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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
c9b2f3 | sequence_fibonacci_compute_v1_458359167_1478 | Let $t$ be an integer. Consider the set of all integers $t$ such that $27 \leq t \leq 114$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 12$, $1 \leq b \leq 2$, and $t = 6a + 21b$. Let $n$ be the number of elements in this set.
Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defin... | 46,368 | 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=12)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:37:44.627250Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T04:37:44.628288Z"
} | 46d7b8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 1286
},
"timestamp": "2026-02-10T17:21:28.261Z",
"answer": 46368
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
823a9e | nt_count_coprime_v1_1439011603_539 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 37$ and $t = 2a + 5b$ for some integers $a$ with $1 \leq a \leq 11$ and $b$ with $1 \leq b \leq 3$. Let $k$ be the number of elements in $T$. Let $R$ be the set of all integers $n$ such that $1 \leq n \leq 74529$ and $\gcd(n, k) = 1$. Let $r$ be the number... | 43,663 | graphs = [
Graph(
let={
"_n": Const(72312),
"upper": Const(74529),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'),... | NT | COMB | COUNT | sympy | K2 | [
"LIN_FORM"
] | 1ae498 | nt_count_coprime_v1 | bell_mod | 6 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 31.967 | 2026-02-08T15:33:11.197387Z | {
"verified": true,
"answer": 43663,
"timestamp": "2026-02-08T15:33:43.164533Z"
} | 4ed23e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 1839
},
"timestamp": "2026-02-16T08:00:46.477Z",
"answer": 43663
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
072e58 | diophantine_fbi2_count_v1_1918700295_2360 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14400$. Let $k$ be the minimum value of $x + y$ over all such pairs. Compute the number of integers $d$ such that $2 \leq d \leq 91$, $d$ divides $k$, $\frac{k}{d} \geq 2$, and $\frac{k}{d} \leq \sum_{k=1}^{13} k$. | 16 | graphs = [
Graph(
let={
"_n": Const(13),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14400)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | dee757 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.008 | 2026-02-08T07:50:59.101374Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T07:50:59.109711Z"
} | ecdb0f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1379
},
"timestamp": "2026-02-13T12:50:30.596Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ca8ccd | diophantine_fbi2_min_v1_1520064083_7467 | Let $d$ be the smallest integer such that $2 \leq d \leq 36$, $d$ divides 26, and $\frac{26}{d} \geq 4$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|d| + 2$. | 6 | graphs = [
Graph(
let={
"k": Const(26),
"upper": Const(36),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4))))),
... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"K2"
] | 6897ab | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.093 | 2026-02-08T09:03:39.666362Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T09:03:39.759483Z"
} | 01a25d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 544
},
"timestamp": "2026-02-13T23:38:30.785Z",
"answer": 6
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9fcfb1 | nt_min_coprime_above_v1_971394319_2022 | Let $n$ be a positive integer. Define $\phi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $S$ be the set of all positive divisors of $8331$. Define $$A = \sum_{d \in S} \phi(d).$$ Let $B = 8192$ and $M = 129$. Consider the set of all integers $n$ such that $n ... | 14,122 | graphs = [
Graph(
let={
"start": Const(8192),
"upper": SumOverDivisors(n=Const(value=8331), var='d', expr=EulerPhi(n=Var(name='d'))),
"modulus": Const(129),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("... | NT | null | EXTREMUM | sympy | K3 | [
"K3"
] | 54c41e | nt_min_coprime_above_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.026 | 2026-02-08T14:05:38.472866Z | {
"verified": true,
"answer": 14122,
"timestamp": "2026-02-08T14:05:38.499007Z"
} | 24b81d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1536
},
"timestamp": "2026-02-16T00:11:51.531Z",
"answer": 14122
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1b7e84 | nt_count_intersection_v1_124444284_3955 | Let $N$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 200$. Let $a = 11$ and $b = 12$. Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq N$, $11$ divides $n$, and $\gcd(n, 12) = 1$. Let $Q$ be the remainder when $24923 \cdot \text{re... | 46,685 | graphs = [
Graph(
let={
"_n": Const(200),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_intersection_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.328 | 2026-02-08T05:41:28.454089Z | {
"verified": true,
"answer": 46685,
"timestamp": "2026-02-08T05:41:28.781731Z"
} | 4ac964 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1338
},
"timestamp": "2026-02-12T12:52:25.335Z",
"answer": 46685
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
7e3edb | nt_count_coprime_v1_168721529_55 | Let $\binom{n}{k}$ denote the binomial coefficient. Define
$$
S = \left\{ j \in \mathbb{Z}_{\geq 0} \mid 0 \leq j \leq 66565 \text{ and } \binom{66565}{j} \text{ is odd} \right\},
$$
and let $k = |S| + 5$.
Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 78400$ and $\gcd(n, k) = 1$.
Find th... | 44,800 | graphs = [
Graph(
let={
"_n": Const(66565),
"upper": Const(78400),
"k": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(66565)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2",
"V8"
] | 299d97 | nt_count_coprime_v1 | null | 6 | 0 | [
"ONE_PHI_2",
"V8"
] | 2 | 6.986 | 2026-02-08T12:47:20.851990Z | {
"verified": true,
"answer": 44800,
"timestamp": "2026-02-08T12:47:27.838367Z"
} | ce3b85 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 1259
},
"timestamp": "2026-02-08T20:59:38.973Z",
"answer": 44800
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": 1.49,
"mid": 4.54,
"hi": 7.77
} | ||
f5bdd7 | sequence_lucas_compute_v1_784195855_509 | Let $n$ be the sum of all positive integers at most $20$ that are divisible by $20$. Compute the $n$-th Lucas number. | 15,127 | graphs = [
Graph(
let={
"_n": Const(20),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(20)), Const(0))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Re... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T04:25:06.543322Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T04:25:06.544214Z"
} | c8a0b8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 818
},
"timestamp": "2026-02-10T16:30:19.667Z",
"answer": 15127
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
369eff | nt_count_intersection_v1_1440796553_702 | Let $N = 5000$, $a = 11$, $b = 10$, and $m = 307$. Consider the set of all integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. Let $r$ be the number of elements in this set. Let $p$ be the largest prime number less than or equal to $319$. Compute the remainder when $r + 5003 \cdot (r \bmod ... | 42,471 | graphs = [
Graph(
let={
"_n": Const(307),
"N": Const(5000),
"a": Const(11),
"b": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_intersection_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.168 | 2026-02-08T11:55:24.980518Z | {
"verified": true,
"answer": 42471,
"timestamp": "2026-02-08T11:55:25.148849Z"
} | 372270 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1202
},
"timestamp": "2026-02-14T20:44:55.412Z",
"answer": 42471
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5f497d | comb_binomial_compute_v1_124444284_8658 | Let $n_2 = 9$. Define $e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = e$. Define $v = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 16v$. Compute $\binom{n}{7}$. | 11,440 | graphs = [
Graph(
let={
"n2": Const(9),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("e"),
"v": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T11:51:37.058541Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T11:51:37.059485Z"
} | 5896eb | 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": 760
},
"timestamp": "2026-02-24T14:52:52.730Z",
"answer": 11440
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
deb5b0 | nt_min_crt_v1_151522320_267 | Determine the value of the smallest positive integer $n$ such that $1 \leq n \leq 63$, $n \equiv 4 \pmod{7}$, and $n \equiv 5 \pmod{9}$. | 32 | graphs = [
Graph(
let={
"m": Const(7),
"k": Const(9),
"a": Const(4),
"b": Const(5),
"upper": Const(63),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"COUNT_FIB_DIVISIBLE/B1/B3"
] | c2689b | nt_min_crt_v1 | null | 4 | 0 | [
"B1",
"B3",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 4 | 0.089 | 2026-02-08T03:07:01.829259Z | {
"verified": true,
"answer": 32,
"timestamp": "2026-02-08T03:07:01.918560Z"
} | 4f0e48 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 352
},
"timestamp": "2026-02-10T13:06:16.723Z",
"answer": 32
},
{
"id":... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
6c34ef | antilemma_cartesian_v1_1470522791_318 | Let $ x $ be the number of ordered pairs $ (i,j) $ such that $ 1 \leq i \leq 10 $ and $ 1 \leq j \leq 41 $. Compute the smallest positive integer $ k $ such that the $ k $-th Fibonacci number is divisible by $ |x| + 2 $. | 312 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(41)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T12:56:39.130085Z | {
"verified": true,
"answer": 312,
"timestamp": "2026-02-08T12:56:39.131212Z"
} | 298725 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 5244
},
"timestamp": "2026-02-24T16:41:30.907Z",
"answer": 312
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
368cbe | antilemma_sum_equals_v1_1439011603_1193 | Let $m = 44$. Define $a$ to be the number of ordered pairs $(i, j)$ of integers with $1 \leq i, j \leq 44$ such that $i + j = m$. Let $b$ be the number of ordered pairs $(i_1, j_1)$ of integers with $1 \leq i_1, j_1 \leq 41$ such that $i_1 + j_1 = a$. Let $S$ be the set of all integers $t$ with $5 \leq t \leq 17$ for w... | 877 | graphs = [
Graph(
let={
"_m": Const(44),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(44)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/LIN_FORM/COUNT_SUM_EQUALS",
