921Z",
"answer": 177606
},
{
"id": 1... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
d30528 | comb_count_permutations_fixed_v1_1915831931_1636 | Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 10$ and $1 \leq j \leq 10$ such that $i + j = 10$. Let $k = 5$. Compute the remainder when $33203 \cdot \binom{n}{k} \cdot !(n - k)$ is divided by $51195$, where $!m$ denotes the subfactorial of $m$. Enter your answer as an integer between ... | 23,877 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(10)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(10))))),
"k": ... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.017 | 2026-02-08T16:19:00.780129Z | {
"verified": true,
"answer": 23877,
"timestamp": "2026-02-08T16:19:00.797474Z"
} | 706b1d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 1162
},
"timestamp": "2026-02-24T20:47:16.552Z",
"answer": 23877
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
3dba8a | modular_sum_quadratic_residues_v1_1470522791_1111 | Let $m = 4$ and $n = 2$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 114921$. For each such pair, compute $x + y$, and let $s_{\min}$ be the smallest such sum. Let $p$ be the largest prime number satisfying $2 \leq p \leq s_{\min}$. Define $r = \frac{p(p-1)}{m}$. Compute... | 55,877 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=V... | NT | null | SUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T13:26:17.254311Z | {
"verified": true,
"answer": 55877,
"timestamp": "2026-02-08T13:26:17.258182Z"
} | 1da40c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1313
},
"timestamp": "2026-02-15T15:40:28.458Z",
"answer": 55877
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1366fb | comb_bell_compute_v1_1874849503_1644 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1323000$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of an $n$-element set. Compute the remainder whe... | 74,496 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=1323000)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T14:00:46.881233Z | {
"verified": true,
"answer": 74496,
"timestamp": "2026-02-08T14:00:46.882408Z"
} | 664707 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 2204
},
"timestamp": "2026-02-10T06:07:33.212Z",
"answer": 74496
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
2de2c5 | comb_sum_binomial_row_v1_1520064083_10200 | Let $n$ be the number of prime numbers in the interval $[2, N]$, where $N$ is the number of integers $t$ in the range $[11, 59]$ that can be expressed as $3a + 5b + 3$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 12$ and $1 \leq b \leq 4$. Compute $10404 - 2^n$. | 2,212 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Va... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/COUNT_PRIMES"
] | a88a1b | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T11:16:04.639075Z | {
"verified": true,
"answer": 2212,
"timestamp": "2026-02-08T11:16:04.641031Z"
} | 98484f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2517
},
"timestamp": "2026-02-14T11:10:30.414Z",
"answer": 2212
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
edae30 | antilemma_count_primes_v1_50713871_94 | Let $x$ be the number of prime numbers between 2 and 1423, inclusive. Compute $$\sum_{n=1}^{x} \tau(n),$$ where $\tau(n)$ denotes the number of positive divisors of $n$. | 1,252 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1423)), IsPrime(Var("n"))))),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='x')), expr=NumDivisors(n=Var("n"))),
},
goal... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0 | 2026-02-08T02:45:17.645422Z | {
"verified": true,
"answer": 1252,
"timestamp": "2026-02-08T02:45:17.645888Z"
} | 6295da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 3475
},
"timestamp": "2026-02-10T00:11:09.757Z",
"answer": 1238
},
... | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
e83daa | comb_catalan_compute_v1_1915831931_2085 | Let $m = 18$. Define $\mu$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Define $n$ to be the number of ordered triples $(x_{11}, x_{21}, x_3)$ of positive odd integers such that $x_{11} + x_{21} + x_3 = \mu$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"_m": Const(18),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T16:36:31.527476Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T16:36:31.531368Z"
} | 7fa142 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1184
},
"timestamp": "2026-02-17T07:40:22.541Z",
"answer": 16796
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
a09d7c | antilemma_k2_v1_1520064083_6942 | Compute $$ \sum_{k=1}^{371} \phi(k) \left\lfloor \frac{371}{k} \right\rfloor, $$ where $\phi(k)$ denotes Euler's totient function. | 69,006 | graphs = [
Graph(
let={
"_n": Const(371),
"x": Summation(var="k", start=Const(1), end=Const(371), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T08:25:47.595097Z | {
"verified": true,
"answer": 69006,
"timestamp": "2026-02-08T08:25:47.595495Z"
} | 2b872e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 803
},
"timestamp": "2026-02-13T18:15:28.425Z",
"answer": 69006
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
542203 | alg_qf_psd_orbit_v1_601307018_9437 | Let $B = \max\{ d \geq 1 : d \mid 234734 \text{ and } d^2 \le 234734 \}$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le B$ such that $9a^2 + 9b^2 = 1781685$. | 6 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"B3_CLOSEST",
"B3"
] | a6b579 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"B3",
"B3_CLOSEST",
"MAX_PRIME_BELOW"
] | 3 | 2.595 | 2026-03-10T09:50:09.586603Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-03-10T09:50:12.181725Z"
} | 89d57a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 4296
},
"timestamp": "2026-04-19T11:21:20.125Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f7a074 | comb_count_permutations_fixed_v1_784195855_3612 | Let $n = 7$ and $k = 2$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $s$ be the number of decimal digits of $|\text{result}|$. Define the sum $\sum_{i=0}^{s-1} \left( \text{digit}_i(|\text{result}|) \cdot (i + 1)^2 \right)$, where $\text{digit... | 100 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"_c": Const(7),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(... | NT | COMB | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"ONE_PHI_1"
] | 1 | 0.003 | 2026-02-08T06:32:37.674052Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T06:32:37.677519Z"
} | 3ce4ea | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 307
},
"timestamp": "2026-02-19T10:36:28.731Z",
"answer": 100
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
b25c8b | nt_min_phi_inverse_v1_865884756_493 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 625$. Define $\sigma$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $k = 12$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq \sigma$ and $\varphi(n) = k$, where $\varphi$ denotes Euler's... | 13 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(625)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(12),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.017 | 2026-02-08T15:26:17.379666Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T15:26:17.396337Z"
} | d4d065 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1944
},
"timestamp": "2026-02-16T06:22:48.946Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6f219 | algebra_poly_eval_v1_677425708_3023 | Let $z = 10$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 576$. Let $s_{\text{min}}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the value of
$$
\frac{24z^3 + s_{\text{min}} \cdot z^2 + 42z + 12}{\sum_{d \mid 63} \phi(d)}.
