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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
583576 | diophantine_product_count_v1_1978505735_4011 | Let $k = 180$. Let $u$ be the number of integers $t$ such that $30 \leq t \leq 198$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 15$, and $t = 21a + 9b$. Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Compute $r$. | 12 | graphs = [
Graph(
let={
"k": Const(180),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=V... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.032 | 2026-02-08T17:58:46.076753Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T17:58:46.108998Z"
} | 185c99 | 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": 2275
},
"timestamp": "2026-02-18T10:40:37.967Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
582721 | modular_count_residue_v1_153355830_1003 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 26$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 4$, $1 \leq b \leq 7$, and $t = 3a + 2b$. Let $m = |T|$. Let $A$ be the set of all integers $n$ such that $1 \leq n \leq 43264$ and $n \equiv 16 \pmod{m}$. Compute the remainder when $75379... | 1,897 | graphs = [
Graph(
let={
"_n": Const(64064),
"upper": Const(43264),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'),... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.604 | 2026-02-08T04:21:04.387260Z | {
"verified": true,
"answer": 1897,
"timestamp": "2026-02-08T04:21:05.991734Z"
} | 1af461 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 2524
},
"timestamp": "2026-02-10T16:11:40.491Z",
"answer": 1897
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2ec347_l | modular_product_range_v1_1742523217_5260 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 419904$. Define $P = \prod_{i=8}^{m} i$, where $m$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $r = P \mod 11351$. Compute the Bell number $B_s$, ... | 1 | COMB | null | COMPUTE | sympy | LIN_FORM | [
"B3/B3"
] | 8ffef9 | modular_product_range_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.027 | 2026-02-08T10:53:39.535153Z | {
"verified": false,
"answer": 15,
"timestamp": "2026-02-08T10:53:39.562551Z"
} | 1db05a | 2ec347 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T12:29:27.813Z",
"answer": 52
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | |
909b4f | modular_mod_compute_v1_1125832087_1863 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 19518724$. Find the remainder when $-20164$ is divided by $m$. | 6,344 | graphs = [
Graph(
let={
"a": Const(-20164),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(19518724)))), expr=Sum(Var("x"), Var("y"... | NT | null | COMPUTE | sympy | K13 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3",
"K13"
] | 2 | 0.093 | 2026-02-08T03:59:07.830007Z | {
"verified": true,
"answer": 6344,
"timestamp": "2026-02-08T03:59:07.923391Z"
} | 547d9f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 830
},
"timestamp": "2026-02-10T14:53:24.777Z",
"answer": 6344
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9794b7 | sequence_fibonacci_compute_v1_151522320_1136 | Let $S_1$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1562500$. Define $m$ to be the minimum value of $x + y$ over all such pairs. Let $S_2$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Define $n$ to be the minimum value of $x + y$ over all such pai... | 6,765 | graphs = [
Graph(
let={
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1562500)))), expr=Sum(Var("x"), Var("y")))),
"_n": MinOverS... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3"
] | 8ffef9 | sequence_fibonacci_compute_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:49:07.622792Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T03:49:07.625193Z"
} | c440e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 1783
},
"timestamp": "2026-02-10T15:49:57.707Z",
"answer": 6765
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
b8ad1a | nt_count_gcd_equals_v1_809748730_18 | Let $k$ be the number of ordered pairs $(a,b)$ such that $a$ is an integer with $1 \leq a \leq 11$ and $b$ is an integer with $1 \leq b \leq 16$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 10000$ and $\gcd(n, k) = 1$. Compute the remainder when $90431$ multiplied by the number of elements ... | 43,143 | graphs = [
Graph(
let={
"_n": Const(55446),
"upper": Const(10000),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(11)), right=IntegerRange(start=Const(1), end=Const(16)))),
"d": Const(1),
"result": CountOverSet(s... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.913 | 2026-02-08T11:17:29.550897Z | {
"verified": true,
"answer": 43143,
"timestamp": "2026-02-08T11:17:30.463861Z"
} | 0def2a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 2200
},
"timestamp": "2026-02-14T11:35:20.581Z",
"answer": 43143
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
71e223 | antilemma_sum_factor_cartesian_v1_677425708_1559 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 15$ and $1 \leq j \leq 6$. Define $T$ to be the set of all products $i \cdot j$ where $(i,j) \in S$. Compute the sum of all elements in $T$. | 2,520 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=Const(2)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Const(6)))), expr=Mul(Var("i"), Var("... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"ONE_PHI_2"
] | 09bd3b | antilemma_sum_factor_cartesian_v1 | null | 2 | 0 | [
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T04:16:45.786595Z | {
"verified": true,
"answer": 2520,
"timestamp": "2026-02-08T04:16:45.787365Z"
} | 8c337f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 6204
},
"timestamp": "2026-02-09T21:30:49.172Z",
"answer": 1698
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
f5e079 | geo_count_lattice_rect_v1_48377204_1464 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 121$ and $0 \leq y \leq 129$. | 15,860 | graphs = [
Graph(
let={
"a": Const(121),
"b": Const(129),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T16:05:57.862125Z | {
"verified": true,
"answer": 15860,
"timestamp": "2026-02-08T16:05:57.864915Z"
} | 9dabe0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 201
},
"timestamp": "2026-02-24T19:53:12.092Z",
"answer": 15860
},
{
"... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
ae368c | comb_factorial_compute_v1_1218484723_3224 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 25$ such that $25b^2 + 10a^2 - 18ab \leq 3332$. Let $n$ be the number of integers $j$ with $0 \leq j \leq 265$ such that $\binom{M}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(3332),
"_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)), Leq(Sum(Mul(Const(25), Pow(Var("b"), Const(2)))... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/V8"
] | 4709b3 | comb_factorial_compute_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"V8"
] | 2 | 0.004 | 2026-02-25T04:54:55.941194Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T04:54:55.945558Z"
} | 099e44 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:05:03.402Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
23fbad | diophantine_fbi2_count_v1_1125832087_56 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 240$. Let $r$ be the number of integers $d$ satisfying $4 \leq d \leq 123$, such that $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 124$. Let $m = r + 2$. Define $F_k$ to be the Fibonacci sequence with $F_1 = 1$, $F_2 = ... | 10 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(240))))),
"re... | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"COMB1"
] | 567f58 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"COMB1",
"EULER_TOTIENT_SUM"
] | 2 | 0.087 | 2026-02-08T02:51:09.375070Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T02:51:09.461585Z"