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | a98aaf | antilemma_sum_equals_v1 | bell_mod | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.025 | 2026-02-08T15:58:03.138385Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T15:58:03.163314Z"
} | 8aab6c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 1151
},
"timestamp": "2026-02-24T19:04:15.485Z",
"answer": 877
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
35bdbf | alg_qf_psd_sum_v1_1218484723_6042 | Let $m = \min\{ 5a_1^2 - 8a_1b_1 + 32b_1^2 \mid a_1, b_1 \in \mathbb{Z},\ 1 \le a_1, b_1 \le 8 \}$. Compute the remainder when $\sum_{a=1}^{m} \sum_{b=1}^{29} (26a^2 - 4ab + 10b^2)$ is divided by $95607$. | 47,925 | graphs = [
Graph(
let={
"_n": Const(95607),
"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(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1"... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_qf_psd_sum_v1 | null | 4 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.01 | 2026-02-25T07:40:37.487933Z | {
"verified": true,
"answer": 47925,
"timestamp": "2026-02-25T07:40:37.497743Z"
} | daa835 | 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": 2557
},
"timestamp": "2026-03-29T23:58:33.322Z",
"answer": 47925
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
888fa6 | comb_count_permutations_fixed_v1_601307018_6637 | Let $D_n$ denote the number of derangements of $n$ elements. Compute the remainder when $72785 \cdot \binom{9}{6} D_{3}$ is divided by $61278$. | 33,558 | graphs = [
Graph(
let={
"n": Const(9),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"_c": Const(72785),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(6127... | COMB | null | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/HALFPLANE_COUNT"
] | 2ad970 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"HALFPLANE_COUNT",
"POLY_ORBIT_HENSEL"
] | 2 | 0.083 | 2026-03-10T07:17:38.246607Z | {
"verified": true,
"answer": 33558,
"timestamp": "2026-03-10T07:17:38.329744Z"
} | 37742c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 899
},
"timestamp": "2026-04-19T04:55:14.259Z",
"answer": 33558
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "HALFPLANE_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
b1a407 | nt_num_divisors_compute_v1_1520064083_10298 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 51$. Let $d$ be the number of positive divisors of $n$. Compute $13762 \cdot d$. | 27,524 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(51)), IsPrime(Var("n"))))),
"result": NumDivisors(n=Ref("n")),
"_c": Const(13762),
"Q": Mul(Ref("_c")... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T11:20:45.525183Z | {
"verified": true,
"answer": 27524,
"timestamp": "2026-02-08T11:20:45.527351Z"
} | fbeb67 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 330
},
"timestamp": "2026-02-15T21:44:50.894Z",
"answer": 27524
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status"... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
54987f | nt_count_gcd_equals_v1_677425708_2978 | Let $N$ be the number of positive integers $n \leq 30000$ such that $\gcd(n, 408) = 8$. Let $p_{\max}$ be the largest prime number at most $308$. Let $A = N \bmod p_{\max}$ and $B = N \bmod 317$. Compute the remainder when $A + 7001B$ is divided by $86188$. | 76,458 | graphs = [
Graph(
let={
"upper": Const(30000),
"k": Const(408),
"d": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
"... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_gcd_equals_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.434 | 2026-02-08T05:24:46.724905Z | {
"verified": true,
"answer": 76458,
"timestamp": "2026-02-08T05:24:49.159045Z"
} | 6ac3e2 | 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": 1899
},
"timestamp": "2026-02-12T08:46:53.791Z",
"answer": 76458
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
82bac8 | antilemma_k3_v1_2051736721_3099 | Let $x = \sum_{d \mid 37402} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $78728 \cdot x$ is divided by 51347. | 39,594 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=37402), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(78728),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(51347)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:06:44.604258Z | {
"verified": true,
"answer": 39594,
"timestamp": "2026-02-08T17:06:44.604799Z"
} | dd86e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 1078
},
"timestamp": "2026-02-17T19:05:48.576Z",
"answer": 39594
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
edfb4d | comb_factorial_compute_v1_865884756_2699 | Let $m = 5929$. Let $d$ be the smallest integer such that $d \geq 2$ and $d$ divides $m$. Let $r = d!$. Define $Q$ to be the remainder when $44121 \cdot r$ is divided by $61727$. Find the value of $Q$. | 29,186 | graphs = [
Graph(
let={
"_n": Const(61727),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(5929))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result"))... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T16:53:31.495398Z | {
"verified": true,
"answer": 29186,
"timestamp": "2026-02-08T16:53:31.497970Z"
} | 3ac756 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1956
},
"timestamp": "2026-02-17T14:40:01.502Z",
"answer": 29186
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6e261a | nt_sum_divisors_mod_v1_458359167_5640 | Let $n = 120$ and $M = 11299$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $r$ be the remainder when $\sigma(n)$ is divided by $M$. Let $p$ be the largest prime number such that $2 \leq p \leq 7011$. Compute the remainder when $\left(r \bmod 317\right) + p \cdot \left(r \bmod 313\right)$ is di... | 8,858 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(120),
"M": Const(11299),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Const(317)), Mul(MaxO... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_sum_divisors_mod_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:37:57.313843Z | {
"verified": true,
"answer": 8858,
"timestamp": "2026-02-08T12:37:57.315793Z"
} | 8f45c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1405
},
"timestamp": "2026-02-15T03:12:01.428Z",
"answer": 8858
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f0c7a9 | nt_count_with_divisor_count_v1_1520064083_7304 | Let $n$ be a positive integer such that $1 \leq n \leq 82944$ and the number of positive divisors of $n$ is equal to $\sum_{k=1}^{4} k$. Compute the number of such integers $n$. | 907 | graphs = [
Graph(
let={
"upper": Const(82944),
"div_count": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 3.731 | 2026-02-08T08:53:30.668635Z | {
"verified": true,
"answer": 907,
"timestamp": "2026-02-08T08:53:34.399924Z"
} | de8cff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 3938
},
"timestamp": "2026-02-13T22:54:14.264Z",
"answer": 907
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
02d141 | sequence_count_fib_divisible_v1_784195855_4872 | Let $d = 16$ and let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 959$ and $d$ divides the $n$th Fibonacci number. Compute the number of elements in $S$. | 79 | graphs = [
Graph(
let={
"upper": Const(959),
"d": Const(16),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 0.197 | 2026-02-08T07:26:46.040443Z | {
"verified": true,
"answer": 79,
"timestamp": "2026-02-08T07:26:46.237638Z"
} | 623a0a | 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": 1353
},
"timestamp": "2026-02-13T10:34:40.303Z",
"answer": 79
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
6fb0aa | algebra_vieta_sum_v1_898971024_2033 | Let $r_1, r_2, \dots, r_k$ be all real solutions $x$ to the equation
\[
- x^3 + 8x^2 + 4x - 32 = 0.
\]
Let $\text{result}$ be the sum of all such solutions. Define $Q = (44121 \cdot \text{result}) \mod 84848$. Compute $Q$. | 13,576 | graphs = [
Graph(
let={
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(-1), Pow(Var("x"), Const(3))), Mul(Const(8), Pow(Var("x"), Const(2))), Mul(Const(4), Var("x")), Const(-32)), Const(0)))),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Co... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | algebra_vieta_sum_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.027 | 2026-02-08T16:30:11.558793Z | {
"verified": true,
"answer": 13576,
"timestamp": "2026-02-08T16:30:11.585842Z"
} | afc091 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 695
},
"timestamp": "2026-02-17T04:23:45.858Z",
"answer": 13576
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ec9cc2 | comb_count_surjections_v1_1978505735_2017 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2$ equals the number of integers $t$ in the range $7 \leq t \leq 24$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 5a + 2b$.
Let $k$ be the number of ordered pairs $(i, j)$ w... | 1,806 | graphs = [
Graph(
let={
"_n": Const(6),
"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")), Cou... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1",
"COUNT_SUM_EQUALS"
] | 5a3f8e | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.029 | 2026-02-08T16:37:13.516178Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T16:37:13.545120Z"
} | d6da8c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1216
},
"timestamp": "2026-02-17T07:17:56.543Z",
"answer": 1806
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
e45420 | sequence_lucas_compute_v1_1978505735_3032 | Let $n$ be the largest prime number satisfying
$$
2 \leq n \leq \sum_{k=1}^{7} \varphi(k) \left\lfloor \frac{7}{k} \right\rfloor.
$$
Compute the $n$-th Lucas number. | 64,079 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Summation(var="k", start=Const(1), end=Const(7), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(7), Var("k")))))), IsPrime(Var("n1"))))),
... | NT | null | COMPUTE | sympy | K2 | [
"K2/MAX_PRIME_BELOW"
] | f058da | sequence_lucas_compute_v1 | null | 4 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T17:18:30.520990Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T17:18:30.523294Z"
} | 72b926 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1120
},
"timestamp": "2026-02-18T00:31:00.362Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
735335 | diophantine_fbi2_min_v1_1978505735_6885 | Let $k = 15$. Define $t$ to be expressible if there exist integers $a$ and $b$, each at least 1 and at most 5, such that $t = 5a + 4b$. Let $u$ be the number of expressible integers $t$ in the range $9 \leq t \leq 45$.