$$
Determine the value of this... | 464 | graphs = [
Graph(
let={
"_m": Const(63),
"_n": Const(12),
"z": Const(10),
"result": Div(Sum(Mul(Const(24), Pow(Ref("z"), Const(3))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name=... | NT | null | COMPUTE | sympy | K3 | [
"K3",
"B3"
] | b88822 | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3",
"K3"
] | 2 | 0.005 | 2026-02-08T05:26:14.301790Z | {
"verified": true,
"answer": 464,
"timestamp": "2026-02-08T05:26:14.306651Z"
} | e71f3a | 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": 1002
},
"timestamp": "2026-02-12T08:50:53.416Z",
"answer": 464
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
612878 | comb_catalan_compute_v1_784195855_3786 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $54658 \cdot C_n$ is divided by $63485$. | 22,368 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(22))))),
"res... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T06:38:11.837356Z | {
"verified": true,
"answer": 22368,
"timestamp": "2026-02-08T06:38:11.838849Z"
} | 76520d | 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": 3950
},
"timestamp": "2026-02-24T06:41:11.458Z",
"answer": 22368
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
75ff84 | antilemma_sum_equals_v1_1742523217_392 | Let $ S $ be the set of all ordered pairs of integers $ (i, j) $ such that $ 1 \leq i \leq 18 $, $ 1 \leq j \leq 18 $, and $ i + j = 20 $. Let $ x $ be the number of elements in $ S $. Compute the remainder when $ 82543 \cdot x $ is divided by $ 62969 $. | 17,913 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(20)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(18))))),
"_c":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.015 | 2026-02-08T03:00:46.229241Z | {
"verified": true,
"answer": 17913,
"timestamp": "2026-02-08T03:00:46.244328Z"
} | 785da2 | 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": 820
},
"timestamp": "2026-02-09T17:21:09.774Z",
"answer": 17913
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
4db181 | comb_count_permutations_fixed_v1_1248542787_644 | Let $n = \sum_{k=1}^{4} k = 10$ and $k = 7$. Compute $\binom{n}{k}$ multiplied by the number of derangements of $n - k$ elements. Let $\text{result}$ denote this product. Let $m = 83028$. Find the remainder when $m \cdot \text{result}$ is divided by $98393$. Determine the value of $Q$. | 51,334 | graphs = [
Graph(
let={
"_n": Const(83028),
"n": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"k": Const(7),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Mod(... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T03:17:00.959392Z | {
"verified": true,
"answer": 51334,
"timestamp": "2026-02-08T03:17:00.961843Z"
} | 0205d6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 904
},
"timestamp": "2026-02-09T06:32:46.467Z",
"answer": 51334
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.46,
"mid": 0.46,
"hi": 3.54
} | ||
88f530 | sequence_fibonacci_compute_v1_124444284_6581 | Let $n$ be the largest prime number less than or equal to $24$. Define $F_n$ to be the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $Q$ be the remainder when $44121 \cdot F_n$ is divided by $80743$. Compute $Q$. | 20,860 | graphs = [
Graph(
let={
"_n": Const(24),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result"... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T08:32:52.205656Z | {
"verified": true,
"answer": 20860,
"timestamp": "2026-02-08T08:32:52.206414Z"
} | 400d05 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2057
},
"timestamp": "2026-02-13T19:22:28.063Z",
"answer": 20860
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
28935f | algebra_quadratic_discriminant_v1_458359167_2512 | Let $n_0 = 4$. Let $A$ be the set of all positive integers $n$ such that $1 \le n \le 8$, $n$ is divisible by $n_0$, and $\gcd(n, 35) = 1$. Let $k = |A|$, the number of elements in $A$. Compute $(-4)^k - 4(-1)(-4)$. | 0 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": Const(4),
"c": Const(-4),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(8)), Divides(divisor=Ref("_n")... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"C5"
] | 1d9668 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"C5"
] | 2 | 0.008 | 2026-02-08T05:27:36.289056Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T05:27:36.297125Z"
} | 0a093a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 384
},
"timestamp": "2026-02-15T17:24:38.259Z",
"answer": 32
},
{
"id": 11,
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
18bfc2 | antilemma_sum_factor_cartesian_v1_1742523217_502 | Let $n$ be the number of positive integers $k$ with $1\le k\le 38$ such that $19$ divides $k$. Let $m=\varphi(\varphi(n))$, where $\varphi$ denotes Euler's totient function.
Consider all ordered pairs $(i,j)$ of integers such that $1\le i\le 25$ and $1\le j\le 7$. Among these pairs, keep only those for which $\varphi(... | 9,100 | graphs = [
Graph(
let={
"_n": Const(38),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divi... | NT | null | COMPUTE | sympy | C2 | [
"C2/ONE_PHI_2/ONE_PHI_1/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | d16791 | antilemma_sum_factor_cartesian_v1 | null | 6 | 0 | [
"C2",
"ONE_PHI_1",
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 4 | 0.002 | 2026-02-08T03:04:55.354316Z | {
"verified": true,
"answer": 9100,
"timestamp": "2026-02-08T03:04:55.356642Z"
} | 1a42a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 651
},
"timestamp": "2026-02-09T18:50:22.304Z",
"answer": 9100
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok_later"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -6.51,
"mid": -0.32,
"hi": 5.36
} | ||
853ad3 | nt_count_gcd_equals_v1_124444284_7508 | Let $d$ be the number of integers $t$ with $7 \leq t \leq 61$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 7$, $1 \leq b \leq 10$, and $t = 3a + 4b$. Let $k = 98$ and let $U = 32768$. Determine the number of integers $n$ with $1 \leq n \leq U$ such that $\gcd(n, k) = d$. | 334 | graphs = [
Graph(
let={
"upper": Const(32768),
"k": Const(98),
"d": 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'), rig... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 6.446 | 2026-02-08T09:10:25.477418Z | {
"verified": true,
"answer": 334,
"timestamp": "2026-02-08T09:10:31.923692Z"
} | 3227ca | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 2926
},
"timestamp": "2026-02-14T01:17:15.699Z",
"answer": 334
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a469b6 | alg_sum_powers_v1_1218484723_6142 | Find the remainder when $\sum_{k=1}^{N} k^3$ is divided by $4212$, where $N = \left| \left\{ (a,b) : 1\le a,b \le 40,\, 13a^2 - 2ab + 2b^2 \le 16362 \right\} \right|$. | 1,764 | graphs = [
Graph(
let={
"_n": Const(16362),
"result": Mod(value=Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_sum_powers_v1 | null | 4 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.059 | 2026-02-25T07:45:35.301911Z | {
"verified": true,
"answer": 1764,
"timestamp": "2026-02-25T07:45:35.361377Z"
} | 086e13 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 20198
},
"timestamp": "2026-03-30T00:21:35.776Z",
"answer": 1764
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
5cc8dc | modular_mod_compute_v1_601307018_9793 | Let $m$ be the number of positive integers $t$ such that $t = 15c + 6b + 18$ for some integers $c, b$ with $1 \leq c \leq 183$, $1 \leq b \leq 1172$, and $39 \leq t \leq 9795$. Let $S = 37249 \bmod m$. Find the remainder when $42304 \cdot S$ is divided by $73413$. | 9,730 | graphs = [
Graph(
let={
"_n": Const(73413),
"a": Const(37249),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), rig... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-03-10T10:13:22.455419Z | {
"verified": true,
"answer": 9730,
"timestamp": "2026-03-10T10:13:22.463178Z"
} | ffc4c5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3939
},
"timestamp": "2026-04-19T12:03:23.586Z",
"answer": 9730
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
8cca07 | sequence_lucas_compute_v1_865884756_2808 | Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 99$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 3$, and $t = 9a + 12b$. Let $n = |T|$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_m = L_{m-1} + L_{m-2}$ for $m \geq 3$. Find t... | 71,622 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:57:06.954552Z | {
"verified": true,
"answer": 71622,
"timestamp": "2026-02-08T16:57:06.956236Z"
} | 1cc4c1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2346
},
"timestamp": "2026-02-17T16:15:51.951Z",
"answer": 71622
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1279c0 | comb_bell_compute_v1_717093673_2541 | Let $ n = 9 $. Define $ c = \sum_{k=0}^{0} (-1)^k \binom{0}{k} $. Let $ u $ be $ c $ multiplied by the number of ordered pairs $ (x_1, x_2) $ of positive odd integers such that $ x_1 + x_2 = 16 $. Let $ n_1 = u + 1 $. Define $ v = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1} $. Let $ n = 9 + v $. Compute the Bell num... | 21,147 | graphs = [
Graph(
let={
"_n": Const(9),