} | b3c7ef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 1638
},
"timestamp": "2026-02-10T11:41:04.450Z",
"answer": 10
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -3.06,
"mid": -0.92,
"hi": 1.06
} | ||
b65b3a | comb_factorial_compute_v1_1419126231_532 | Let $e = \sum_{k=0}^{3} (-1)^k \binom{3}{k}$, $a = 5 + e$, $R = a + 1$, $u = \sum_{k_2 = \binom{7}{0} - \binom{17}{17}}^{0} (-1)^{k_2} \binom{0}{k_2}$, $v = \sum_{k_1=0}^{R} (-1)^{k_1} \binom{R}{k_1}$, and $n = (8 + v) \cdot u$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n3": Const(3),
"e": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"a": Sum(Const(5), Ref("e")),
"b": Const(1),
"n2": Sum(Ref("a"), Ref("b")),
... | COMB | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0",
"ONE_BINOM_N"
] | 55bba9 | comb_factorial_compute_v1 | null | 2 | 3 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N",
"POLY_ORBIT_HENSEL",
"ZERO_BINOM_0"
] | 4 | 0.3 | 2026-02-25T10:03:40.917968Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T10:03:41.218288Z"
} | 0b5563 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 637
},
"timestamp": "2026-03-30T08:52:37.115Z",
"answer": 40320
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
384add | sequence_lucas_compute_v1_349078426_1064 | Let $n = 22$ and let $L_n$ be the $n$-th Lucas number. Let $M$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 20$. Let $Q$ be the remainder when $M - L_n$ is divided by $51997$. Compute $Q$. | 12,494 | graphs = [
Graph(
let={
"_n": Const(51997),
"n": Const(22),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | sequence_lucas_compute_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T13:23:34.984791Z | {
"verified": true,
"answer": 12494,
"timestamp": "2026-02-08T13:23:34.987222Z"
} | dbadb9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 940
},
"timestamp": "2026-02-15T14:30:31.730Z",
"answer": 12494
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
677440 | antilemma_sum_equals_v1_458359167_4051 | Let $T$ be the set of all integers $t$ such that $30 \leq t \leq 240$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 8$, satisfying $t = 9a + 21b$. Let $n$ be the number of elements in $T$. Determine the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 58$... | 58 | 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=8)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.105 | 2026-02-08T11:29:37.163143Z | {
"verified": true,
"answer": 58,
"timestamp": "2026-02-08T11:29:37.267896Z"
} | 7b829e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T14:13:55.884Z",
"answer": null
},
{
... | 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": "V8",
"status... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
67ce1f | nt_sum_divisors_range_v1_677425708_545 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 10080$. For each $n \in S$, let $d(n)$ denote the number of positive divisors of $n$. Define $r$ to be the sum of $d(n)$ over all $n \in S$. Let $t$ be the number of digits in $|r|$. For each digit position $i$ from 0 to $t-1$, let $d_i$ be the $i... | 598 | graphs = [
Graph(
let={
"upper": Const(10080),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")))), expr=NumDivisors(n=Var("n")))),
"_c": Const(256),
"Q": Sum(Summation(var="i"... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | a9a663 | nt_sum_divisors_range_v1 | digits_weighted_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.011 | 2026-02-08T03:35:46.685372Z | {
"verified": true,
"answer": 598,
"timestamp": "2026-02-08T03:35:47.696521Z"
} | e71290 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 330,
"completion_tokens": 5097
},
"timestamp": "2026-02-10T05:34:11.231Z",
"answer": 598
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8df531 | nt_num_divisors_compute_v1_865884756_1293 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 122500$. Let $T$ be the set of all values of $x + y$ as $(x, y)$ ranges over $S$. Let $n$ be the smallest element of $T$. Determine the value of the number of positive divisors of $n$. | 18 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(122500)))), expr=Sum(Var("x"), Var("y")))),
"result": NumDiv... | NT | null | COMPUTE | sympy | COMB1 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"B3",
"COMB1"
] | 2 | 0.019 | 2026-02-08T15:52:13.418416Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T15:52:13.437508Z"
} | dde52a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 937
},
"timestamp": "2026-02-16T17:51:53.078Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
375f3c | nt_sum_divisors_mod_v1_1915831931_2881 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $11719$. | 7,625 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1171... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T17:13:37.937099Z | {
"verified": true,
"answer": 7625,
"timestamp": "2026-02-08T17:13:37.940226Z"
} | f3c992 | 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": 2227
},
"timestamp": "2026-02-17T22:33:17.026Z",
"answer": 7625
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dfb0cf | comb_catalan_compute_v1_1978505735_7154 | Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 10$ and $1 \leq j \leq 10$ such that $i + j = 11$. Let $r = C_n$, the $n$-th Catalan number. Compute the remainder when $90535 \cdot r$ is divided by $69452$. | 43,772 | graphs = [
Graph(
let={
"_n": Const(69452),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(11)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T20:05:39.194837Z | {
"verified": true,
"answer": 43772,
"timestamp": "2026-02-08T20:05:39.207595Z"
} | 3f1d3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2325
},
"timestamp": "2026-02-18T23:55:33.019Z",
"answer": 43772
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
8a5e45 | sequence_fibonacci_compute_v1_168721529_1930 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 60$ and there exist integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 4$, and $t = 4a + 6b$. Let $F_n$ denote the $n$-th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $24153 \cdot... | 39,024 | graphs = [
Graph(
let={
"_n": Const(99070),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T14:00:28.887601Z | {
"verified": true,
"answer": 39024,
"timestamp": "2026-02-08T14:00:28.891815Z"
} | a0c364 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 3159
},
"timestamp": "2026-02-09T23:43:40.727Z",
"answer": 39024
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
a3dc37 | comb_sum_binomial_row_v1_784195855_7565 | Let $m = 2$. Let $d_0$ be the smallest divisor of $115002253$ that is at least $m$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq d_0$ and $\gcd(n, 12) = 1$. Let $n_0$ be the number of elements in $A$. Compute the remainder when $44121 \cdot 2^{n_0}$ is divided by $83089$. | 2,082 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), di... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/C4"
] | bf3815 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T09:24:00.700602Z | {
"verified": true,
"answer": 2082,
"timestamp": "2026-02-08T09:24:00.702597Z"
} | 94da70 | 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": 2003
},
"timestamp": "2026-02-14T03:34:58.343Z",
"answer": 2082
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2cc8fa | nt_min_coprime_above_v1_151522320_1744 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 15015$ and the sum of the decimal digits of $n$ is odd. Let $u$ be the number of elements in $S$. Find the smallest integer $n$ such that $n > 7396$, $n \leq u$, and $\gcd(n, 102) = 1$. Let this value be $r$. Compute the remainder when $84514 \cdo... | 39,915 | graphs = [
Graph(
let={
"start": Const(7396),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(15015)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"modulus": Const(102),