Let $d$ be a positive integer satisfying $4 \leq d \leq u$, $d \mid k$, and $k/d \geq 3$. Determine ... | 54,393 | graphs = [
Graph(
let={
"k": Const(15),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-08T19:52:31.184053Z | {
"verified": true,
"answer": 54393,
"timestamp": "2026-02-08T19:52:31.194632Z"
} | 2efd76 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1519
},
"timestamp": "2026-02-18T23:37:56.412Z",
"answer": 54393
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6c8486 | geo_count_lattice_rect_v1_971394319_1227 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 32$ and $0 \leq y \leq 61$. | 2,046 | graphs = [
Graph(
let={
"a": Const(32),
"b": Const(61),
"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 | 2026-02-08T13:32:12.769208Z | {
"verified": true,
"answer": 2046,
"timestamp": "2026-02-08T13:32:12.769795Z"
} | f2558c | 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": 160
},
"timestamp": "2026-02-24T18:38:16.472Z",
"answer": 2046
},
{
"id... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
eeac8a_n | algebra_poly_eval_v1_1419126231_1881 | Two positive integers $x$ and $y$ add up to 4. A landscape designer wants to maximize the area $xy$ of a rectangular garden. Let $M$ be this maximum area. For each integer $k$ from 1 to $M$, she calculates $\varphi(k)$ (the number of integers from 1 to $k$ coprime to $k$) multiplied by the number of multiples of $k$ th... | 254 | ALG | null | COMPUTE | sympy | B1 | [
"B1/K2"
] | ebd04c | algebra_poly_eval_v1 | null | 4 | null | [
"B1",
"K2"
] | 2 | 0.002 | 2026-02-25T11:26:29.836986Z | null | eea776 | eeac8a | narrative | 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": 887
},
"timestamp": "2026-03-31T05:11:15.016Z",
"answer": 254
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
511ba7 | antilemma_sum_equals_v1_2051736721_5633 | Let $n = 66$. Determine the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 65$, $1 \leq j \leq 65$, and $i + j = n$. Find the value of this count. | 65 | graphs = [
Graph(
let={
"_n": Const(66),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(65)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.041 | 2026-02-08T18:42:11.051704Z | {
"verified": true,
"answer": 65,
"timestamp": "2026-02-08T18:42:11.093055Z"
} | c699fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1140
},
"timestamp": "2026-02-18T18:38:16.474Z",
"answer": 65
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
6d9bd7 | comb_bell_compute_v1_1520064083_3279 | Let $T$ be the set of all integers $t$ such that $9 \leq t \leq 19$ and there exist positive integers $a$ and $b$, each at most $3$, satisfying $$
t = 2a + 3b + 4.
$$
Let $n$ be the number of elements in $T$. Let $B_n$ denote the $n$th Bell number, which counts the number of ways to partition a set of $n$ elements. C... | 21,147 | 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=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:33:32.587212Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T05:33:32.588627Z"
} | 3737e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 882
},
"timestamp": "2026-02-24T03:53:49.771Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
731bdd | diophantine_fbi2_min_v1_1918700295_433 | Let $k$ be the number of integers $t$ with $27 \leq t \leq 204$ that can be expressed in the form $t = 15a + 12b$ for positive integers $a \leq 8$ and $b \leq 7$. Let $d$ be the smallest integer such that $5 \leq d \leq 58$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Determine the value of $d$. | 6 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | EXTREMUM | sympy | LTE_SUM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"LIN_FORM",
"LTE_SUM"
] | 2 | 0.042 | 2026-02-08T03:13:27.197565Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T03:13:27.239306Z"
} | 4cb565 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2378
},
"timestamp": "2026-02-10T13:42:42.909Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
967a6b | modular_modexp_compute_v1_1125832087_391 | Let $a = 23$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 3364$. Define $s_{\text{min}}$ as the minimum value of $x + y$ over all such pairs. Now let $U$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s_{\text{min}}$. Define $e$ as the m... | 23,225 | graphs = [
Graph(
let={
"a": Const(23),
"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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tup... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T03:02:44.307745Z | {
"verified": true,
"answer": 23225,
"timestamp": "2026-02-08T03:02:44.309714Z"
} | d498b5 | 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": 7302
},
"timestamp": "2026-02-23T15:51:07.470Z",
"answer": 23225
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": ... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
cff36d | antilemma_k2_v1_601307018_282 | Let $M$ be the number of positive integers $n$ with $1 \le n \le 2802$ such that $\gcd(n, 35) = 1$ and $6 \mid n$. Let $x = \sum_{k=1}^{M} \varphi(k) \cdot \left\lfloor \frac{d_{\max}}{k} \right\rfloor$, where $d_{\max}$ is the largest positive divisor $d$ of $106251$ such that $d^2 \le 106251$. Compute $x$. | 51,681 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2802)), Divides(divisor=Ref("_m"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"x": Summation(var="k... | NT | null | COMPUTE | sympy | C5 | [
"C5/B3_CLOSEST/K2",
"K2"
] | 5a9164 | antilemma_k2_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"C5",
"K2"
] | 3 | 0.004 | 2026-03-10T00:49:40.609352Z | {
"verified": true,
"answer": 51681,
"timestamp": "2026-03-10T00:49:40.613696Z"
} | 9c84c1 | CC BY 4.0 | null | null | [
{
"lemma": "B3_CLOSEST",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
77fae2 | comb_count_surjections_v1_1978505735_4587 | Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 8$ such that $i + j = 8$. Compute $2! \cdot S(n, 2)$, where $S(n, 2)$ denotes the Stirling number of the second kind. | 126 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), 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 | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T18:21:15.323280Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T18:21:15.333557Z"
} | 0d003b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 960
},
"timestamp": "2026-02-18T16:09:49.528Z",
"answer": 126
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
7d408f | nt_count_phi_equals_v1_1918700295_917 | Let $ k = 2834 $. Determine the number of positive integers $ n $ with $ 1 \le n \le 3000 $ such that Euler's totient function $ \phi(n) = k $. | 0 | graphs = [
Graph(
let={
"upper": Const(3000),
"k": Const(2834),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
},
goal=Ref("result"),
)
] | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | nt_count_phi_equals_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.439 | 2026-02-08T05:23:52.651066Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T05:23:53.089892Z"
} | 637b33 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 3893
},
"timestamp": "2026-02-12T07:54:10.645Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACT... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
c8b2d1 | comb_count_permutations_fixed_v1_1742523217_261 | Let $m = 2$. Let $n$ be the number of positive integers $j$ such that $1 \le j \le 6$ and $j^5 \le x$, where $x$ is a real root of the equation $x^m - 7776x - 739780 = 0$. Let $k = 1$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!a$ denotes the number of derangements of $a$ elements. | 264 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-7776), Var("x")), Const(-739780)), Const(0)))),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const... | COMB | null | COUNT | sympy | COPRIME_PAIRS | [
"VIETA_SUM/C3"
] | 50b29a | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"C3",
"COPRIME_PAIRS",
"VIETA_SUM"
] | 3 | 0.014 | 2026-02-08T02:56:57.489504Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T02:56:57.503600Z"
} | 0c3d15 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1572
},
"timestamp": "2026-02-09T15:38:16.586Z",
"answer": 264
},
{
"id... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": ... | {
"lo": -4.92,
"mid": -2.93,
"hi": -0.93
} | ||
9a947b | nt_count_digit_sum_v1_124444284_3430 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 20$ and $n$ is divisible by 10. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 50176$ and the sum of the decimal digits of $n$ equals the sum of the elements of $S$. Let $c = 72645$ and $m = 76694$. Compute the remainder when $c \... | 1,245 | graphs = [
Graph(
let={
"_n": Const(76694),
"upper": Const(50176),
"target_sum": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(20)), Eq(Mod(value=Var("n"), modulus=Const(10)), Const(0))))),
"result": Count... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_count_digit_sum_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 2.766 | 2026-02-08T05:24:07.217666Z | {
"verified": true,
"answer": 1245,
"timestamp": "2026-02-08T05:24:09.983642Z"
} | 83749e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 4989
},
"timestamp": "2026-02-12T07:45:33.887Z",
"answer": 1245
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2c21c4 | comb_factorial_compute_v1_784195855_770 | Let $m = 64$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = s$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ range... | 65,032 | graphs = [
Graph(
let={
"_m": Const(64),
"_n": Const(85208),
"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")), MinOverSet(set=Ma... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_factorial_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:36:06.597230Z | {
"verified": true,
"answer": 65032,
"timestamp": "2026-02-08T04:36:06.599116Z"
} | 989a63 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T01:23:32.366Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
b3f029 | algebra_poly_eval_v1_124444284_4894 | Let $C$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 70436520$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $C$.