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_bell_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.002 | 2026-02-08T16:55:45.282226Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T16:55:45.284157Z"
} | 1e5032 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 722
},
"timestamp": "2026-02-17T15:03:55.999Z",
"answer": 21147
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
18b40d | nt_count_divisors_in_range_v1_2051736721_4050 | Let $P$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 38$. Let $M$ be the maximum value of $x_1 y_1$ over all such pairs. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = M$. Let $a$ be the minimum value of $x + y$ over all such pairs in $S... | 136 | graphs = [
Graph(
let={
"n": Const(277200),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.157 | 2026-02-08T17:41:25.493492Z | {
"verified": true,
"answer": 136,
"timestamp": "2026-02-08T17:41:25.650803Z"
} | 57344a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 3157
},
"timestamp": "2026-02-18T06:01:04.371Z",
"answer": 136
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
431a27 | geo_count_lattice_rect_v1_124444284_2175 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 128$ and $0 \leq y \leq 468$. | 60,501 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(468),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T04:29:29.573288Z | {
"verified": true,
"answer": 60501,
"timestamp": "2026-02-08T04:29:29.574064Z"
} | 6e8580 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 174
},
"timestamp": "2026-02-24T00:55:44.352Z",
"answer": 60501
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||||
f4d883 | comb_count_derangements_v1_971394319_824 | Let $S$ be the set of nonnegative integers $j$ such that $0 \leq j \leq 66056$ and $\binom{66056}{j}$ is odd. Let $n$ be the number of positive integers $j$ such that $j \leq |S|$ and $j^5 \leq 32768$. Compute the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(32768),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(66056))... | COMB | null | COUNT | sympy | V8 | [
"V8/C3"
] | e55eeb | comb_count_derangements_v1 | null | 6 | 0 | [
"C3",
"V8"
] | 2 | 0.003 | 2026-02-08T13:19:11.192114Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T13:19:11.194993Z"
} | 0ff526 | 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": 1848
},
"timestamp": "2026-02-24T17:49:07.482Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
251930 | antilemma_k3_v1_1125832087_1231 | Compute $\sum_{d \mid 28009} \varphi(d)$, where $\varphi$ denotes Euler's totient function. | 28,009 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=28009), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:37:40.037292Z | {
"verified": true,
"answer": 28009,
"timestamp": "2026-02-08T03:37:40.037858Z"
} | 14dd23 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 549
},
"timestamp": "2026-02-10T15:10:32.825Z",
"answer": 28009
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
6cda69 | geo_count_lattice_rect_v1_677425708_2396 | Let $a = 128$ and $b = 401$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $Q$ be the remainder when $961 - \text{result}$ is divided by $79749$. Find the value of $Q$. | 28,852 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(401),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Sub(Const(961), Ref("result")), modulus=Const(79749)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T05:01:53.296191Z | {
"verified": true,
"answer": 28852,
"timestamp": "2026-02-08T05:01:53.297382Z"
} | 9a17be | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 880
},
"timestamp": "2026-02-24T02:35:05.228Z",
"answer": 28852
},
{
"i... | 1 | [] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||||
7d707e | alg_poly_preperiod_count_v1_601307018_9555 | Let $N = (2a^3 - 3a) \bmod 19$, $M = (2N^3 - 3N) \bmod 19$, $R = (2M^3 - 3M) \bmod 19$, $S = (2R^3 - 3R) \bmod 19$, and $T = (2S^3 - 3S) \bmod 19$. Find the number of non-negative integers $a$ with $0 \le a \le 19265$ such that $T = N$, $M \neq N$, $R \neq N$, and $S \neq N$. | 8,112 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(-3), Var("a"))), modulus=Const(19)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(-3), Ref("p1"))), modulus=Const(19)),
"p3": Mod(value=Sum(Mul(Const(2)... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.034 | 2026-03-10T09:58:42.987429Z | {
"verified": true,
"answer": 8112,
"timestamp": "2026-03-10T09:58:43.021275Z"
} | 568c4f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 3542
},
"timestamp": "2026-04-19T11:33:19.474Z",
"answer": 8112
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
ee43d4 | antilemma_cartesian_v1_1915831931_432 | Let $S$ be the set of all ordered pairs $(i,j)$ where $i$ and $j$ are integers with $1 \leq i \leq 20$ and $1 \leq j \leq 28$. Let $x$ be the number of elements in $S$. Compute $\sum_{n=1}^{x} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 3,641 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(28)))),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='x')), expr=NumDivisors(n=Var("n"))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T15:24:53.822299Z | {
"verified": true,
"answer": 3641,
"timestamp": "2026-02-08T15:24:53.823157Z"
} | ac0ed8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 3202
},
"timestamp": "2026-02-24T21:01:41.928Z",
"answer": 3641
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
951cf0 | lin_form_endings_v1_717093673_2236 | Let $a = 63$, $b = 45$, and $k = 74$. Define $d = \gcd(a, b)$ and $g = \gcd(k, d)$. Let $r = \left\lfloor \frac{k}{g} \right\rfloor$. Compute the remainder when $8101 \cdot r$ is divided by 56654. | 32,934 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(45),
"k_val": Const(74),
"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(81... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:41:43.396830Z | {
"verified": true,
"answer": 32934,
"timestamp": "2026-02-08T16:41:43.397953Z"
} | ce6fda | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 616
},
"timestamp": "2026-02-17T10:20:20.793Z",
"answer": 32934
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
af7845 | diophantine_product_count_v1_655260480_886 | Let $n = 18927$. Let $k$ be the number of ordered pairs $(a, b)$ of positive integers such that $1 \leq a \leq 20$ and $1 \leq b \leq 21$. Define $u$ to be the number of positive integers $t$ such that $14 \leq t \leq 199$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 20$, $1 \leq b \leq 31$, and $t... | 9,044 | graphs = [
Graph(
let={
"_n": Const(18927),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(21)))),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | efa619 | diophantine_product_count_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.013 | 2026-02-08T15:41:03.746377Z | {
"verified": true,
"answer": 9044,
"timestamp": "2026-02-08T15:41:03.759004Z"
} | 726540 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 5959
},
"timestamp": "2026-02-16T12:55:24.072Z",
"answer": 9044
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21b52e | alg_poly_preperiod_count_v1_601307018_8018 | For a non-negative integer $a$, define a sequence $N, M, R, S$ by:
\[
N = (2a^3 + a^2 - 3a - 3) \bmod 37,\quad M = (2N^3 + N^2 - 3N - 3) \bmod 37,
\]
\[
R = (2M^3 + M^2 - 3M - 3) \bmod 37,\quad S = (2R^3 + R^2 - 3R - 3) \bmod 37.
\]
Find the number of integers $a$ with $0 \le a \le 4254$ such that $S = N$, $M \neq N$, ... | 575 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Pow(Var("a"), Const(2)), Mul(Const(-3), Var("a")), Const(-3)), modulus=Const(37)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Pow(Ref("p1"), Const(2)), Mul(Const(-3), Ref("p1")), Con... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.055 | 2026-03-10T08:31:05.606002Z | {
"verified": true,
"answer": 575,
"timestamp": "2026-03-10T08:31:05.661408Z"
} | 23f263 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 9097
},
"timestamp": "2026-04-19T08:06:25.784Z",
"answer": 575
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
48b10f | antilemma_k3_v1_1520064083_4468 | Let $n = 23369$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Compute the remainder when $12033x$ is divided by $78830$. | 12,567 | graphs = [
Graph(
let={
"_n": Const(23369),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(12033), Ref("x")), modulus=Const(78830)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T06:17:33.951081Z | {
"verified": true,
"answer": 12567,
"timestamp": "2026-02-08T06:17:33.951517Z"
} | 33e31c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 1100
},
"timestamp": "2026-02-12T22:13:08.071Z",
"answer": 12567
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2dc6a9 | comb_bell_compute_v1_124444284_1017 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 298116$. Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le m$ and $\binom{m}{j}$ is odd. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. Find... | 4,140 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(298116)))), expr=Sum(Var("x"), Var("y")))),... | COMB | null | COMPUTE | sympy | B3 | [
"B3/B3/V8"
] | 408b30 | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.003 | 2026-02-08T03:39:09.361825Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T03:39:09.364843Z"