"res... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | nt_min_coprime_above_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.012 | 2026-02-08T04:20:38.422126Z | {
"verified": true,
"answer": 39915,
"timestamp": "2026-02-08T04:20:38.434336Z"
} | e3b5ca | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 3274
},
"timestamp": "2026-02-10T16:18:44.618Z",
"answer": 39915
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b79d94 | comb_count_permutations_fixed_v1_865884756_3684 | Let $n = 10$ and $k = 6$. Define $\text{result}$ to be $\binom{n}{k}$ multiplied by the number of derangements of $n - k$ elements. Let $Q = \sum_{n_1=1}^{\left|\text{result}\right|} \tau(n_1)$, where $\tau(n_1)$ denotes the number of positive divisors of $n_1$. Find the value of $Q$. | 14,569 | graphs = [
Graph(
let={
"n": Const(10),
"k": Const(6),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Summation(var="n1", start=Const(1), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Va... | NT | COMB | COUNT | sympy | ONE_PHI_1 | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_PHI_1"
] | 2 | 0.027 | 2026-02-08T17:32:18.330090Z | {
"verified": true,
"answer": 14569,
"timestamp": "2026-02-08T17:32:18.357393Z"
} | f98c8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 2627
},
"timestamp": "2026-02-18T03:39:25.379Z",
"answer": 14569
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b43e9c | nt_num_divisors_compute_v1_717093673_1192 | Let $n = 121$. Define $d$ to be the number of positive divisors of $n$. Compute $$\sum_{k=1}^{d} \phi(k),$$ where $\phi(k)$ denotes the number of positive integers less than or equal to $k$ that are relatively prime to $k$. | 4 | graphs = [
Graph(
let={
"n": Const(121),
"result": NumDivisors(n=Ref("n")),
"Q": Summation(var="n1", start=Const(1), end=Abs(arg=Ref(name='result')), expr=EulerPhi(n=Var("n1"))),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID/B1"
] | 1da870 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B1",
"COUNT_COPRIME_GRID"
] | 2 | 0.017 | 2026-02-08T15:56:01.470882Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T15:56:01.487721Z"
} | a27c1b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 359
},
"timestamp": "2026-02-16T17:14:18.911Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dfdc64 | comb_count_surjections_v1_1918700295_1955 | Let $c = 8$. Define $m$ to be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = c$. Define $n$ to be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 5$, $1 \leq j \leq 5$, and $i + j = m$. Let $a$ be the number of ordered pairs $(i,j)$ such that $i... | 5,796 | graphs = [
Graph(
let={
"_c": Const(8),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_c")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Cons... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | 2b449a | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.03 | 2026-02-08T06:12:00.275812Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T06:12:00.305772Z"
} | 4be10c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 339,
"completion_tokens": 1847
},
"timestamp": "2026-02-24T08:16:11.602Z",
"answer": 5796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
0944c1 | nt_lcm_compute_v1_971394319_1921 | Let $n = 1705$ and $a = 1744$. Define $b = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$. Let $L = \operatorname{lcm}(a, b)$. Compute the remainder when $90746 \cdot L$ is divided by $52439$. | 50,693 | graphs = [
Graph(
let={
"_n": Const(1705),
"a": Const(1744),
"b": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": LCM(a=Ref("a"), b=Ref("b")),
"_c": Const(90746),
"Q": Mod(value=Mul(Ref("_c"), Ref("... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | nt_lcm_compute_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T14:00:25.968489Z | {
"verified": true,
"answer": 50693,
"timestamp": "2026-02-08T14:00:25.970388Z"
} | 21d801 | 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": 1408
},
"timestamp": "2026-02-15T23:34:10.540Z",
"answer": 50693
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dfa249 | antilemma_sum_equals_v1_1978505735_7093 | Let $n = 64$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 62$, $1 \leq j \leq 62$, and $i + j = n$. | 61 | graphs = [
Graph(
let={
"_n": Const(64),
"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(62)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.082 | 2026-02-08T20:02:26.302367Z | {
"verified": true,
"answer": 61,
"timestamp": "2026-02-08T20:02:26.384404Z"
} | fa48c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 1181
},
"timestamp": "2026-02-18T23:52:59.284Z",
"answer": 61
},
{
... | 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_SUM",
"stat... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
304094 | diophantine_product_count_v1_124444284_4166 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 44100$. Let $T = \sum_{i=1}^{23} i$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq T$, $x$ divides $k$, and $\frac{k}{x} \leq T$. Let $r$ be the number of elements in $S$. Compute the ... | 10,846 | graphs = [
Graph(
let={
"_n": Const(23),
"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(44100)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | dee757 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.033 | 2026-02-08T05:49:27.258009Z | {
"verified": true,
"answer": 10846,
"timestamp": "2026-02-08T05:49:27.291411Z"
} | 9e825c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1431
},
"timestamp": "2026-02-12T15:27:47.273Z",
"answer": 10846
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a96f08 | nt_sum_over_divisible_v1_1520064083_1304 | Let $T$ be the set of all integers $t$ with $7 \leq t \leq 24$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 5a + 2b$. Let $d$ be the number of elements in $T$. Let $S$ be the set of all positive integers $n$ such that $n \leq 15376$ and $n$ is divisible by $d$. Let... | 26,454 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(15376),
"divisor": 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... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.497 | 2026-02-08T03:55:00.487478Z | {
"verified": true,
"answer": 26454,
"timestamp": "2026-02-08T03:55:00.984880Z"
} | 1d32cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 4501
},
"timestamp": "2026-02-10T16:10:30.994Z",
"answer": 26454
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
65131b | nt_count_phi_equals_v1_2051736721_68 | Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 13124722191619115103367764423000$, and $\gcd(p, q) = 1$. Let $S$ be the set of positive integers $n$ with $1 \leq n \leq N$ such that $\phi(n) = 1864$. Compute the number of elements in $S$. | 0 | graphs = [
Graph(
let={
"upper": 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=13124722191619115103367764423000)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COUNT | sympy | LIN_FORM | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_phi_equals_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.856 | 2026-02-08T15:11:00.386751Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T15:11:01.242643Z"
} | 11fe8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 7873
},
"timestamp": "2026-02-16T01:14:33.070Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad4c60 | nt_count_gcd_equals_v1_784195855_1107 | Let $k = 210$ and let $d = \sum_{i=1}^{5} i$. Determine the number of positive integers $n$ such that $1 \leq n \leq 44444$ and $\gcd(n, k) = d$. Compute this number. | 1,269 | graphs = [
Graph(
let={
"upper": Const(44444),
"k": Const(210),
"d": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(G... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 4.631 | 2026-02-08T04:51:42.818100Z | {
"verified": true,
"answer": 1269,