Now consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = N$. For each such pair, compute $x + ... | 12,460 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(44121),
"_n": Const(55205),
"x": 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"... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3",
"SUM_ARITHMETIC"
] | ecda0b | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 3 | 0.008 | 2026-02-08T06:16:56.579986Z | {
"verified": true,
"answer": 12460,
"timestamp": "2026-02-08T06:16:56.587628Z"
} | 49f414 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 2695
},
"timestamp": "2026-02-12T22:33:25.440Z",
"answer": 12460
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3650db | comb_binomial_compute_v1_784195855_7725 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 25467750$, $\gcd(p, q) = 1$, and $p < q$. Compute $\binom{n}{9}$. | 11,440 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=25467750)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_binomial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T09:28:19.883338Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T09:28:19.884735Z"
} | 4b662c | 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": 2526
},
"timestamp": "2026-02-14T04:22:16.482Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
93676b | algebra_poly_eval_v1_1248542787_785 | Let $m$ be the number of positive integers $n \leq 89$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Compute $m^3 - m^2 - 8m + 4$. | 23,320 | graphs = [
Graph(
let={
"_n": Const(2),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(89)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"re... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | algebra_poly_eval_v1 | null | 4 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T03:25:19.704873Z | {
"verified": true,
"answer": 23320,
"timestamp": "2026-02-08T03:25:19.706554Z"
} | ded57d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1261
},
"timestamp": "2026-02-09T08:14:02.050Z",
"answer": 23320
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
380a70 | modular_modexp_compute_v1_458359167_4213 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4000000$. Let $e$ be the minimum value of $x + y$ over all such pairs.
Compute the remainder when $13^e$ is divided by $11236$.
Let $Q$ be the remainder when $16969$ times this result is divided by $68121$. Compute $Q$. | 53,039 | graphs = [
Graph(
let={
"a": Const(13),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4000000)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T11:38:13.850717Z | {
"verified": true,
"answer": 53039,
"timestamp": "2026-02-08T11:38:13.854633Z"
} | 738cf6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 4267
},
"timestamp": "2026-02-14T16:40:18.709Z",
"answer": 53039
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
36b789 | nt_sum_divisors_compute_v1_1742523217_197 | Let $n_2 = 1$. Define $m = \sum_{d \mid n_2} \mu(d)$, where $\mu$ is the M\"obius function. Let $p = 59$ and $q = 29m$. Define $n_1 = p \cdot q$. Let $t = \mu(n_1)^2$ and $n = 50625 \cdot t$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $85543 \cdot \sigma(n)$ is divided by... | 76,745 | graphs = [
Graph(
let={
"n2": Const(1),
"m": SumOverDivisors(n=Ref(name='n2'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"p": Const(59),
"q": Mul(Const(29), Ref("m")),
"n1": Mul(Ref("p"), Ref("q")),
"t": Pow(MoebiusMu(n=Ref(name='n1'))... | NT | null | COMPUTE | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE",
"MOBIUS_SUM"
] | 60a6e7 | nt_sum_divisors_compute_v1 | null | 4 | 2 | [
"MOBIUS_SQUAREFREE",
"MOBIUS_SUM"
] | 2 | 0.002 | 2026-02-08T02:55:42.596577Z | {
"verified": true,
"answer": 76745,
"timestamp": "2026-02-08T02:55:42.598404Z"
} | 24327d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 8042
},
"timestamp": "2026-02-09T14:40:25.537Z",
"answer": 76745
},
{
"... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
35a27f | modular_mod_compute_v1_1470522791_559 | Let $A$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $M$ be the maximum value of $xy$ as $(x, y)$ ranges over $A$. Let $a$ be the number of positive integers $n$ such that $1 \leq n \leq 82668$ and $M$ divides the $n$th Fibonacci number. Define $r$ to be the remainder when $a... | 60,538 | graphs = [
Graph(
let={
"_n": Const(82668),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(... | NT | null | COMPUTE | sympy | B1 | [
"B1/COUNT_FIB_DIVISIBLE"
] | fd3ba1 | modular_mod_compute_v1 | null | 5 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.004 | 2026-02-08T13:06:11.190728Z | {
"verified": true,
"answer": 60538,
"timestamp": "2026-02-08T13:06:11.194434Z"
} | a06521 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2180
},
"timestamp": "2026-02-15T09:52:02.258Z",
"answer": 60538
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9dc894 | diophantine_product_count_v1_1353956133_191 | Let $k = 480$ and $u = 122$. Determine the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. | 18 | graphs = [
Graph(
let={
"k": Const(480),
"upper": Const(122),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | C3 | [
"COPRIME_PAIRS/VIETA_SUM"
] | 815fe1 | diophantine_product_count_v1 | null | 3 | 0 | [
"C3",
"COPRIME_PAIRS",
"VIETA_SUM"
] | 3 | 0.702 | 2026-02-08T11:20:28.994067Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T11:20:29.696171Z"
} | 114b4e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 1569
},
"timestamp": "2026-02-14T11:48:09.370Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"st... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
b1f1f7 | diophantine_fbi2_count_v1_168721529_749 | Let $t$ be the number of positive integers $d$ such that $5 \le d \le 103$, $d$ divides 120, $\frac{120}{d} \ge 6$, and $\frac{120}{d} \le \sum_{d' \mid s} \phi(d')$, where $s$ is the number of integers $t'$ with $11 \le t' \le 132$ for which there exist positive integers $a \le 19$ and $b \le 8$ such that $t' = 4a + 7... | 135 | graphs = [
Graph(
let={
"_n": Const(103),
"k": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(Div(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/K3"
] | c7df50 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T13:15:53.172157Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T13:15:53.181939Z"
} | dd1581 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 7906
},
"timestamp": "2026-02-09T08:45:09.695Z",
"answer": 135
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.9
} | ||
2c6f4e | nt_count_digit_sum_v1_124444284_2186 | Let $c = 2500$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = c$. Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = s$. Let $t$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that... | 230 | graphs = [
Graph(
let={
"_c": Const(2500),
"_m": 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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | COUNT | sympy | B3 | [
"B3/B1/B3",
"B1/B1/B3"
] | 343a63 | nt_count_digit_sum_v1 | digits_weighted_mod | 7 | 0 | [
"B1",
"B3"
] | 2 | 7.146 | 2026-02-08T04:29:45.908034Z | {
"verified": true,
"answer": 230,
"timestamp": "2026-02-08T04:29:53.053734Z"
} | 72a3c4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 360,
"completion_tokens": 2081
},
"timestamp": "2026-02-10T16:58:12.222Z",
"answer": 230
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
aa5d0f | diophantine_fbi2_min_v1_898971024_1985 | Let $d$ be an integer such that $2 \leq d \leq 32$, $d$ divides $22$, and $\frac{22}{d} \geq 2$. Let $r$ be the smallest such $d$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq T$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$, where $T$ is the number of integers $t$ with $5 \leq t \leq 41$... | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(22),
"upper": Const(32),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"),... | NT | COMB | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/L3C"
] | 274bb1 | diophantine_fbi2_min_v1 | bell_mod | 7 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T16:28:42.799940Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:28:42.806563Z"
} | 306065 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2540
},
"timestamp": "2026-02-17T04:21:29.967Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
63b192 | alg_qf_psd_min_v1_1218484723_1484 | Find the minimum value of $33600a^2 + 20800b^2 + 20800c^2 - 40000ab + 14400ac + 17600bc$ over all ordered triples $(a, b, c)$ of positive integers such that $1 \leq a \leq 41$, $1 \leq b \leq \min\{d : d \geq 2, d \mid 82861\}$, and $1 \leq c \leq \max\{n : n \geq 2, n \leq 42, n \text{ is prime}\}$. | 67,200 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(41),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOve... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | 9f9e96 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.162 | 2026-02-25T03:11:27.395440Z | {
"verified": true,
"answer": 67200,
"timestamp": "2026-02-25T03:11:27.557021Z"
} | c797df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T04:06:06.337Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
4287c3 | alg_poly_orbit_count_v1_1218484723_5430 | For an integer $a$, define
$$N \equiv a^{4} - 3a^{3} - 5a^{2} - 5a - 1 \pmod{37},$$
$$M \equiv N^{4} - 3N^{3} - 5N^{2} - 5N - 1 \pmod{37},$$
$$R \equiv M^{4} - 3M^{3} - 5M^{2} - 5M - 1 \pmod{37},$$
$$S \equiv R^{4} - 3R^{3} - 5R^{2} - 5R - 1 \pmod{37},$$
$$T \equiv S^{4} - 3S^{3} - 5S^{2} - 5S - 1 \pmod{37},$$
$$K \equ... | 7,134 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(4)), Mul(Const(-3), Pow(Var("a"), Const(3))), Mul(Const(-5), Pow(Var("a"), Const(2))), Mul(Const(-5), Var("a")), Const(-1)), modulus=Const(37)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(4)), Mul(Const(-3), Pow(Ref("p1"),... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.383 | 2026-02-25T06:59:49.469592Z | {
"verified": true,
"answer": 7134,
"timestamp": "2026-02-25T06:59:49.852604Z"
} | 7e05cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 416,
"completion_tokens": 15847
},
"timestamp": "2026-03-29T21:05:57.845Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
f231b3 | nt_lcm_compute_v1_151522320_1686 | Let $a = 2874$ and $b = 707$. Define $L = \mathrm{lcm}(a, b)$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4362$. Let $T$ be the number of elements in $S$. Let $U$ be the number of positive integers $n$ such that $1 \leq n \leq T$, $3$ divides $n$, and $\gcd(n, 3... | 17,062 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(2003),
"a": Const(2874),
"b": Const(707),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Const(199)), Mul(Ref("_n"), Mod(value=Ref("result"... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1/C5"
] | de2e11 | nt_lcm_compute_v1 | two_moduli | 7 | 0 | [
"C5",
"COMB1"
] | 2 | 0.006 | 2026-02-08T04:11:53.252266Z | {
"verified": true,
"answer": 17062,
"timestamp": "2026-02-08T04:11:53.257927Z"
} | a2ba1a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 2361
},
"timestamp": "2026-02-10T15:38:43.675Z",
"answer": 17062
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9397a8 | nt_count_divisible_v1_784195855_887 | Let $m = 26$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $n$ be the maximum value of $xy$ over all such pairs.