} | b03b19 | 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": 1885
},
"timestamp": "2026-02-10T01:24:32.651Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
c1ebaf | nt_sum_totient_over_divisors_v1_153355830_517 | Let $m = 53751$ and $n = 50569$. Let $d_0$ be the smallest integer greater than 1 that divides 10051. Define $k_{\text{max}}$ to be the number of positive integers $k$ such that $1 \leq k \leq m$ and $d_0$ divides $k$. Let $n$ be the largest positive divisor of 8042847 that is at most $k_{\text{max}}$. Compute the sum ... | 38,897 | graphs = [
Graph(
let={
"_m": Const(53751),
"_n": Const(50569),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_m")),... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/C2/MAX_DIVISOR"
] | f4f44c | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"C2",
"MAX_DIVISOR",
"MIN_PRIME_FACTOR"
] | 3 | 0.005 | 2026-02-08T03:08:26.750464Z | {
"verified": true,
"answer": 38897,
"timestamp": "2026-02-08T03:08:26.755805Z"
} | 2f2ed5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 11184
},
"timestamp": "2026-02-23T16:34:19.887Z",
"answer": 38897
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
... | {
"lo": 0.77,
"mid": 2.83,
"hi": 5
} | ||
762b10 | nt_sum_divisors_range_v1_168721529_1684 | Let $N = 16384$. Define $S$ as the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = N$. Let $u$ be the number of elements in $S$. Let $R$ be the sum of $\tau(n)$ over all positive integers $n$ such that $1 \leq n \leq u$, where $\tau(n)$ denotes the number of positive divisors of $n... | 75,108 | graphs = [
Graph(
let={
"_n": Const(16384),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2... | NT | null | SUM | sympy | ONE_PHI_2 | [
"COMB1"
] | 567f58 | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"COMB1",
"ONE_PHI_2"
] | 2 | 1.763 | 2026-02-08T13:50:43.593985Z | {
"verified": true,
"answer": 75108,
"timestamp": "2026-02-08T13:50:45.357482Z"
} | bc4700 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 6127
},
"timestamp": "2026-02-11T08:00:50.160Z",
"answer": 75108
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
b5cb79 | antilemma_sum_equals_v1_655260480_3934 | Let $n$ be the number of integers $t$ with $21 \leq t \leq 189$ such that there exist positive integers $a \leq 5$ and $b \leq 19$ satisfying $t = 15a + 6b$. Compute the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 51$ and $1 \leq j \leq 51$ such that $i + j = n$. | 50 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.096 | 2026-02-08T17:37:40.515136Z | {
"verified": true,
"answer": 50,
"timestamp": "2026-02-08T17:37:40.611304Z"
} | be0e0a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 2761
},
"timestamp": "2026-02-18T05:11:30.230Z",
"answer": 50
},
{
... | 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": "LIN_F... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
1757e7 | algebra_vieta_sum_v1_1978505735_8314 | Let $r$ be the product of all real roots of the equation $x^3 + 12x^2 + 45x + 54 = 0$. Compute $\sum_{n=1}^{|r|} \phi(n)$, where $\phi$ denotes Euler's totient function. | 900 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=3)), Mul(Const(value=12), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=45), Var(name='x')), Const(value=54)), right=Const(value=0)))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"ONE_PHI_1"
] | 81fa00 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_1"
] | 2 | 0.033 | 2026-02-08T20:47:28.349850Z | {
"verified": true,
"answer": 900,
"timestamp": "2026-02-08T20:47:28.382582Z"
} | babf8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 2590
},
"timestamp": "2026-02-19T01:05:13.718Z",
"answer": 900
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c2f56b | geo_count_lattice_triangle_v1_601307018_10695 | Let $R \equiv 3a^5 - 3a^4 + a^3 - 2a^2 - 2a - 2 \pmod{169}$, $S \equiv 3R^5 - 3R^4 + R^3 - 2R^2 - 2R - 2 \pmod{169}$, and $T \equiv 3S^5 - 3S^4 + S^3 - 2S^2 - 2S - 2 \pmod{169}$. Let $K = \left|131 \cdot 120 + \min\{ -12a b + 20a^2 + 41b^2 : a, b \in \mathbb{Z}^+,\, 1 \leq a, b \leq 26 \} \cdot (-27)\right|$. Let $L = ... | 7,198 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(120),
"area_2x": Abs(arg=Sum(Mul(Const(value=131), Const(value=120)), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), right=Const(v... | GEOM | NT | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL",
"QF_PSD_MIN"
] | b699a8 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL",
"QF_PSD_MIN"
] | 2 | 0.012 | 2026-03-10T11:09:53.041157Z | {
"verified": true,
"answer": 7198,
"timestamp": "2026-03-10T11:09:53.053606Z"
} | d0c688 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 371,
"completion_tokens": 1762
},
"timestamp": "2026-04-19T14:33:20.623Z",
"answer": 7198
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
54e7d9 | modular_mod_compute_v1_168721529_2106 | Let $n = 126$. Define
$$
a = \sum_{k=1}^{126} \phi(k) \left\lfloor \frac{126}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function.
Let $r$ be the remainder when $a$ is divided by $12100$.
Compute the remainder when $44121 \cdot r$ is divided by $83549$. | 17,596 | graphs = [
Graph(
let={
"_n": Const(126),
"a": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(126), Var("k"))))),
"m": Const(12100),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Mod(value=M... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | modular_mod_compute_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T14:07:17.422146Z | {
"verified": true,
"answer": 17596,
"timestamp": "2026-02-08T14:07:17.423799Z"
} | 151f84 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2870
},
"timestamp": "2026-02-10T02:14:06.248Z",
"answer": 17596
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
3daf0a | comb_count_permutations_fixed_v1_1218484723_5408 | Let $D_n$ denote the number of derangements of $n$ elements. Let $n = 7$. Define $M = \sum_{k=0}^{2} (-1)^k \binom{2}{k}$, $m = \sum_{k=0}^{M} (-1)^k \binom{M}{k}$, $t = \sum_{k=0}^{11} (-1)^k \binom{11}{k}$, and $R = 7 + \binom{10}{10}$. Let $v = \sum_{k=0}^{R} (-1)^k \binom{R}{k}$. Let $k = (2 + v) \cdot m + t$. Comp... | 924 | graphs = [
Graph(
let={
"u": Const(7),
"n3": Sum(Ref("u"), Binom(n=Const(10), k=Const(10))),
"v": Summation(var="k1", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n3"), k=Var("k1")))),
"n2": Summation(var="k2", start=Sub(Bino... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N",
"ONE_BINOM_N"
] | 843369 | comb_count_permutations_fixed_v1 | null | 5 | 3 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N",
"ZERO_BINOM_N"
] | 3 | 0.006 | 2026-02-25T06:58:38.520691Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-25T06:58:38.526589Z"
} | af7e2d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 1407
},
"timestamp": "2026-03-29T20:57:07.269Z",
"answer": 924
},
{
"id... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
620b0a | algebra_quadratic_discriminant_v1_717093673_1926 | Compute $(-2)^2 - (-4) \cdot 10 \cdot k$, where $k$ is the number of positive integers $p$ for which there exists an integer $q$ such that $p < q$, $pq = 4500$, and $\gcd(p, q) = 1$. | 164 | graphs = [
Graph(
let={
"a": Const(-4),
"b": Const(-2),
"c": Const(10),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(... | NT | null | COMPUTE | sympy | B3 | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.016 | 2026-02-08T16:24:22.356537Z | {
"verified": true,
"answer": 164,
"timestamp": "2026-02-08T16:24:22.373008Z"
} | f429ff | 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": 1373
},
"timestamp": "2026-02-17T03:01:27.490Z",
"answer": 164
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
de63a3 | comb_binomial_compute_v1_1874849503_544 | Let $n = 14$ and let $k = \sum_{i=1}^{3} i$. Let $\text{result} = \binom{n}{k}$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16777216$. Compute the minimum value of $x + y$ over all elements of $S$, and subtract $\text{result}$ from this minimum. | 5,189 | graphs = [
Graph(
let={
"n": Const(14),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(I... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3",
"SUM_ARITHMETIC"
] | d67904 | comb_binomial_compute_v1 | negation_mod | 4 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.004 | 2026-02-08T13:09:38.901890Z | {
"verified": true,
"answer": 5189,
"timestamp": "2026-02-08T13:09:38.905675Z"
} | fd1e55 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 863
},
"timestamp": "2026-02-09T18:16:14.576Z",
"answer": 5189
},
{
"id... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
fefd55 | alg_poly_preperiod_count_v1_1218484723_1491 | For a non-negative integer $a$ with $0 \le a \le 48708$, define a sequence by $N = a^2 - 22 \bmod 67$, $M = N^2 - 22 \bmod 67$, $R = M^2 - 22 \bmod 67$, and $S = R^2 - 22 \bmod 67$. Find the number of values of $a$ such that $S = N$, $M \ne N$, and $R \ne N$. | 8,724 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-22)), modulus=Const(67)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-22)), modulus=Const(67)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-22)), modulus=Const(67)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.017 | 2026-02-25T03:11:59.294164Z | {