"timestamp": "2026-02-08T04:51:47.448609Z"
} | 826d77 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1860
},
"timestamp": "2026-02-11T22:15:39.788Z",
"answer": 1269
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status":... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
6c2f5b | antilemma_sum_equals_v1_48377204_290 | Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $i + j = 100$, $1 \leq i \leq 98$, and $1 \leq j \leq 98$. Let $x$ be the number of elements in $S$. Define $Q$ to be the Bell number $B_{|x| \bmod 11}$. Find the value of $Q$. | 21,147 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(100)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(98)), right=IntegerRange(start=Const(1), end=Const(98))))),
"Q":... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T15:20:04.078966Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T15:20:04.083064Z"
} | 915892 | 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": 825
},
"timestamp": "2026-02-24T20:23:39.162Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
f29c7e | diophantine_fbi2_min_v1_1439011603_884 | Let $k = 81$. Determine the smallest integer $d \geq 2$ such that $d \leq 91$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Find the value of $d$. | 3 | graphs = [
Graph(
let={
"k": Const(81),
"a": Const(1),
"b": Const(5),
"upper": Const(91),
"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... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.055 | 2026-02-08T15:47:29.892824Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T15:47:29.948105Z"
} | e56534 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 518
},
"timestamp": "2026-02-16T14:06:24.066Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc4441 | comb_count_derangements_v1_1440796553_1344 | Let $d$ be the smallest positive integer greater than or equal to 2 that divides 3773. Let $n$ be this value of $d$. Define $\text{result}$ to be the subfactorial of $n$, denoted $!n$, which counts the number of derangements of $n$ elements. Let $Q$ be the remainder when $87800 \cdot \text{result}$ is divided by $93923... | 12,641 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(3773))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(87800), Ref("... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T13:39:38.831753Z | {
"verified": true,
"answer": 12641,
"timestamp": "2026-02-08T13:39:38.833295Z"
} | 4e56a9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1433
},
"timestamp": "2026-02-15T19:31:44.404Z",
"answer": 12641
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "VAL_SUM... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
48afff | diophantine_fbi2_count_v1_677425708_2938 | Let $k = 480$. Define $\text{result}$ to be the number of positive integers $d$ such that $3 \leq d \leq 123$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 122$. Define $T$ to be the set of all positive integers $t$ such that $21 \leq t \leq 19137$ and there exist positive integers $a \leq 1277$ and $b \leq 765$ for w... | 46,742 | graphs = [
Graph(
let={
"k": Const(480),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(123)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(Ref("k"), Var("d")), Const(12... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | diophantine_fbi2_count_v1 | affine_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-08T05:22:52.845595Z | {
"verified": true,
"answer": 46742,
"timestamp": "2026-02-08T05:22:52.861486Z"
} | cb8422 | 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": 5786
},
"timestamp": "2026-02-12T07:29:47.573Z",
"answer": 46742
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
44759d | nt_count_gcd_equals_v1_458359167_2980 | Let $ S $ be the set of all ordered pairs of positive integers $ (x, y) $ such that $ xy = 23104 $. Let $ k $ be the minimum value of $ x + y $ over all such pairs. Compute the number of positive integers $ n $ such that $ 1 \leq n \leq 47895 $ and $ \gcd(n, k) = 152 $. Find the remainder when $ 61781 $ times this numb... | 55,658 | graphs = [
Graph(
let={
"upper": Const(47895),
"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(23104)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 3.695 | 2026-02-08T06:52:35.873289Z | {
"verified": true,
"answer": 55658,
"timestamp": "2026-02-08T06:52:39.568090Z"
} | 6946ed | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1524
},
"timestamp": "2026-02-13T05:30:18.622Z",
"answer": 55658
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
51fbd9_n | modular_mod_compute_v1_601307018_6977 | A spacecraft can execute up to $j$ jumps on mission $j$, where $j$ ranges from 1 to 8464, but only if $j^5 \leq 43438845422363213824$. Let $m$ be the number of valid missions. The final protocol uses $M = 41 \bmod m$ as a security offset. The launch code is $9801 - M$. What is the code? | 9,760 | graphs = [
Graph(
let={
"a": Const(41),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(8464)), Leq(Pow(Var("j"), Const(5)), Const(43438845422363213824))), domain='positive_integers')),
"result": Mod(value=Ref("a... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | modular_mod_compute_v1 | null | 3 | null | [
"C3"
] | 1 | 0.004 | 2026-03-10T07:37:47.954310Z | null | b051f5 | 51fbd9 | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 538
},
"timestamp": "2026-04-23T12:49:08.214Z",
"answer": 9760
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
ad15d0 | nt_count_gcd_equals_v1_124444284_2195 | Let $k = 301$ and $d = 7$. Determine the number of positive integers $n$ such that $1 \leq n \leq 7569$ and $\gcd(n, k) = d$. | 1,056 | graphs = [
Graph(
let={
"upper": Const(7569),
"k": Const(301),
"d": Const(7),
"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 | B3 | [
"B3/V5",
"LIN_FORM"
] | 3e5ff3 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM",
"V5"
] | 3 | 1.946 | 2026-02-08T04:30:36.616167Z | {
"verified": true,
"answer": 1056,
"timestamp": "2026-02-08T04:30:38.562381Z"
} | 130e20 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 835
},
"timestamp": "2026-02-10T16:58:26.429Z",
"answer": 1056
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "ok_later"
},
{
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
4bac65 | diophantine_fbi2_count_v1_458359167_2765 | Let $k = 1260$. Compute the number of integers $d$ such that $3 \leq d \leq 79$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 79$. | 12 | graphs = [
Graph(
let={
"k": Const(1260),
"a": Const(2),
"b": Const(2),
"upper": Const(77),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(79)), Divides(divisor=Var("d"), dividend=Re... | NT | null | COUNT | sympy | K2 | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.22 | 2026-02-08T06:45:53.855615Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T06:45:54.075202Z"
} | dd8cb1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 2113
},
"timestamp": "2026-02-13T04:05:05.916Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1199cd | nt_count_coprime_v1_717093673_1208 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 900900$. Let $r$ be the number of positive integers $n$ from 1 to 54289 inclusive that are relatively prime to $k$. Compute the remainder when $47415 \cdot r$ is divided by 86489. | 37,366 | graphs = [
Graph(
let={
"_n": Const(47415),
"upper": Const(54289),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=900900)), ... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_coprime_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.327 | 2026-02-08T15:56:35.354676Z | {
"verified": true,
"answer": 37366,
"timestamp": "2026-02-08T15:56:39.681861Z"
} | fb4922 | 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": 2667
},
"timestamp": "2026-02-16T17:18:01.012Z",
"answer": 37366
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