Now consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Let $d$ be the minimum value of $x + y$ over all such pairs.
Let ... | 1,878 | graphs = [
Graph(
let={
"_m": Const(26),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisible_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 1.71 | 2026-02-08T04:40:23.930272Z | {
"verified": true,
"answer": 1878,
"timestamp": "2026-02-08T04:40:25.640450Z"
} | 5d7617 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1139
},
"timestamp": "2026-02-11T21:45:33.381Z",
"answer": 1878
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
50c224_n | alg_poly4_sum_v1_1218484723_3049 | A city grid has 85 east-west streets and 85 north-south streets, forming intersections labeled by coordinates $(a,b)$ with $1 \leq a, b \leq 85$. Each intersection generates energy based on the expression: $\min\{x+y : x>0, y>0, xy=38025\} \cdot a^2b^2 + 257a^4 + 17b^4 + 516a^3b + 132ab^3$. The total energy is summed o... | 66,396 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_sum_v1 | null | 6 | null | [
"B3"
] | 1 | 0.028 | 2026-02-25T04:48:58.755852Z | null | 5e2482 | 50c224 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 7197
},
"timestamp": "2026-03-30T19:25:41.058Z",
"answer": 31678
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
458460 | comb_sum_binomial_row_v1_397696148_547 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $p < q$, $\gcd(p, q) = 1$, and $pq = 18$. Compute the remainder when $11449 - |S|^{14}$ is divided by 98650. | 93,715 | graphs = [
Graph(
let={
"_n": Const(98650),
"n": Const(14),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T11:33:39.289864Z | {
"verified": true,
"answer": 93715,
"timestamp": "2026-02-08T11:33:39.291090Z"
} | c5441c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 838
},
"timestamp": "2026-02-14T16:21:28.290Z",
"answer": 93715
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
59f8cf | alg_poly_preperiod_count_v1_601307018_7320 | Let $N = (a^2 + a - 11) \bmod 29$, $M = (N^2 + N - 11) \bmod 29$, $R = (M^2 + M - 11) \bmod 29$, and $S = (R^2 + R - 11) \bmod 29$. Find the number of non-negative integers $a$ with $0 \le a \le 1565$ such that $S = N$, $M \ne N$, and $R \ne N$. | 648 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-11)), modulus=Const(29)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-11)), modulus=Const(29)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-11)), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.028 | 2026-03-10T07:55:19.086435Z | {
"verified": true,
"answer": 648,
"timestamp": "2026-03-10T07:55:19.114002Z"
} | 2dbbc3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 4678
},
"timestamp": "2026-04-19T06:27:41.460Z",
"answer": 648
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
d51903 | comb_bell_compute_v1_349078426_665 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $n$ be the minimum value of $x + y$ over all pairs $(x, y) \in P$. Define $r = B_n$, the $n$th Bell number. Compute the remainder when $44121 \cdot r$ is divided by $66733$. | 12,719 | graphs = [
Graph(
let={
"_n": Const(66733),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_bell_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T13:12:14.517693Z | {
"verified": true,
"answer": 12719,
"timestamp": "2026-02-08T13:12:14.519702Z"
} | b8d56e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 2299
},
"timestamp": "2026-02-24T17:33:12.537Z",
"answer": 12719
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
8869ac | nt_count_primes_v1_865884756_4041 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Determine the value of $Q$, where $Q$ is the remainder when $46943$ multiplied by the number of prime numbers $n$ satisfying $L \leq n \l... | 15,993 | graphs = [
Graph(
let={
"_n": Const(66713),
"upper": Const(32768),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.198 | 2026-02-08T17:43:28.467110Z | {
"verified": true,
"answer": 15993,
"timestamp": "2026-02-08T17:43:29.665264Z"
} | 119e7a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1218
},
"timestamp": "2026-02-18T06:49:36.253Z",
"answer": 15993
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0fce0c | nt_count_gcd_equals_v1_717093673_2604 | Let $k$ be the number of positive integers $n \leq d_{\text{min}}$ such that the sum of the digits of $n$ is odd, where $d_{\text{min}}$ is the smallest prime factor of 902491 that is at least 2. Let $S$ be the set of all positive integers $n_1 \leq 46225$ such that $\gcd(n_1, k) = 6$. Compute the number of elements in... | 7,607 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(46225),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(2)), Divides(divisor=Var("d1"... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/L3B"
] | 27deec | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"L3B",
"MIN_PRIME_FACTOR"
] | 2 | 3.723 | 2026-02-08T17:00:15.195621Z | {
"verified": true,
"answer": 7607,
"timestamp": "2026-02-08T17:00:18.918816Z"
} | 8747a7 | 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": 2991
},
"timestamp": "2026-02-17T17:07:19.622Z",
"answer": 7607
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cf9854 | comb_count_partitions_v1_168721529_111 | Let $e = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $f = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Let $p$ be the number of integer partitions of 42. Find the remainder when $55781 \cdot e \cdot f \cdot p$ is divided by 56033. | 48,072 | graphs = [
Graph(
let={
"n2": Const(0),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"f": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T12:48:53.505451Z | {
"verified": true,
"answer": 48072,
"timestamp": "2026-02-08T12:48:53.507002Z"
} | 019d6e | CC BY 4.0 | [
{
"id": 1,
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"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1283
},
"timestamp": "2026-02-08T21:03:25.224Z",
"answer": 49072
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": 1.36,
"mid": 4.2,
"hi": 6.62
} | ||
ee1b57 | algebra_quadratic_discriminant_v1_1742523217_3805 | Let $p$ be a positive integer. Define $\delta$ to be the number of such $p$ for which there exists a positive integer $q$ satisfying $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let
$$
D = (-4)^\delta - 4 \cdot 10 \cdot 3.
$$
Define $\alpha = 1$ if $D > 0$, and $0$ otherwise. Define $\beta = 1$ if $D = 0$, and $0$ otherwi... | 0 | graphs = [
Graph(
let={
"a": Const(10),
"b": Const(-4),
"c": Const(3),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T06:06:38.594842Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T06:06:38.596850Z"
} | a7cb55 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 406
},
"timestamp": "2026-02-11T23:35:11.048Z",
"answer": 0
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
41e611 | comb_sum_binomial_row_v1_1742523217_1118 | Let $m = 2$ and $n = 2$. Let $k$ be the number of integers $t$ such that $19 \leq t \leq 61$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 9a + 6b + 4$. Let $N$ be the largest prime number $p$ such that $m \leq p \leq k$. Define $r = n^N$. Compute $11236 - r$. | 3,044 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'),... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T03:25:50.561030Z | {
"verified": true,
"answer": 3044,
"timestamp": "2026-02-08T03:25:50.562967Z"
} | 296487 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 910
},
"timestamp": "2026-02-10T03:36:53.648Z",
"answer": 3044
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
96a30a | nt_lcm_compute_v1_458359167_432 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 279841$. Let $b = 1744$. Compute the Bell number of $\left| \text{lcm}(a, b) \right| \bmod{11}$. | 203 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(279841)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(1744)... | NT | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:17:20.916507Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T03:17:20.917626Z"
} | e3e28b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 3632
},
"timestamp": "2026-02-10T13:21:11.880Z",
"answer": 2
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
200edc | nt_min_coprime_above_v1_1520064083_4518 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 102$. Define $\alpha$ to be the maximum value of $xy$ over all such pairs. Let $\beta$ be the number of integers $t$ such that $27 \leq t \leq 2671$ and there exist positive integers $a \leq 427$ and $b \leq 189$ satisfying $t = 4a... | 877 | graphs = [
Graph(
let={
"_n": Const(102),
"start": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y"))))... | NT | COMB | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.25 | 2026-02-08T06:18:43.591886Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T06:18:43.841431Z"
} | f433b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 5602
},
"timestamp": "2026-02-12T22:18:09.551Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2ef300 | alg_poly3_min_v1_601307018_7736 | Let $F_n$ denote the $n$-th Fibonacci number. Let $S = \left|\{ n \geq 1 : n \leq 24,\, m \mid F_n \}\right|$ where $m = \left|\{ (a_1, b_1) : 1 \leq a_1 \leq b_1 \leq 15,\, 32a_1^2 + 32b_1^2 - 64a_1b_1 = 2048 \}\right|$. Find the remainder when
$$
\min_{\substack{1 \leq a, b, c \leq 9}} \left( 62b^3 - 285b c^2 - 162a^... | 77,201 | graphs = [
Graph(
let={
"_m": Const(32),
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(9)), Geq(Var("b"), Const(1)), Leq(Var("b"... | NT | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/COUNT_FIB_DIVISIBLE"
] | 50cefd | alg_poly3_min_v1 | null | 8 | 0 | [
"COUNT_FIB_DIVISIBLE",
"QF_PSD_ORBIT"
] | 2 | 0.036 | 2026-03-10T08:19:43.051733Z | {
"verified": true,
"answer": 77201,
"timestamp": "2026-03-10T08:19:43.087325Z"
} | d9f02b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 338,
"completion_tokens": 5798
},
"timestamp": "2026-04-19T07:23:29.659Z",
"answer": 77201
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
da2b22 | sequence_count_fib_divisible_v1_1125832087_1112 | Let $n$ be a positive integer. Consider the set of all positive integers $n$ such that $1 \leq n \leq 1213$ and the sum of the decimal digits of $n$ is odd. Let $u$ be the number of such integers $n$.