"verified": true,
"answer": 8724,
"timestamp": "2026-02-25T03:11:59.311130Z"
} | da9e14 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T04:14:39.623Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
eca23e | lte_diff_endings_v1_784195855_3520 | Let $a = 29$, $b = 1$, $p = 2$, and $n = 4$. Compute $a^n - b^n$, and let $v_p$ be the largest integer $k$ such that $p^k$ divides this difference. Let $k = 6480$. Compute the remainder when $k \cdot v_p$ is divided by $100000$. | 25,920 | graphs = [
Graph(
let={
"a_val": Const(29),
"b_val": Const(1),
"p_val": Const(2),
"n_val": Const(4),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("b_po... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T06:28:24.458588Z | {
"verified": true,
"answer": 25920,
"timestamp": "2026-02-08T06:28:24.459222Z"
} | 4f8723 | 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": "2026-02-19T09:10:01.514Z",
"answer": 25920
}
] | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
e3a47a | modular_count_residue_v1_2051736721_1232 | Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 19$, $1 \leq b \leq 5$, and let $T$ be the set of all integers $t$ such that $9 \leq t \leq 101$ and $t = 4a + 5b$ for some $(a,b) \in S$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive inte... | 1,451 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(73307),
"upper": Const(60000),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3",
"COPRIME_PAIRS"
] | f99a15 | modular_count_residue_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 4.751 | 2026-02-08T15:54:37.500513Z | {
"verified": true,
"answer": 1451,
"timestamp": "2026-02-08T15:54:42.251327Z"
} | c2d62c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 3471
},
"timestamp": "2026-02-16T16:04:54.647Z",
"answer": 1451
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5f521b | comb_count_partitions_v1_601307018_2501 | Let $M$ be the number of ordered pairs $(x_1, x_2)$ of positive integers such that $x_1 + x_2 = 4$, $x_1$ is odd, and $x_2$ is odd. Let $n = \sum_{k=0}^{M} 6^k$. Let $Q = p(n)$, where $p(n)$ denotes the number of partitions of $n$. Compute $Q$. | 63,261 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/SUM_GEOM"
] | 5bdb5a | comb_count_partitions_v1 | null | 4 | 0 | [
"COMB1",
"SUM_GEOM"
] | 2 | 0.007 | 2026-03-10T03:13:29.796580Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-03-10T03:13:29.803189Z"
} | 9684c7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 10076
},
"timestamp": "2026-03-29T05:31:51.412Z",
"answer": 63261
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
},
{
"lemma": "V8",
"status"... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
acee36 | antilemma_sum_equals_v1_1918700295_1781 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 84$, $1 \le i \le 82$, and $1 \le j \le 83$. Compute the value of $$
x + \phi\left(|x| + \binom{5}{0}\right) + \tau\left(|x| + 1\right),
$$
where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number of positiv... | 166 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(84)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(82)), right=IntegerRange(start=Const(1), end=Const(83))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | ec98de | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_0"
] | 2 | 0.008 | 2026-02-08T06:01:24.333467Z | {
"verified": true,
"answer": 166,
"timestamp": "2026-02-08T06:01:24.341410Z"
} | cf0ef1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 812
},
"timestamp": "2026-02-24T05:05:27.303Z",
"answer": 166
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
8c1e17 | alg_sym_quad_system_v1_1218484723_4276 | Find the remainder when $$\sum_{\substack{a^2 + b^2 + c^2 = ab + bc + ca \\ 4a + 9b + c = 2058 \\ a,b,c \ge 1}} (a^5 + b^5 + c^5)$$ is divided by $30 \times 317$. | 4,371 | graphs = [
Graph(
let={
"_n": Const(2058),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), ... | ALG | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | alg_sym_quad_system_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.014 | 2026-02-25T05:54:59.748088Z | {
"verified": true,
"answer": 4371,
"timestamp": "2026-02-25T05:54:59.761609Z"
} | a76ac3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 27630
},
"timestamp": "2026-03-29T14:47:59.510Z",
"answer": 5781
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
16b059 | alg_poly4_sum_v1_1218484723_2827 | Let $S = \{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 6, 1 \leq b \leq 17 \text{ such that } t = 21a + 9b, 30 \leq t \leq 279 \}$. Let $T = \min\{ x + y : x > 0, y > 0, xy = 18496 \}$. Let $A = \min\{ 124 b_1^3 + 60 a_1^2 b_1 - 210 a_1 b_1^2 + 98 a_1^3 : 1 \leq a_1, b_1 \leq 5 \}$. Compute the r... | 84,584 | graphs = [
Graph(
let={
"_c": Const(3),
"_m": Const(98),
"_n": Const(82),
"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"), MinOverSet(set=MapOverSet(se... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN",
"LIN_FORM",
"B3"
] | 79a0c1 | alg_poly4_sum_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"POLY3_MIN"
] | 3 | 0.034 | 2026-02-25T04:33:04.548545Z | {
"verified": true,
"answer": 84584,
"timestamp": "2026-02-25T04:33:04.582485Z"
} | 213738 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 362,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T06:53:28.585Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
ec834c | nt_count_digit_sum_v1_1248542787_413 | Let $n = 30$ and let $\text{upper} = 137641$. Let $\text{target\_sum}$ be the largest prime number less than or equal to $30$. Determine the value of $Q$, where $Q$ is the remainder when $67901$ multiplied by the number of positive integers $n$ with $1 \leq n \leq 137641$ and digit sum equal to $\text{target\_sum}$ is ... | 41,621 | graphs = [
Graph(
let={
"_n": Const(30),
"upper": Const(137641),
"target_sum": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n")... | NT | null | COUNT | sympy | C3 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"C3",
"MAX_PRIME_BELOW"
] | 2 | 10.104 | 2026-02-08T03:06:55.050891Z | {
"verified": true,
"answer": 41621,
"timestamp": "2026-02-08T03:07:05.154782Z"
} | 65a6c3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 6644
},
"timestamp": "2026-02-09T16:17:33.446Z",
"answer": 41621
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
d0b3ed | algebra_poly_eval_v1_1978505735_8338 | Let $$y = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. Compute the value of $4y^2 - 3y - 2$. | 1,699 | graphs = [
Graph(
let={
"_n": Const(2),
"y": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Sum(Mul(Const(4), Pow(Ref("y"), Ref("_n"))), Mul(Const(-3), Ref("y")), Const(-2)),
},
g... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T20:48:04.096658Z | {
"verified": true,
"answer": 1699,
"timestamp": "2026-02-08T20:48:04.099079Z"
} | de05d1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 584
},
"timestamp": "2026-02-16T18:54:22.154Z",
"answer": 1709
},
{
"id": 11,... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
dd6647 | antilemma_k2_v1_1080341949_483 | Let $n = 236$. Compute the value of $$\sum_{k=1}^{236} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 27,966 | graphs = [
Graph(
let={
"_n": Const(236),
"x": Summation(var="k", start=Const(1), end=Const(236), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Ref("x"),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:32:17.446237Z | {
"verified": true,
"answer": 27966,
"timestamp": "2026-02-08T13:32:17.446748Z"
} | 0a6701 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 487
},
"timestamp": "2026-02-15T17:20:58.063Z",
"answer": 27966
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f6f8ce | antilemma_k2_v1_1439011603_1284 | Let $x = \sum_{k=1}^{240} \phi(k) \left\lfloor \frac{240}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $d_i$ denote the $i$th decimal digit of $|x|$, starting from the units digit as $i = 0$. Compute
$$
\sum_{i=0}^{t-1} d_i (i+1)^2 + 71289,
$$
where $t$ is the number of decimal digits of $|x... | 71,556 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(240), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(240), Var("k"))))),
"Q": Sum(Summation(var="i", start=Sub(Const(70), Const(70)), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)), expr=Mul(... | NT | COMB | COMPUTE | sympy | IDENTITY_SUB_SELF | [
"IDENTITY_SUB_SELF",
"K2"
] | d684f6 | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_SUB_SELF",
"K2"
] | 2 | 0.004 | 2026-02-08T16:01:07.587572Z | {
"verified": true,
"answer": 71556,
"timestamp": "2026-02-08T16:01:07.591251Z"
} | b61fd9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 1133
},
"timestamp": "2026-02-16T18:40:57.798Z",
"answer": 71556
},
... | 1 | [
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bd288b | sequence_count_fib_divisible_v1_124444284_2923 | Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 6384$ and $16$ divides $k$. Let $u$ be the number of elements in $S$. Let $F_n$ denote the $n$-th Fibonacci number. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $19$ divides $F_n$. | 22 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(6384)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"d": Const(19),