772c19 | comb_binomial_compute_v1_784195855_3268 | Let $n = 12$ and define
$$
k = \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor,
$$
where $\varphi$ denotes Euler's totient function. Let $\binom{n}{k}$ denote the binomial coefficient. Compute the value of $43681 - \binom{n}{k}$. | 42,757 | graphs = [
Graph(
let={
"n": Const(12),
"k": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(43681),
"Q": Sub(Ref("_c"), Ref("res... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T06:19:16.137696Z | {
"verified": true,
"answer": 42757,
"timestamp": "2026-02-08T06:19:16.138911Z"
} | e91fc6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 510
},
"timestamp": "2026-02-15T17:23:46.601Z",
"answer": 42757
},
{
"id": 11,
... | 2 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
218ce7 | alg_qf_psd_orbit_v1_1218484723_5713 | Let $M$ be the number of positive integers $v$ with $4 \le v \le 2917$ for which there exist integers $a, b$ such that $1 \le a \le 14$, $1 \le b \le 14$, and $5b^2 - 16ab + 16a^2 = v$. Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 476$ such that $29b^2 - 40ab + 29a^2 = 21... | 5 | graphs = [
Graph(
let={
"_c": Const(29),
"_m": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(4)), Leq(Var("v"), Const(2917)), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(le... | ALG | null | COUNT | sympy | MOBIUS_COPRIME | [
"QF_PSD_DISTINCT/QF_PSD_COUNT/QF_PSD_COUNT_LEQ"
] | 6b909b | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"MOBIUS_COPRIME",
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 4 | 3.005 | 2026-02-25T07:15:47.736068Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T07:15:50.740988Z"
} | 672080 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T22:27:41.010Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
3ceb45 | nt_count_coprime_and_v1_971394319_1926 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Define $k_1$ to be the maximum value of $xy$ over all such pairs. Let $k_2 = 16$ and $U = 50226$. Compute the number of positive integers $n$ with $1 \leq n \leq U$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 16,742 | graphs = [
Graph(
let={
"upper": Const(50226),
"k1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_coprime_and_v1 | null | 6 | 0 | [
"B1"
] | 1 | 17.182 | 2026-02-08T14:00:26.613770Z | {
"verified": true,
"answer": 16742,
"timestamp": "2026-02-08T14:00:43.796207Z"
} | a16d89 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1754
},
"timestamp": "2026-02-15T23:34:17.498Z",
"answer": 16742
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d9532 | nt_num_divisors_compute_v1_1520064083_2138 | Compute the number of positive divisors of 64620. | 36 | graphs = [
Graph(
let={
"n": Const(64620),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | C5 | [
"COPRIME_PAIRS/ONE_PHI_2"
] | 761f00 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"C5",
"COPRIME_PAIRS",
"ONE_PHI_2"
] | 3 | 0.179 | 2026-02-08T04:31:44.871280Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T04:31:45.050191Z"
} | b12c13 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 570
},
"timestamp": "2026-02-10T16:57:25.757Z",
"answer": 36
},
{
"id"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
d1280f | comb_count_surjections_v1_655260480_194 | Let $k$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 8$, $1 \leq i \leq 6$, and $1 \leq j \leq 6$. Let $n = 5$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. Compute $\sum_{n_1 = 1}^{|r|} \phi(n_1... | 4,386 | graphs = [
Graph(
let={
"n": Const(5),
"k": 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(6)), right=IntegerRange(start=Const(1), end=Const(6... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 5b61d1 | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 2 | 0.293 | 2026-02-08T15:16:28.974744Z | {
"verified": true,
"answer": 4386,
"timestamp": "2026-02-08T15:16:29.267658Z"
} | 10e83b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 5456
},
"timestamp": "2026-02-24T20:21:03.679Z",
"answer": 4386
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
3536f4 | diophantine_fbi2_count_v1_865884756_3192 | Let $D_0=182$, $c_0=3$, and $m=2$. Define
$$n_0=\sum_{k=1}^{m} k.$$
Let $T_1$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy=21344400$. Let $S_1$ be the set of all values of $x+y$ as $(x,y)$ ranges over $T_1$, and let $L$ be the smallest element of $S_1$.
Let $k$ be the number of integers ... | 22,198 | graphs = [
Graph(
let={
"_d": Const(182),
"_c": Const(3),
"_m": Const(2),
"_n": Summation(var="k1", start=Const(1), end=Ref("_m"), expr=Var("k1")),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n")... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/B3",
"LIN_FORM/B3",
"B3/L3C"
] | c27fff | diophantine_fbi2_count_v1 | null | 8 | 0 | [
"B3",
"L3C",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 4 | 0.018 | 2026-02-08T17:13:25.280172Z | {
"verified": true,
"answer": 22198,
"timestamp": "2026-02-08T17:13:25.298539Z"
} | d7d6ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 483,
"completion_tokens": 4797
},
"timestamp": "2026-02-17T22:10:54.136Z",
"answer": 22198
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4adde4 | nt_count_coprime_and_v1_458359167_3587 | Let $k_1 = 3$ and $k_2$ be the largest prime number less than or equal to $11$. Define $N$ to be the number of positive integers $n$ with $1 \leq n \leq 34405$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Compute the remainder when $51671 \cdot N$ is divided by $76074$. | 7,630 | graphs = [
Graph(
let={
"upper": Const(34405),
"k1": Const(3),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), I... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | nt_count_coprime_and_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.532 | 2026-02-08T08:27:13.232653Z | {
"verified": true,
"answer": 7630,
"timestamp": "2026-02-08T08:27:16.764451Z"
} | 36acd2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2100
},
"timestamp": "2026-02-13T18:49:49.180Z",
"answer": 7630
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
dcde38 | comb_count_surjections_v1_1520064083_1916 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k = 6$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the value of this expression. | 15,120 | graphs = [
Graph(
let={
"_n": Const(14),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T04:22:24.914504Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T04:22:24.916849Z"
} | 7fbf3a | 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": 825
},
"timestamp": "2026-02-24T00:24:05.276Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
7b5518 | sequence_lucas_compute_v1_1918700295_3029 | Let $ d_{\text{max}} $ be the largest positive divisor of $ 522 $ that is at most $ 18 $. Let $ L $ be the $ d_{\text{max}} $-th Lucas number. Let $ c $ be the number of nonnegative integers $ j $ such that $ 0 \leq j \leq 640 $ and the binomial coefficient $ \binom{640}{j} $ is odd. Compute the remainder when $ c - L ... | 77,130 | graphs = [
Graph(
let={
"_m": Const(82904),
"_n": Const(522),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(18)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Lucas(arg=Ref(name='n')),
... | NT | null | COMPUTE | sympy | V8 | [
"V8",
"MAX_DIVISOR"
] | 786eb5 | sequence_lucas_compute_v1 | negation_mod | 4 | 0 | [
"MAX_DIVISOR",
"V8"
] | 2 | 0.003 | 2026-02-08T08:21:49.582289Z | {
"verified": true,
"answer": 77130,
"timestamp": "2026-02-08T08:21:49.585353Z"
} | e1dc7b | 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": 1413
},
"timestamp": "2026-02-13T17:47:28.808Z",
"answer": 77130
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1dab25 | comb_count_permutations_fixed_v1_124444284_5885 | Let $n = 6$ and define $$
k = \sum_{i=0}^{5} (-1)^i \binom{5}{i}.