Now consider the set of all positive integers $n$ such that $1 \leq n \leq u$ and the $n$-th Fibonacci number is divis... | 60 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1213)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"d": Const(11),
"result": CountOv... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.027 | 2026-02-08T03:31:16.077811Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T03:31:16.104599Z"
} | 2e2a56 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 2444
},
"timestamp": "2026-02-10T13:46:16.639Z",
"answer": 60
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
cdfff2 | alg_qf_psd_min_v1_1218484723_5013 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 25$ such that $-189a^3 = -1512$. Let $S = \left| \left\{ v : M \leq v \leq 15161,\ \exists\, 1 \leq a_1, b_1 \leq 23\ \text{s.t.}\ 29b_1^2 - 8a_1b_1 + 4a_1^2 = v \right\} \right|$. Find the minimum value of $30807b_1^2 + 140343a... | 88,998 | graphs = [
Graph(
let={
"_m": Const(15161),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Mul(Const(-189), Pow(Var("a"), Const(3))), ... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/QF_PSD_DISTINCT"
] | c1868a | alg_qf_psd_min_v1 | null | 5 | 0 | [
"POLY3_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.586 | 2026-02-25T06:38:33.301138Z | {
"verified": true,
"answer": 88998,
"timestamp": "2026-02-25T06:38:33.887586Z"
} | 6ed99d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 10013
},
"timestamp": "2026-03-29T19:04:33.414Z",
"answer": 88998
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
c1bc8e | nt_sum_divisors_compute_v1_865884756_4981 | Let $n = 66564$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14450$. Compute the remainder when $\sigma(n)^2 + 36\sigma(n) + c$ is divided by $93649$. | 10,398 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(66564),
"result": SumDivisors(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(ar... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 0a3d6e | nt_sum_divisors_compute_v1 | quadratic_mod | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T18:18:50.236128Z | {
"verified": true,
"answer": 10398,
"timestamp": "2026-02-08T18:18:50.237688Z"
} | 8ddd1f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 3353
},
"timestamp": "2026-02-18T16:11:24.653Z",
"answer": 10398
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
84d758 | comb_sum_binomial_row_v1_1218484723_3239 | Let $S$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime integer $n$ with $2 \le n \le \min\{d \ge 2 : d \mid 1859\}$. Compute the remainder when $85463 \cdot S^n$ is divided by $66253$. | 54,051 | graphs = [
Graph(
let={
"_d": Const(66253),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=G... | COMB | NT | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 21b694 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.007 | 2026-02-25T04:57:16.747814Z | {
"verified": true,
"answer": 54051,
"timestamp": "2026-02-25T04:57:16.754454Z"
} | 49e1e4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 2045
},
"timestamp": "2026-03-29T09:10:30.453Z",
"answer": 54051
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIM... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
310b69 | diophantine_product_count_v1_784195855_7385 | Let $n = 4900$ and $k = 720$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Define $\ell$ to be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $T$ be the set of all positive integers $x$ such that $1 \le x \le \ell$, $x$ divides $k$, and $\frac{k}{x} \le \ell... | 63,885 | graphs = [
Graph(
let={
"_n": Const(4900),
"k": Const(720),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.025 | 2026-02-08T09:14:34.632495Z | {
"verified": true,
"answer": 63885,
"timestamp": "2026-02-08T09:14:34.657679Z"
} | 02f909 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1767
},
"timestamp": "2026-02-14T02:30:41.920Z",
"answer": 63885
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e89f9c | algebra_poly_eval_v1_1820931509_610 | Let $c = 3$ and $m = 15$. Let $S$ be the set of all integers $d \geq 2$ such that $d$ divides $m$. Define $n = \min(S)$. Let
$$
y = \sum_{k=1}^{c} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $T$ be the set of all positive integers $p$ for which there exists... | 995 | graphs = [
Graph(
let={
"_c": Const(3),
"_m": Const(15),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"y": Summation(var="k", start=Const(1), end=Ref("_c"), expr=Mul(Eu... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2",
"COPRIME_PAIRS"
] | 11a66c | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K2",
"MIN_PRIME_FACTOR"
] | 3 | 0.005 | 2026-02-08T11:46:59.587646Z | {
"verified": true,
"answer": 995,
"timestamp": "2026-02-08T11:46:59.592345Z"
} | 11f818 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1617
},
"timestamp": "2026-02-14T18:47:46.979Z",
"answer": 995
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a63705 | nt_count_divisible_v1_124444284_5586 | Let $A$ be the set of all integers $t$ such that $25 \leq t \leq 277$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 55$, $1 \leq b \leq 19$, and $t = 3a + 5b + 17$. Let $c$ be the number of elements in $A$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $c$. Let $N$ be the numb... | 13,280 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(39601),
"divisor": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), c... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | nt_count_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 2.043 | 2026-02-08T06:43:40.803533Z | {
"verified": true,
"answer": 13280,
"timestamp": "2026-02-08T06:43:42.846049Z"
} | 91b8ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 5128
},
"timestamp": "2026-02-13T03:43:34.786Z",
"answer": 13280
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a064c7 | diophantine_fbi2_count_v1_124444284_2483 | Let $k$ be the number of integers $t$ such that $10 \leq t \leq 861$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 117$, $1 \leq b \leq 14$, and $t = 7a + 3b$. Compute the number of positive integers $d$ such that $6 \leq d \leq 174$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 170$. | 23 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=117)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.027 | 2026-02-08T04:42:33.890126Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T04:42:33.917009Z"
} | 5d720b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 4514
},
"timestamp": "2026-02-11T21:42:52.329Z",
"answer": 6
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
9ef4ea | sequence_count_fib_divisible_v1_717093673_3381 | Find the number of positive integers $n$ such that $1 \leq n \leq 694$ and $17$ divides the $n$-th Fibonacci number. | 77 | graphs = [
Graph(
let={
"upper": Const(694),
"d": Const(17),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"C4"
] | 73aaed | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.171 | 2026-02-08T17:31:45.016207Z | {
"verified": true,
"answer": 77,
"timestamp": "2026-02-08T17:31:45.186954Z"
} | 4f9242 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 683
},
"timestamp": "2026-02-16T11:21:30.353Z",
"answer": 43
},
{
"id": 11,
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
256aef | comb_bell_compute_v1_1520064083_10218 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 8272$ such that $\binom{8272}{j}$ 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(8272),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8272)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T11:17:16.690381Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T11:17:16.691263Z"
} | 081840 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1274
},
"timestamp": "2026-02-24T13:09:03.326Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
44dd31 | modular_count_residue_v1_784195855_4423 | Let $n$ be a positive integer. Consider the set of all integers $n$ such that $1 \leq n \leq 48400$ and $n \equiv 14 \pmod{16}$. Let $A$ be the number of elements in this set.
Let $t$ be a positive integer. Consider the set of all integers $t$ such that $7 \leq t \leq 49$ and there exist positive integers $a$ and $b$,... | 75,139 | graphs = [
Graph(
let={
"upper": Const(48400),
"m": Const(16),
"r": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | modular_count_residue_v1 | negation_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.576 | 2026-02-08T07:05:28.489327Z | {
"verified": true,
"answer": 75139,
"timestamp": "2026-02-08T07:05:30.065530Z"
} | 9fcd77 | 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": 3642
},
"timestamp": "2026-02-13T07:39:30.983Z",
"answer": 75139
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b17b07 | antilemma_k2_v1_2051736721_5708 | Let $m = 357$. Define $N = \sum_{d \mid m} \phi(d)$, where $\phi$ is Euler's totient function. Compute
$$
\sum_{k=1}^{N} \phi(k) \left\lfloor \frac{357}{k} \right\rfloor,
$$
and let $x$ be the value of this sum. Find the remainder when $44121x$ is divided by 67121. | 46,658 | graphs = [
Graph(
let={
"_m": Const(357),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(357), Var("k"))))),
"Q": Mod(value... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.003 | 2026-02-08T18:44:14.060451Z | {
"verified": true,
"answer": 46658,
"timestamp": "2026-02-08T18:44:14.063383Z"
} | fbc5b6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 2351
},
"timestamp": "2026-02-18T19:20:23.363Z",
"answer": 46658
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0f9252 | lin_form_endings_v1_124444284_9437 | Let $a = 63$ and $b = 18$. Define $\ell$ to be the least common multiple of $a$ and $b$. Let $k = 3$ and define
$$
r = k \cdot \ell + a + b.