"resu... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"C2"
] | 9685eb | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"C2",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.082 | 2026-02-08T05:04:32.621440Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T05:04:32.703435Z"
} | 448ec9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1287
},
"timestamp": "2026-02-11T22:52:02.867Z",
"answer": 22
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
6b9325 | comb_bell_compute_v1_784195855_7912 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 4240$ such that $\binom{4240}{j}$ is odd. Compute the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4240)), Eq(Mod(value=Binom(n=Const(4240), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T09:36:53.739001Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T09:36:53.739738Z"
} | 5cf003 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 730
},
"timestamp": "2026-02-24T11:34:59.197Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
596ca6 | antilemma_k2_v1_124444284_594 | Let $S$ be the set of all integers $x$ such that $x^2 - 67x - 10434 = 0$. Let $n$ be the sum of all elements in $S$. Compute $\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{67}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. | 2,278 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-67), Var("x")), Const(-10434)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(67), Var("k"... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T03:22:45.692644Z | {
"verified": true,
"answer": 2278,
"timestamp": "2026-02-08T03:22:45.693452Z"
} | 29b733 | 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": 4510
},
"timestamp": "2026-02-09T19:33:50.700Z",
"answer": 2278
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma":... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e3671c | nt_count_digit_sum_v1_151522320_722 | Let $n$ be a positive integer. Define $A$ as the set of all integers $n$ such that $1 \leq n \leq 19996$ and the sum of the digits of $n$ leaves a remainder of 1 when divided by 2. Let $u$ be the number of elements in $A$. Define $B$ as the set of all integers $n$ such that $1 \leq n \leq u$ and the sum of the digits o... | 415 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19996)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"target_sum": Const(24),
"result... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | nt_count_digit_sum_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.709 | 2026-02-08T03:28:25.837921Z | {
"verified": true,
"answer": 415,
"timestamp": "2026-02-08T03:28:26.547080Z"
} | f5ea70 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 5058
},
"timestamp": "2026-02-10T14:34:33.354Z",
"answer": 415
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
d2e017 | sequence_fibonacci_compute_v1_1431428450_993 | Let $n$ be the number of integers $t$ in the interval $[9, 36]$ that can be expressed in the form $7a + 2b$ for positive integers $a \le 2$ and $b \le 11$. Compute the $n$-th Fibonacci number. | 17,711 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:50:53.059479Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T13:50:53.062559Z"
} | ae68f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1298
},
"timestamp": "2026-02-15T21:26:24.882Z",
"answer": 17711
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8b6c6b | sequence_count_fib_divisible_v1_124444284_314 | Let $d$ be the largest positive divisor of $497718$ that is less than or equal to $702$. Let $r$ be the number of positive integers $n$, where $1 \leq n \leq d$, such that $6$ divides the $n$-th Fibonacci number.
Let $c$ be the number of positive integers $n$, where $1 \leq n \leq 20999$, such that $\gcd(n, 14) = 1$.
... | 13,640 | graphs = [
Graph(
let={
"_n": Const(20999),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(702)), Divides(divisor=Var("d"), dividend=Const(497718))))),
"d": Const(6),
"result": CountOverSet(set=Sol... | NT | null | COUNT | sympy | C4 | [
"C4",
"MAX_DIVISOR"
] | c42700 | sequence_count_fib_divisible_v1 | quadratic_mod | 5 | 0 | [
"C4",
"MAX_DIVISOR"
] | 2 | 0.041 | 2026-02-08T03:10:30.689933Z | {
"verified": true,
"answer": 13640,
"timestamp": "2026-02-08T03:10:30.731294Z"
} | a66f26 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 2584
},
"timestamp": "2026-02-09T15:59:01.941Z",
"answer": 13640
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
83238e | modular_count_residue_v1_397696148_2159 | Let $m$ be the number of positive integers $n \leq 33$ such that $\gcd(n, 10) = 1$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 3000$ and $\gcd(p, q) = 1$. Let $N$ be the number of positive integers $n \leq 31333$ such that $n \equiv r \pmod{m}$. Find... | 54,628 | graphs = [
Graph(
let={
"upper": Const(31333),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(33)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"r": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(I... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"C4"
] | 8c7df5 | modular_count_residue_v1 | null | 6 | 0 | [
"C4",
"COPRIME_PAIRS"
] | 2 | 4.004 | 2026-02-08T12:58:18.764212Z | {
"verified": true,
"answer": 54628,
"timestamp": "2026-02-08T12:58:22.767947Z"
} | 7980dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 2148
},
"timestamp": "2026-02-15T08:15:11.350Z",
"answer": 54628
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
74c1df | nt_count_gcd_equals_v1_397696148_1564 | Let $N = 5178$, and let $U$ be the largest prime number less than or equal to $N$. Let $k$ be the number of integers $t$ with $21 \leq t \leq 891$ that can be expressed as $t = 12a + 9b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 3$ and $1 \leq b \leq 95$. Let $D$ be the number of positive integers $n \leq... | 326 | graphs = [
Graph(
let={
"_n": Const(5178),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condit... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.406 | 2026-02-08T12:38:55.360218Z | {
"verified": true,
"answer": 326,
"timestamp": "2026-02-08T12:38:55.766364Z"
} | 6f3496 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 3434
},
"timestamp": "2026-02-15T03:08:53.604Z",
"answer": 326
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f13db5 | geo_count_lattice_rect_v1_168721529_634 | Let $a = 169$ and $b = 500$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. | 85,170 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(500),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.166 | 2026-02-08T13:10:11.327431Z | {
"verified": true,
"answer": 85170,
"timestamp": "2026-02-08T13:10:11.493305Z"
} | 9d9390 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 209
},
"timestamp": "2026-02-09T07:13:08.360Z",
"answer": 85170
},
{
"i... | 1 | [] | {
"lo": -7.19,
"mid": -5.01,
"hi": -3.03
} | ||||
0a6b46 | algebra_quadratic_discriminant_v1_717093673_2420 | Define $a$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $b = -1$ and $c = -1$. Define $\Delta = b^2 - 4ac$. Compute the remainder when $25299 \cdot \Delta$ is divided by 78772. | 70,147 | graphs = [
Graph(
let={
"_n": Const(4),
"a": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:50:04.971487Z | {
"verified": true,
"answer": 70147,
"timestamp": "2026-02-08T16:50:04.973074Z"
} | e951b0 | 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": 844
},
"timestamp": "2026-02-17T12:29:30.227Z",
"answer": 70147
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
331e9f | comb_count_partitions_v1_1218484723_235 | Let $n$ be the number of integers $t$ in the range $19 \le t \le 64$ that can be expressed as $t = 3a + 5b + 11$ for some integers $a, b$ with $1 \le a \le 11$ and $1 \le b \le 4$. Compute $p(n)$, where $p(n)$ denotes the number of partitions of $n$ into positive integers. | 26,015 | 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 | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-25T01:55:10.847187Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-25T01:55:10.848224Z"
} | 4bef41 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2885
},
"timestamp": "2026-03-10T09:04:46.565Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
2b8d51 | nt_num_divisors_compute_v1_238844314_1088 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Define $m$ as the minimum value of $x + y$ over all pairs in $S$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $m$, where $\phi$ denotes Euler's totient function. Define $r$ as the number of positive divi... | 119 | graphs = [
Graph(
let={
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))),
"n": SumOverDiv... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"B3/K3"
] | 4a4ef2 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B3",
"K3",
"ONE_PHI_1"
] | 3 | 0.036 | 2026-02-08T13:54:35.447371Z | {
"verified": true,
"answer": 119,
"timestamp": "2026-02-08T13:54:35.483294Z"
} | 04c710 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 2085
},
"timestamp": "2026-02-15T22:48:18.329Z",
"answer": 119
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"le... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