$$
Compute the value of $$
\binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements. Find the value of this expression. | 265 | graphs = [
Graph(
let={
"n": Const(6),
"k": Summation(var="k", start=Const(0), end=Const(5), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(5), k=Var("k")))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T06:56:24.940164Z | {
"verified": true,
"answer": 265,
"timestamp": "2026-02-08T06:56:24.942209Z"
} | c9e3e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 652
},
"timestamp": "2026-02-24T07:20:02.149Z",
"answer": 265
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
9dd00f | algebra_quadratic_discriminant_v1_1470522791_1476 | Let $d$ range over the positive divisors of $28$ that are at most $4$. Let $d_{\text{max}}$ be the largest such divisor. Compute $(-19)^2 - (-1) \cdot d_{\text{max}} \cdot (-90)$, and multiply the result by $79754$. Find the value of this product. | 79,754 | graphs = [
Graph(
let={
"_n": Const(28),
"a": Const(-1),
"b": Const(-19),
"c": Const(-90),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(4)), Divides(... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T13:41:01.441444Z | {
"verified": true,
"answer": 79754,
"timestamp": "2026-02-08T13:41:01.443291Z"
} | 5de457 | 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": 310
},
"timestamp": "2026-02-15T19:22:55.205Z",
"answer": 79754
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": ... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
398d42 | antilemma_coprime_grid_v1_677425708_553 | Compute the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 50$ and $1 \leq j \leq 139$ such that $\gcd(i, j) = \phi(2)$, where $\phi$ denotes Euler's totient function. | 4,292 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(2))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(50)), right=IntegerRange(start=Const(1), end=Const(139))))),
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 98ffdc | antilemma_coprime_grid_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 2 | 0.001 | 2026-02-08T03:35:52.850755Z | {
"verified": true,
"answer": 4292,
"timestamp": "2026-02-08T03:35:52.851290Z"
} | f0d54d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 5149
},
"timestamp": "2026-02-08T20:45:22.550Z",
"answer": 4292
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
569310 | nt_sum_totient_over_divisors_v1_717093673_1156 | Let $n = 53037$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 53,037 | graphs = [
Graph(
let={
"n": Const(53037),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V5",
"L3B/V5"
] | 9a9e68 | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"L3B",
"LIN_FORM",
"V5"
] | 3 | 0.086 | 2026-02-08T15:53:27.796259Z | {
"verified": true,
"answer": 53037,
"timestamp": "2026-02-08T15:53:27.882469Z"
} | 7c2b98 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 731
},
"timestamp": "2026-02-16T06:34:57.804Z",
"answer": 60790
},
{
"id": 11,... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "ok_later"
},
{
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
65196d | antilemma_k2_v1_677425708_3593 | Let $n = 138$. Compute the value of
$$
\sum_{k=1}^{138} \phi(k) \left\lfloor \frac{138}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. | 9,591 | graphs = [
Graph(
let={
"_n": Const(138),
"x": Summation(var="k", start=Div(Const(60), Const(60)), end=Const(138), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 7 | 0 | [
"IDENTITY_DIV_SELF",
"K2"
] | 2 | 0.001 | 2026-02-08T05:51:19.444713Z | {
"verified": true,
"answer": 9591,
"timestamp": "2026-02-08T05:51:19.445570Z"
} | daff58 | 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": 680
},
"timestamp": "2026-02-12T15:13:32.503Z",
"answer": 9591
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b5eeb6 | nt_sum_over_divisible_v1_798873815_67 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. Let $N$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$.