$$Then let $s = 6049 \cdot r$, and define $x$ to be the remainder when $s$ is divided by $60715$. Find the value of $x$. | 44,316 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(18),
"k_val": Const(3),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:27:06.732577Z | {
"verified": true,
"answer": 44316,
"timestamp": "2026-02-08T12:27:06.733564Z"
} | bbd0a6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 674
},
"timestamp": "2026-02-15T01:41:50.030Z",
"answer": 44316
},
{... | 1 | [
{
"lemma": "C2",
"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": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
92ae37 | antilemma_v7_kummer_168721529_1707 | Let $M$ be the set of all positive integers $k$ such that $1 \leq k \leq 237696$ and $48$ divides $k$. Let $m = |M|$. Let $T$ be the set of all integers $t$ such that $12 \leq t \leq 2016$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 263$, $1 \leq b \leq 35$, and $t = 7a + 5b$. Let $t = |T|$. Let $... | 11 | graphs = [
Graph(
let={
"_m": Const(48),
"_n": Const(2),
"x": MaxKDivides(target=Binom(n=CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(237696)), Divides(divisor=Ref("_m"), dividend=Var("k"))), domain='positive_integ... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V7",
"C2/V7",
"V7"
] | 824f3b | antilemma_v7_kummer | null | 6 | 0 | [
"C2",
"LIN_FORM",
"V7"
] | 3 | 0.047 | 2026-02-08T13:53:10.920642Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T13:53:10.968056Z"
} | 0c7e47 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 8052
},
"timestamp": "2026-02-09T20:35:24.936Z",
"answer": 11
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
3c411d | diophantine_sum_product_min_v1_655260480_4248 | Let $S$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 3$ and $1 \leq b \leq 6$.
Let $P$ be the number of integers $t$ with $27 \leq t \leq 273$ for which there exist positive integers $a \in [1,3]$ and $b \in [1,35]$ such that $t = 21a + 6b$.
Let $T$ be the set of all positive integers $x$ such tha... | 4,976 | graphs = [
Graph(
let={
"_n": Const(33497),
"S": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(6)))),
"P": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), con... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"LIN_FORM",
"COMB1"
] | e75991 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.01 | 2026-02-08T17:49:23.736329Z | {
"verified": true,
"answer": 4976,
"timestamp": "2026-02-08T17:49:23.745931Z"
} | 0c17a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 2506
},
"timestamp": "2026-02-18T08:50:08.236Z",
"answer": 4976
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e68d0c | diophantine_sum_product_min_v1_809748730_1581 | Let $S$ be the number of integers $t$ such that $19 \leq t \leq 217$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 24$, and $t = 10a + 6b + 3$. Let $P = 1632$. Determine the smallest positive integer $x \leq 91$ such that $x(S - x) = P$. | 24 | graphs = [
Graph(
let={
"_n": Const(91),
"S": 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=Var(n... | NT | null | EXTREMUM | sympy | V1 | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"LIN_FORM",
"V1"
] | 2 | 0.116 | 2026-02-08T12:33:59.975846Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T12:34:00.091888Z"
} | 1b1240 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 2670
},
"timestamp": "2026-02-15T02:18:14.764Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9c54ba | comb_factorial_compute_v1_1218484723_4391 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that $$17b^4 + 68ab^3 + 102a^2b^2 + 68a^3b + 17a^4 = 5640192.$$ Let $n$ be this number. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Sum(Mul(Const(17), Pow(Var("b"), Const(4))), Mul... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_factorial_compute_v1 | null | 4 | 0 | [
"POLY4_COUNT"
] | 1 | 0.001 | 2026-02-25T06:00:41.998545Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T06:00:41.999958Z"
} | 9a9b4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 882
},
"timestamp": "2026-03-29T15:26:03.035Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
cec84b | nt_count_divisors_in_range_v1_458359167_5392 | Let $ n = 498960 $. Let $ A $ be the set of all positive integers $ t $ such that $ 10 \leq t \leq 9094 $ and there exist positive integers $ a $, $ b $ with $ 1 \leq a \leq 691 $, $ 1 \leq b \leq 1003 $, and $ t = 3a + 7b $. Let $ b $ be the number of elements in $ A $. Let $ D $ be the set of all positive divisors $ ... | 65,458 | graphs = [
Graph(
let={
"n": Const(498960),
"a": Const(37),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.08 | 2026-02-08T12:27:21.105787Z | {
"verified": true,
"answer": 65458,
"timestamp": "2026-02-08T12:27:21.185640Z"
} | 4da788 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 7690
},
"timestamp": "2026-02-15T01:03:30.539Z",
"answer": 65458
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
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"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
04a3cf_n | comb_count_surjections_v1_1218484723_4634 | A teacher assigns 7 students to groups, where each group must have at least one student. The number of allowed group configurations depends on a parameter $k$, computed from the totients of 1 and 2 and floor division: $k = \sum_{d=1}^2 \varphi(d) \cdot \lfloor 2/d \rfloor$. The total number of ways to partition the stu... | 1,806 | COMB | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_surjections_v1 | null | 3 | null | [
"K2"
] | 1 | 0.002 | 2026-02-25T06:19:08.347796Z | null | 0c3dc0 | 04a3cf | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 942
},
"timestamp": "2026-03-30T21:58:35.049Z",
"answer": 1806
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
2beaf1_l | diophantine_product_count_v1_784195855_5570 | Let $k = 60$ and let the upper bound be $41$. Compute the number of positive integers $x$ such that $1 \leq x \leq 41$, $x$ divides $60$, and $\frac{60}{x} \leq 41$. | 11 | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_product_count_v1 | null | 3 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 8.839 | 2026-02-08T07:58:23.335977Z | {
"verified": false,
"answer": 10,
"timestamp": "2026-02-08T07:58:32.175189Z"
} | 91fcfa | 2beaf1 | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 986
},
"timestamp": "2026-02-13T13:39:24.963Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | |
786e50 | nt_count_digit_sum_v1_784195855_9888 | Let $m = 5$ and let $n = \sum_{k=1}^{m} k$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 300000$ and the sum of the digits of $n$ is 24. Let $r$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 54$, $\gcd(p, q) = 1... | 18,899 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")),
"upper": Const(300000),
"target_sum": Const(24),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/COPRIME_PAIRS"
] | c6fbdb | nt_count_digit_sum_v1 | mod_exp | 6 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 11.305 | 2026-02-08T17:15:30.052981Z | {
"verified": true,
"answer": 18899,
"timestamp": "2026-02-08T17:15:41.358152Z"
} | 9ebccb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 4566
},
"timestamp": "2026-02-18T00:08:46.488Z",
"answer": 18899
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d714ba | sequence_count_fib_divisible_v1_1125832087_2294 | Compute the number of positive integers $n$ such that $1 \leq n \leq 815$ and $7$ divides the $n$-th Fibonacci number. | 101 | graphs = [
Graph(
let={
"upper": Const(815),
"d": Const(7),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.145 | 2026-02-08T04:30:10.848701Z | {
"verified": true,
"answer": 101,
"timestamp": "2026-02-08T04:30:10.993882Z"
} | 0d824f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 1760
},
"timestamp": "2026-02-10T16:47:44.250Z",
"answer": 101
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemm... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
71f7b8_n | comb_binomial_compute_v1_1218484723_7526 | A statistician first counts how many prime numbers $n_2$ lie between $2$ and $389$ inclusive, and calls this count $N$. Then they look at all integers $n_1$ between $1$ and $N$ that are multiples of $77$, and sum them to obtain $S$.