de3e9b | nt_max_prime_below_v1_784195855_4999 | Let $T$ be the set of all positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 108$ and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $T$. Let $R$ be the set of all prime numbers $n$ such that $m \le n \le 17424$. Let $M$ be the largest element of $R$. Let $S$ be the set of all in... | 56,245 | 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 | LIN_FORM | [
"LIN_FORM",
"COPRIME_PAIRS"
] | e30a8c | nt_max_prime_below_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.559 | 2026-02-08T07:32:46.955778Z | {
"verified": true,
"answer": 56245,
"timestamp": "2026-02-08T07:32:47.514279Z"
} | 66c1cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2976
},
"timestamp": "2026-02-13T11:16:59.203Z",
"answer": 56245
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VA... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
095c04 | antilemma_k3_v1_865884756_3220 | Let $n = 12969$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 12,969 | graphs = [
Graph(
let={
"_n": Const(12969),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:14:42.346353Z | {
"verified": true,
"answer": 12969,
"timestamp": "2026-02-08T17:14:42.346934Z"
} | 76a8ae | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 511
},
"timestamp": "2026-02-16T09:13:36.600Z",
"answer": 6917
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
fe5523 | nt_count_gcd_equals_v1_655260480_1585 | Let $n$ be a positive integer such that $1 \leq n \leq 28657$. Let $k$ be the smallest integer greater than or equal to 2 that divides 5543093. Suppose $d = 173$. Determine the number of such integers $n$ for which $\gcd(n, k) = d$. Compute this number. | 165 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(28657),
"k": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Ref("_n")), Divides(divisor=Var("d1"), dividend=Const(5543093))))),
"d": Const(173),
"result": CountOverSet(... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.568 | 2026-02-08T16:13:41.741005Z | {
"verified": true,
"answer": 165,
"timestamp": "2026-02-08T16:13:44.308613Z"
} | 268d72 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 591
},
"timestamp": "2026-02-16T07:11:00.232Z",
"answer": 165
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
423ef6 | comb_binomial_compute_v1_349078426_854 | Let $D$ be the set of all positive divisors $d$ of $4672$ such that $1 \leq d \leq 64$. Let $m$ be the largest element of $D$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = m$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when $\binom{n}{8} \... | 7,990 | graphs = [
Graph(
let={
"_m": Const(64),
"_n": Const(66961),
"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")), MaxOverSet(set=So... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/B3"
] | 51e324 | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.004 | 2026-02-08T13:18:33.300929Z | {
"verified": true,
"answer": 7990,
"timestamp": "2026-02-08T13:18:33.304580Z"
} | c88cac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2735
},
"timestamp": "2026-02-15T12:34:17.913Z",
"answer": 7990
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3006d6 | nt_max_prime_below_v1_1125832087_1091 | Let $C$ be the number of positive integers $p$ for which there exist positive integers $q$ satisfying $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Let $S$ be the set of all prime numbers $n$ such that $C \le n \le 53824$. Let $R$ be the largest element of $S$. Compute the remainder when $21904 - R$ is divided by 60758. | 28,843 | graphs = [
Graph(
let={
"upper": Const(53824),
"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 | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.717 | 2026-02-08T03:31:02.954866Z | {
"verified": true,
"answer": 28843,
"timestamp": "2026-02-08T03:31:05.671432Z"
} | 9dadd1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 3393
},
"timestamp": "2026-02-10T13:45:36.033Z",
"answer": 28843
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
3f25b4 | alg_poly_preperiod_count_v1_601307018_1686 | Let $N = (a^2 - 31) \bmod 73$, $M = (N^2 - 31) \bmod 73$, $R = (M^2 - 31) \bmod 73$, $S = (R^2 - 31) \bmod 73$, and $T = (S^2 - 31) \bmod 73$. Find the number of non-negative integers $a$ with $0 \le a \le 18176$ such that $T = N$, $M \ne N$, $R \ne N$, and $S \ne N$. | 3,984 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-31)), modulus=Const(73)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-31)), modulus=Const(73)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-31)), modulus=Const(73)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.019 | 2026-03-10T02:27:40.114323Z | {
"verified": true,
"answer": 3984,
"timestamp": "2026-03-10T02:27:40.133698Z"
} | 4d31f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 17626
},
"timestamp": "2026-03-29T03:09:41.210Z",
"answer": 1494
},
{
... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
332641 | modular_mod_compute_v1_1125832087_857 | Let $a = 10946$. Let $m$ be the number of integers $t$ in the range $8 \leq t \leq 2237$ for which there exist positive integers $a$ and $b$ with $1 \leq a \leq 34$, $1 \leq b \leq 689$, and $t = 5a + 3b$. Compute the remainder when $a$ is divided by $m$. | 2,058 | graphs = [
Graph(
let={
"a": Const(10946),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=34)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:20:44.710779Z | {
"verified": true,
"answer": 2058,
"timestamp": "2026-02-08T03:20:44.714036Z"
} | 42b70a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 4994
},
"timestamp": "2026-02-10T14:01:01.776Z",
"answer": 42
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",... | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
20d353 | comb_count_derangements_v1_1419126231_786 | Let $D_n$ denote the number of derangements of $n$ elements. Let $n$ be the number of integers $t$ such that $5 \leq t \leq 14$ and $t = 2a + 3b$ for some integers $a,b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$. Let $R = D_n$. Find the remainder when $16579 \cdot R$ is divided by $55536$. | 2,899 | graphs = [
Graph(
let={
"_n": Const(55536),
"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=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T10:16:38.365280Z | {
"verified": true,
"answer": 2899,
"timestamp": "2026-02-25T10:16:38.367191Z"
} | 0b27be | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 2112
},
"timestamp": "2026-03-30T09:58:58.640Z",
"answer": 2899
},
{
"i... | 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": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
973f78 | geo_count_lattice_triangle_v1_1439011603_162 | Let $A$ be the area of the triangle with vertices at $(128, 64)$, $(36, 111)$, and $(0, 0)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each side of the triangle:
- $\gcd(|128 - 0|, |64 - 0|)$,
- $\gcd(|36 - 128|, |111 - 64|)$,
... | 66,442 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=111)), Mul(Const(value=36), Sub(left=Const(value=0), right=Const(value=64))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=64))), GCD(a=Abs(arg=Sub(left=Const(value=36), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.005 | 2026-02-08T15:18:03.604876Z | {
"verified": true,
"answer": 66442,
"timestamp": "2026-02-08T15:18:03.609628Z"
} | 0e249b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 806
},
"timestamp": "2026-02-16T03:47:37.691Z",
"answer": 66442
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
37c38b | antilemma_sum_equals_v1_458359167_449 | Let $m$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 6$ and $1 \leq b \leq 29$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Define $x$ to be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 85$ and $1 \leq j \leq 85$ such that $i + j ... | 391 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(29)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 9b4db5 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.005 | 2026-02-08T03:19:59.428000Z | {
"verified": true,
"answer": 391,
"timestamp": "2026-02-08T03:19:59.432709Z"
} | f3eb3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 5680
},
"timestamp": "2026-02-23T22:11:45.951Z",
"answer": 391
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
27ce34 | antilemma_cartesian_v1_1978505735_3824 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 22$ and $1 \leq b \leq 37$. Compute $x + \phi(|x| + \binom{5}{5}) + \tau(|x| + 1)$, where $\phi(n)$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. | 1,466 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(22)), right=IntegerRange(start=Const(1), end=Const(37)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Binom(n=Const(5), k=Const(5)))), NumDivisors(n=Sum(Abs(arg=R... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | f14704 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | 2 | 0.002 | 2026-02-08T17:52:15.705271Z | {
"verified": true,
"answer": 1466,
"timestamp": "2026-02-08T17:52:15.707019Z"
} | 972cab | 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": 597
},
"timestamp": "2026-02-24T23:08:03.289Z",
"answer": 1466
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"sta... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