Let $d = \gcd(84, 14)$. Compute the sum of all positive integers $n \leq N$ such that
$$
n \equiv \sum_{d'\mid d} \mu(d') \pmod{186},
$$
where $\mu$ denot... | 70,308 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"divisor": ... | NT | null | SUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.16 | 2026-02-08T02:25:37.683669Z | {
"verified": true,
"answer": 70308,
"timestamp": "2026-02-08T02:25:37.843617Z"
} | cec31a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1883
},
"timestamp": "2026-02-08T18:57:35.549Z",
"answer": 70308
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COP... | {
"lo": -1.91,
"mid": 1.73,
"hi": 4.76
} | ||
09f151_n | geo_count_lattice_rect_v1_601307018_2863 | A digital artist creates a pixel grid that is $50$ pixels wide (columns $0$ to $49$) and $b+1$ pixels tall, where $b$ is computed as the sum of powers of two from $2^0$ up to $2^s$, and $s = \sum_{d=1}^{3} \varphi(d) \cdot \lfloor \frac{3}{d} \rfloor$. How many total pixels are in this grid? | 6,400 | GEOM | GEOM | COUNT | sympy | K2 | [
"K2/SUM_GEOM",
"IDENTITY_SUB_SELF"
] | 6c10f9 | geo_count_lattice_rect_v1 | null | 4 | null | [
"IDENTITY_SUB_SELF",
"K2",
"SUM_GEOM"
] | 3 | 0.002 | 2026-03-10T03:28:58.092027Z | null | 611992 | 09f151 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 608
},
"timestamp": "2026-03-29T16:52:06.257Z",
"answer": 6400
},
{
"id... | 1 | [
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok_later"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
7f0247_l | comb_catalan_compute_v1_124444284_7563 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 17$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $n$ be the number of elements in $T$. Let $P$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 10$ and $1 \leq j \leq 1... | 58,786 | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_catalan_compute_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T09:11:28.138218Z | {
"verified": false,
"answer": 16796,
"timestamp": "2026-02-08T09:11:28.149949Z"
} | d3149f | 7f0247 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 9104
},
"timestamp": "2026-02-24T10:53:40.197Z",
"answer": 58786
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | |
7c5257 | nt_max_prime_below_v1_1520064083_5711 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $k = |S|$. Let $P$ be the set of all prime numbers $n$ such that $k \leq n \leq 65536$. Let $p_{\text{max}}$ be the largest element of $P$. Compute the remainder when $44... | 43,741 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(65536),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 5.039 | 2026-02-08T07:33:08.684351Z | {
"verified": true,
"answer": 43741,
"timestamp": "2026-02-08T07:33:13.723443Z"
} | ffb378 | 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": 2918
},
"timestamp": "2026-02-13T11:05:01.080Z",
"answer": 43741
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
37a829 | sequence_lucas_compute_v1_1520064083_4745 | Let $n$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 4$ and $1 \leq j \leq 5$. Compute the $n$-th Lucas number, where the Lucas numbers are defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. | 15,127 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | sequence_lucas_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T06:25:13.253490Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T06:25:13.256195Z"
} | 38ccd8 | 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": 560
},
"timestamp": "2026-02-12T23:34:55.239Z",
"answer": 15127
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"stat... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
348e7e | nt_max_prime_below_v1_677425708_1538 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $n \geq m$ and $n \leq 25921$. Determine the value of the largest element in ... | 25,919 | graphs = [
Graph(
let={
"upper": Const(25921),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.591 | 2026-02-08T04:14:41.513942Z | {
"verified": true,
"answer": 25919,
"timestamp": "2026-02-08T04:14:42.104963Z"
} | 0f7d52 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 2457
},
"timestamp": "2026-02-10T16:00:34.874Z",
"answer": 25919
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
066db2 | nt_count_divisible_v1_1742523217_2525 | Let $n$ be a positive integer such that $1 \leq n \leq 77841$ and $$n \equiv \sum_{d \mid m} \mu(d) \pmod{18},$$ where $m$ is the greatest prime number satisfying $2 \leq m \leq 19$, and $\mu$ denotes the M\"obius function. Compute the number of such integers $n$. | 4,324 | graphs = [
Graph(
let={
"upper": Const(77841),
"divisor": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), SumOverDivisors(n=GCD(a=Const(val... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_PRIME_BELOW/MOBIUS_COPRIME"
] | 35b4c5 | nt_count_divisible_v1 | null | 6 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 3 | 4.968 | 2026-02-08T04:49:58.459736Z | {
"verified": true,
"answer": 4324,
"timestamp": "2026-02-08T04:50:03.427420Z"
} | 50b664 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 496
},
"timestamp": "2026-02-18T14:00:16.969Z",
"answer": 4324
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "V1",
"st... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
e5fac8 | geo_visible_lattice_v1_784195855_7389 | Let $n = 77$. A visible lattice point $(x, y)$ is a point in the first quadrant with integer coordinates such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $v$ be the number of visible lattice points for this $n$. Let $c = 169$. Compute the remainder when $c - v$ is divided by $54154$. | 50,660 | graphs = [
Graph(
let={
"n": Const(77),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(169),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(54154)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.266 | 2026-02-08T09:14:34.881245Z | {
"verified": true,
"answer": 50660,
"timestamp": "2026-02-08T09:14:35.147468Z"
} | f289df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T11:02:25.205Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
e00ceb | comb_count_surjections_v1_1742523217_4 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. 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("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(14))))),
"k":... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T02:50:17.450729Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T02:50:17.452026Z"
} | c27090 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 785
},
"timestamp": "2026-02-08T19:52:48.809Z",
"answer": 126
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7... | {
"lo": -3.89,
"mid": -1.91,
"hi": 0.05
} | ||
079306 | comb_sum_binomial_row_v1_124444284_6107 | Let $n = 12$. Let $T$ be the set of all integers $t$ such that $14 \leq t \leq 16218$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 115$, $1 \leq b \leq 3767$, and $t = 10a + 4b$. Let $k$ be the number of elements in $T$. Compute the remainder when $k \cdot 2^{12}$ is divided by $59965$. | 12,859 | graphs = [
Graph(
let={
"_n": Const(59965),
"n": Const(12),
"result": Pow(Const(2), Ref("n")),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(nam... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | comb_sum_binomial_row_v1 | affine_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:08:33.507069Z | {
"verified": true,
"answer": 12859,
"timestamp": "2026-02-08T08:08:33.508217Z"
} | ee18b2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 5513
},
"timestamp": "2026-02-13T14:53:36.708Z",
"answer": 12859
},
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
b9dd40 | sequence_lucas_compute_v1_124444284_7873 | Let $n$ be the number of integers $t$ with $7 \leq t \leq 32$ for which there exist positive integers $a \leq 11$ and $b \leq 2$ such that $t = 2a + 5b$. Compute the $n$th Lucas number. | 39,603 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=11)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T09:24:11.159161Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T09:24:11.162069Z"
} | 482415 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1546
},
"timestamp": "2026-02-14T04:10:51.168Z",
"answer": 39603
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
207cf2_n | comb_bell_compute_v1_1218484723_10 | A zoo designs enclosures for animals using a $3$-by-$3$ grid of zones, where each zone can house one animal. The zoo staff partitions the $9$ zones into non-empty groups, where each group forms a connected habitat. The number of ways to form such habitats is given by the $9$-th Bell number. Compute the remainder when $... | 36,561 | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_bell_compute_v1 | null | 3 | null | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-25T01:41:20.841279Z | null | 3e6a77 | 207cf2 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1570