They define $k$ to be the smallest positive integer that evenly divides this sum $S$. ... | 6,435 | COMB | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/SUM_DIVISIBLE/MIN_PRIME_FACTOR"
] | 86b77f | comb_binomial_compute_v1 | null | 7 | null | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 3 | 0.003 | 2026-02-25T08:57:13.315723Z | null | cc13f5 | 71f7b8 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 2044
},
"timestamp": "2026-03-31T02:34:44.690Z",
"answer": 6435
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
224d01 | nt_min_crt_v1_124444284_5661 | Let $m = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k$ be the largest prime number between 2 and 6, inclusive. Determine the value of the smallest positive integer $n \leq 15$ such that $n \equiv 2 \pmod{m}$ and $n \equiv 4 \pmod{k}$. Let $Q$ be t... | 19,890 | graphs = [
Graph(
let={
"_n": Const(99634),
"m": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6))... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"K2"
] | e3ad1e | nt_min_crt_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T06:46:02.284370Z | {
"verified": true,
"answer": 19890,
"timestamp": "2026-02-08T06:46:02.289853Z"
} | a70bd7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 724
},
"timestamp": "2026-02-13T04:23:08.074Z",
"answer": 19890
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
58d9ad | nt_count_divisible_and_v1_349078426_1434 | Let $r$ be the number of positive integers $n$ at most 19104 that are divisible by both 4 and 6. Let $d$ be the smallest integer at least 2 that divides 143. Compute the Bell number $B_s$, where $s$ is the remainder when $|r|$ is divided by $d$. | 4,140 | graphs = [
Graph(
let={
"upper": Const(19104),
"d1": Const(4),
"d2": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(Mo... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_divisible_and_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.999 | 2026-02-08T13:38:41.998414Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T13:38:42.997335Z"
} | 6d7e9b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 549
},
"timestamp": "2026-02-15T19:07:45.320Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
278a93 | nt_num_divisors_compute_v1_1915831931_405 | Let $m = 95713$ and let $p_{\text{count}}$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 54$, $\gcd(p,q) = 1$, and $p < q$. Let $T$ be the set of integers $t$ with $15 \le t \le 25917$ such that there exist positive integers $a \le 2185$ and $b \le 1423$ sat... | 45,185 | graphs = [
Graph(
let={
"_m": Const(95713),
"_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=54)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR",
"LIN_FORM/MIN_PRIME_FACTOR"
] | c75b83 | nt_num_divisors_compute_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.009 | 2026-02-08T15:24:22.802447Z | {
"verified": true,
"answer": 45185,
"timestamp": "2026-02-08T15:24:22.811393Z"
} | 0f2d56 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 5003
},
"timestamp": "2026-02-16T05:12:52.113Z",
"answer": 45185
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4a55bf | geo_visible_lattice_v1_1526740231_468 | Let $n = 60$. Define $L$ to be the number of lattice points $(x, y)$ with $1 \le x, y \le n$ such that $\gcd(x, y) = 1$. Compute the remainder when $35095 \cdot L$ is divided by $74148$. | 52,069 | graphs = [
Graph(
let={
"n": Const(60),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(35095), Ref("result")), modulus=Const(74148)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.345 | 2026-02-08T11:33:45.555489Z | {
"verified": true,
"answer": 52069,
"timestamp": "2026-02-08T11:33:45.900067Z"
} | 1c8f36 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 3491
},
"timestamp": "2026-02-24T14:18:19.983Z",
"answer": 52069
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
a53671 | nt_min_coprime_above_v1_2051736721_3535 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i, j \leq 27$ and $\gcd(i, j) = 1$. Let $m$ be the number of elements in $S$. Find the smallest integer $n$ such that $69696 < n \leq 70165$ and $\gcd(n, m) = 1$. Compute the remainder when $44121 \cdot n$ is divided by $82294$. Fin... | 21,439 | graphs = [
Graph(
let={
"start": Const(69696),
"upper": Const(70165),
"modulus": 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=Cons... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.089 | 2026-02-08T17:24:06.052150Z | {
"verified": true,
"answer": 21439,
"timestamp": "2026-02-08T17:24:06.140953Z"
} | 8dffd1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 3991
},
"timestamp": "2026-02-18T01:07:42.203Z",
"answer": 21439
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cefd7c | diophantine_fbi2_min_v1_655260480_5956 | Let $S_1$ be the set of all nonnegative integers $j_1$ with $0 \leq j_1 \leq 1536$ such that $\binom{1536}{j_1}$ is odd. Let $N$ be the number of elements in $S_1$.
Let $S_2$ be the set of all prime numbers $n$ such that $2 \leq n \leq N$. Let $e$ be the maximum element of $S_2$.
Let $S_3$ be the set of all positiv... | 3 | graphs = [
Graph(
let={
"_m": Const(46),
"_n": Const(97336),
"k": Const(36),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_m")), Leq(Pow(Var("j"), MaxOverSet(set=SolutionsSet(var=Var("n"), condi... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"V8/MAX_PRIME_BELOW/C3"
] | ca43e3 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"C3",
"COUNT_COPRIME_GRID",
"MAX_PRIME_BELOW",
"V8"
] | 4 | 0.025 | 2026-02-08T18:45:52.308804Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T18:45:52.334113Z"
} | d54ca8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2046
},
"timestamp": "2026-02-18T19:07:49.559Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BE... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b5b30a | comb_count_surjections_v1_717093673_3709 | Let $a = 4! \cdot S(5, 4)$, where $S(5, 4)$ is the Stirling number of the second kind. Let $T$ be the set of all integers $t$ such that $13 \le t \le 25$ and there exist integers $a$ and $b$ with $1 \le a \le 4$, $1 \le b \le 3$, and $t = 2a + 3b + 8$. Let $m$ be the number of elements in $T$. Define $Q = B_{|a| \bmod ... | 21,147 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | comb_count_surjections_v1 | bell_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:46:36.300195Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T17:46:36.302067Z"
} | 3d8bb8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1398
},
"timestamp": "2026-02-18T07:20:20.761Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
a9f5ad | modular_count_residue_v1_151522320_110 | Let $n$ be a positive integer such that $1 \le n \le 85264$ and $n \equiv 5 \pmod{14}$. Let $r$ be the number of such integers $n$. Let $k$ be the largest integer such that $5^k$ divides $4^{9765625} + 1^{9765625}$. Compute the Bell number $B_{r \bmod k}$. | 877 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(85264),
"m": Const(14),
"r": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=R... | NT | COMB | COUNT | sympy | LTE_SUM | [
"LTE_SUM"
] | 97353c | modular_count_residue_v1 | bell_mod | 4 | 0 | [
"LTE_SUM"
] | 1 | 10.222 | 2026-02-08T02:59:01.014623Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T02:59:11.236192Z"
} | 4b6328 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 1654
},
"timestamp": "2026-02-08T23:06:04.387Z",
"answer": 877
},
{
"i... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
b5162b | comb_catalan_compute_v1_865884756_6346 | Let $$
n_2 = \sum_{k=0}^{6} (-1)^k \binom{6}{k}.
$$ Let $$
s = \sum_{k_1=0}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}.
$$ Let $a = 4$ and $b = 3s$, and define $n_1 = a + b$. Let $$
t = \sum_{k_2=0}^{n_1} (-1)^{k_2} \binom{n_1}{k_2}.
$$ Define $n = 11 + t$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n2": Summation(var="k", start=Const(0), end=Const(6), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(6), k=Var("k")))),
"s": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_catalan_compute_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T19:09:49.802846Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T19:09:49.804731Z"
} | 2268e9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 869
},
"timestamp": "2026-02-18T21:25:37.174Z",
"answer": 58786
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
aab8e3 | nt_count_divisible_and_v1_655260480_4491 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 410881$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $d_2$ be the number of nonnegative integers $j$ such that $0 \leq j \leq s_{\text{min}}$ and $\binom{1282}{j}$ is odd. Compute the number... | 4,048 | graphs = [
Graph(
let={
"upper": Const(97152),
"d1": Const(6),
"d2": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | ALG | COMB | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 3.616 | 2026-02-08T17:57:47.304754Z | {
"verified": true,
"answer": 4048,
"timestamp": "2026-02-08T17:57:50.921065Z"
} | 235a9c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1603
},
"timestamp": "2026-02-18T10:25:37.211Z",
"answer": 4048
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b3732d | nt_min_phi_inverse_v1_151522320_1314 | Let $r$ be the smallest positive integer $n$ such that $1 \leq n \leq 60$ and $\phi(n) = 18$, where $\phi$ denotes Euler's totient function. Let $p$ be the largest prime number less than or equal to $3002$. Compute the value of $\left(r \bmod 293\right) + p \cdot \left(r \bmod 337\right)$. | 57,038 | graphs = [
Graph(
let={
"_n": Const(3002),
"upper": Const(60),
"k": Const(18),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Sum(M... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_min_phi_inverse_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.008 | 2026-02-08T03:52:48.719918Z | {
"verified": true,
"answer": 57038,
"timestamp": "2026-02-08T03:52:48.727927Z"
} | a210c5 | 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": 2013
},
"timestamp": "2026-02-10T16:19:06.249Z",
"answer": 57038
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -5.5,
"mid": -0.08,
"hi": 5.44
} | ||
0ff36e | modular_sum_quadratic_residues_v1_601307018_5936 | Let $p$ be the minimum value of $10ab + 41b^2 + 50a^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 23$. Let $M = \frac{p(p - 1)}{4}$. Find the remainder when $44121M$ is divided by $63158$. | 57,971 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(23)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(23)))), expr=Sum(Mul(Const(10), Var("a"), Va... | NT | null | SUM | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.004 | 2026-03-10T06:30:07.266725Z | {
"verified": true,
"answer": 57971,
"timestamp": "2026-03-10T06:30:07.270425Z"
} | feb6a1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1764
},
"timestamp": "2026-04-19T03:12:48.861Z",
"answer": 57971
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
55a0d4 | sequence_fibonacci_compute_v1_601307018_10326 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 30$ such that $-100ab + 50a^2 + 50b^2 = 1250$. Let $Q = F_n$, where $F_n$ denotes the $n$-th Fibonacci number. Compute $Q$. | 75,025 | graphs = [
Graph(
let={
"_n": Const(30),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(-100), V... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.002 | 2026-03-10T10:49:21.091998Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-03-10T10:49:21.093674Z"
} | eb299d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 660
},
"timestamp": "2026-04-19T13:31:23.362Z",
"answer": 75025
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} |
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