cf83c9 | comb_binomial_compute_v1_1248542787_488 | Let $n$ be the number of nonnegative integers $j$ such that $\binom{664}{j}$ is odd and $j \le m$, where $m$ is the smallest positive integer for which $2^{660}$ divides $m!$. Compute $\binom{n}{9}$. | 11,440 | graphs = [
Graph(
let={
"_m": Const(660),
"_n": Const(664),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(2))... | NT | null | COMPUTE | sympy | V5 | [
"V5/V8"
] | 1e58c2 | comb_binomial_compute_v1 | null | 7 | 0 | [
"V5",
"V8"
] | 2 | 0.003 | 2026-02-08T03:10:25.266516Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T03:10:25.269113Z"
} | 57dc4a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2075
},
"timestamp": "2026-02-09T04:41:27.612Z",
"answer": 11440
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
},
{
"lemma": "V8",
"status": "ok_later"
},
{
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
c96e57 | comb_count_surjections_v1_124444284_9301 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 9$, where $1 \le i \le 7$ and $1 \le j \le 8$. Let $k = 3$. Compute $k! \cdot S(n,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Report the result as an integer. | 1,806 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(9)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(8))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T12:21:52.463800Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T12:21:52.476142Z"
} | 4d17d6 | 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": 1163
},
"timestamp": "2026-02-24T15:38:25.346Z",
"answer": 1806
},
{
"i... | 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": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
734f58 | nt_sum_over_divisible_v1_458359167_969 | Let $N = 44121$. Let $d$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 6$ and $\gcd(p, q) = 1$. Let $S$ be the set of all positive integers $n \leq 21609$ such that $n$ is divisible by $d$. Let $T$ be the sum of all elements in $S$. Find the remainder when $N \... | 24,510 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(21609),
"divisor": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)),... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.393 | 2026-02-08T04:12:43.418923Z | {
"verified": true,
"answer": 24510,
"timestamp": "2026-02-08T04:12:44.811761Z"
} | ad6d21 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1860
},
"timestamp": "2026-02-10T15:52:41.131Z",
"answer": 24510
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
1929bb | nt_min_crt_v1_458359167_2933 | Let $m = 9$ and $k = 11$. Let $a = 1$ and $b = 4$. Let $\text{upper}$ be the number of integers $t$ with $22 \leq t \leq 242$ such that there exist positive integers $a \leq 7$ and $b \leq 21$ satisfying $t = 10a + 8b + 4$. Determine the value of the smallest positive integer $n \leq \text{upper}$ such that $n \equiv a... | 37 | graphs = [
Graph(
let={
"m": Const(9),
"k": Const(11),
"a": Const(1),
"b": Const(4),
"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'), ... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"LIN_FORM"
] | 7b2633 | nt_min_crt_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.03 | 2026-02-08T06:50:33.030324Z | {
"verified": true,
"answer": 37,
"timestamp": "2026-02-08T06:50:33.060161Z"
} | 5f8660 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 585
},
"timestamp": "2026-02-15T17:48:27.841Z",
"answer": 19
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
97dc89 | nt_count_intersection_v1_1918700295_3980 | Let $N$ be the number of positive integers $n \leq 20001$ such that the sum of the digits of $n$ is even. Let $S$ be the set of positive divisors $d$ of $543165$ that are at least $1$ and at most $735$. Define $a$ to be the smallest integer $d \geq 2$ that divides the maximum element of $S$. Let $b = 16$. Compute the n... | 1,667 | graphs = [
Graph(
let={
"_n": Const(2),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(20001)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), co... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/MIN_PRIME_FACTOR",
"L3B"
] | 0680cd | nt_count_intersection_v1 | null | 5 | 0 | [
"L3B",
"MAX_DIVISOR",
"MIN_PRIME_FACTOR"
] | 3 | 0.916 | 2026-02-08T09:04:20.797607Z | {
"verified": true,
"answer": 1667,
"timestamp": "2026-02-08T09:04:21.713214Z"
} | 577be9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 2219
},
"timestamp": "2026-02-14T00:02:25.814Z",
"answer": 1667
},
{... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2a9d83 | sequence_fibonacci_compute_v1_1742523217_3922 | Let $n$ be the smallest divisor of $317205857$ that is at least $2$. Compute the $n$th Fibonacci number. | 28,657 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(317205857))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T06:08:42.041318Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T06:08:42.042184Z"
} | f053d0 | 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": 923
},
"timestamp": "2026-02-12T20:02:31.036Z",
"answer": 28657
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a161a1 | modular_modexp_compute_v1_971394319_1119 | Let $e$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 128$. Let $a = 19$ and $m = 66666$. Compute $r = a^e \bmod m$, and let $s = |r|$. Finally, let $Q$ be the Bell number $B_t$, where $t = s \bmod 11$. Find the value of $Q$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(128),
"a": Const(19),
"e": 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=M... | NT | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 7 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T13:30:26.907378Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T13:30:26.909130Z"
} | 65bd54 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 2594
},
"timestamp": "2026-02-15T16:33:38.259Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
fee7b6 | sequence_fibonacci_compute_v1_677425708_3564 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 100$. Let $F_n$ denote the $n$th Fibonacci number, defined by $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $B_k$ denote the $k$th Bell number, which counts the number of partitions of a set of $k$ elemen... | 1 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T05:49:11.152686Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T05:49:11.153642Z"
} | 122735 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 727
},
"timestamp": "2026-02-24T04:38:37.258Z",
"answer": 1
},
{
"id": ... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
9687ef | algebra_poly_eval_v1_153355830_2200 | Let $b = 17$. Define $r$ to be the result of the expression
$$
\left(60^2 \cdot \text{the number of positive integers } k \text{ such that } 1 \leq k \leq 240 \text{ and } 60 \mid k\right) + b - 10.
$$
Let $Q$ be the Bell number $B_{|r| \mod 11}$, where $B_n$ denotes the number of partitions of a set of size $n$. Compu... | 4,140 | graphs = [
Graph(
let={
"b": Const(17),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(240)), Divides(divisor=Const(60), dividend=Var("k"))), domain='positive_integers')), Pow(Ref("b"), Const(2))), Ref("b"), Co... | COMB | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | algebra_poly_eval_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T06:58:47.436344Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T06:58:47.438303Z"
} | 5b7c7f | 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": 685
},
"timestamp": "2026-02-13T06:43:18.496Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fecd6a | antilemma_coprime_grid_v1_168721529_220 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 24$, $1 \leq j \leq 176$, and $\gcd(i,j) = 1$. Compute the number of elements in $S$. | 2,607 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(24)), right=IntegerRange(start=Const(1), end=Const(176))))),
},
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T12:54:22.408441Z | {
"verified": true,
"answer": 2607,
"timestamp": "2026-02-08T12:54:22.409203Z"
} | 201ea6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1859
},
"timestamp": "2026-02-09T02:39:02.942Z",
"answer": 2607
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status"... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
119649 | nt_sum_divisors_mod_v1_2051736721_4566 | Let $n = 7560$. Define $\sigma$ to be the sum of all positive divisors of $n$. Let $M = 10069$. Compute the remainder when $\sigma$ is divided by $M$; call this value $r$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 154$. Determine the value of $$
Q = (r^2 + 10r +... | 35,746 | graphs = [
Graph(
let={
"_n": Const(10),
"n": Const(7560),
"M": Const(10069),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var(... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 0a3d6e | nt_sum_divisors_mod_v1 | quadratic_mod | 4 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T18:02:36.266820Z | {
"verified": true,
"answer": 35746,
"timestamp": "2026-02-08T18:02:36.271168Z"
} | 4b6738 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1488
},
"timestamp": "2026-02-18T12:12:53.056Z",
"answer": 35746
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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