},
"timestamp": "2026-03-30T14:37:40.107Z",
"answer": 36561
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
846815 | diophantine_product_count_v1_1742523217_3907 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 129600$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum element of $T$. Let $k$ be the largest positive divisor of 527760 that is at most $m$. Now, let $U$ be the set of all positive integers $x$... | 4 | graphs = [
Graph(
let={
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var(... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_DIVISOR"
] | 33b851 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.006 | 2026-02-08T06:07:50.499011Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T06:07:50.504920Z"
} | 4a798b | 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": 1645
},
"timestamp": "2026-02-12T20:01:41.830Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8b165f | comb_count_derangements_v1_1978505735_2744 | Let $p$ and $q$ be positive integers such that $p \cdot q = 5250$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such integers $p$. Define $D$ as the number of derangements of $n$ elements, that is, the number of permutations of $n$ elements with no fixed points. Compute the remainder when $44121 \cdot D$ is ... | 30,975 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=5250)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T17:09:07.402765Z | {
"verified": true,
"answer": 30975,
"timestamp": "2026-02-08T17:09:07.406338Z"
} | 476a4e | 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": 2742
},
"timestamp": "2026-02-17T20:16:15.226Z",
"answer": 30975
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b252c8 | lin_form_endings_v1_1918700295_383 | Let $a = 30$ and $b = 40$. Let $d = \gcd(a, b)$. Let $k = 17879$ and define $s = k \cdot d$. Compute the remainder when $s$ is divided by $75180$. | 28,430 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(40),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(17879),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(75180),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:12:04.682685Z | {
"verified": true,
"answer": 28430,
"timestamp": "2026-02-08T03:12:04.683213Z"
} | eb2098 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 296
},
"timestamp": "2026-02-10T13:24:23.555Z",
"answer": 28530
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
43b18f | modular_mod_compute_v1_1520064083_6139 | Let $m$ be the largest prime number between $2$ and $2111$, inclusive. Compute the remainder when $-120$ is divided by $m$. | 1,991 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-120),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(2111)), IsPrime(Var("n"))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_mod_compute_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T07:52:59.187453Z | {
"verified": true,
"answer": 1991,
"timestamp": "2026-02-08T07:52:59.190234Z"
} | 6e48f6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 80,
"completion_tokens": 589
},
"timestamp": "2026-02-13T13:22:48.154Z",
"answer": 1991
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
d3b0b3 | comb_catalan_compute_v1_124444284_1269 | Let $m = 21$. Define $k$ to be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 20$, $1 \leq j \leq 21$, and $i + j = m$. Define $n$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = k$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"_m": Const(21),
"_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(20)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.01 | 2026-02-08T03:48:19.445861Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:48:19.456245Z"
} | 7fdcd0 | 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": 791
},
"timestamp": "2026-02-10T05:19:09.584Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
58a207 | comb_binomial_compute_v1_1978505735_5006 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 49$. Let $k = 7$ and let $\binom{n}{k}$ be the binomial coefficient. Compute the remainder when $44702 \cdot \binom{n}{k}$ is divided by $54367$.
Find this remainder. | 47,957 | graphs = [
Graph(
let={
"_n": Const(54367),
"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(49)))), expr=Sum(Var("x"), Var("y")))),
... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T18:44:23.682741Z | {
"verified": true,
"answer": 47957,
"timestamp": "2026-02-08T18:44:23.684175Z"
} | 4e44ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1765
},
"timestamp": "2026-02-18T18:53:17.047Z",
"answer": 47957
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
f9d2ae | antilemma_v8_lucas_1248542787_223 | Determine the number of nonnegative integers $j$ such that $0 \le j \le 98287$ and $\binom{98287}{j}$ is odd. | 32,768 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(98287)), Eq(Mod(value=Binom(n=Const(98287), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | antilemma_v8_lucas | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T03:01:32.846646Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T03:01:32.847160Z"
} | 8b96d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1154
},
"timestamp": "2026-02-09T01:32:44.824Z",
"answer": 32768
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
153f85 | nt_count_digit_sum_v1_151522320_548 | Let $ N $ be the number of positive integers $ n $ such that $ n \leq 32041 $ and the sum of the decimal digits of $ n $ is equal to 27. Let $ m = |N| $. Find the smallest integer $ d \geq 2 $ such that $ d $ divides 224939, and compute the $ m \mod d $-th Bell number. Determine the value of this Bell number. | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(32041),
"target_sum": Const(27),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_digit_sum_v1 | bell_mod | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.442 | 2026-02-08T03:22:25.620798Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T03:22:27.062351Z"
} | 859a5e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 4539
},
"timestamp": "2026-02-10T13:26:23.680Z",
"answer": 203
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4df1a7 | sequence_count_fib_divisible_v1_124444284_10138 | Let $S$ be the set of all positive integers $t$ such that $8 \le t \le 870$ and $t = 3a + 5b$ for some positive integers $a$, $b$ with $1 \le a \le 190$ and $1 \le b \le 60$. Let $u$ be the number of elements in $S$. Let $d$ be the smallest divisor of $323$ that is at least $2$. Determine the number of positive integer... | 95 | graphs = [
Graph(
let={
"_n": Const(323),
"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=190)), Geq(lef... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.182 | 2026-02-08T12:50:28.502907Z | {
"verified": true,
"answer": 95,
"timestamp": "2026-02-08T12:50:28.685018Z"
} | 698402 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 4342
},
"timestamp": "2026-02-15T06:28:52.097Z",
"answer": 95
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MIN_PRI... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b1772a | nt_count_divisors_in_range_v1_1918700295_2464 | Let $n = 55440$, $a = 62$, and $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1929321$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 71 | graphs = [
Graph(
let={
"n": Const(55440),
"a": Const(62),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1929321)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.163 | 2026-02-08T07:54:18.361162Z | {
"verified": true,
"answer": 71,
"timestamp": "2026-02-08T07:54:18.524268Z"
} | a37f88 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 4040
},
"timestamp": "2026-02-13T13:14:50.764Z",
"answer": 71
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
10bc1c | antilemma_k2_v1_1874849503_552 | Let $n = 172$. Define $$x = \sum_{k=1}^{172} \phi(k) \left\lfloor \frac{172}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the Bell number $B_r$, where $r$ is the remainder when $|x|$ is divided by $11$. Compute $Q$. | 203 | graphs = [
Graph(
let={
"_n": Const(172),
"x": Summation(var="k", start=Const(1), end=Const(172), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | SUM_INDEPENDENT | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.053 | 2026-02-08T13:09:48.819387Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T13:09:48.872686Z"
} | cfd4d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 547
},
"timestamp": "2026-02-09T18:22:30.440Z",
"answer": 203
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
bf0bd7 | diophantine_fbi2_min_v1_865884756_2288 | Let $k = 180$, $a = 3$, $b = 4$, and $u = 190$. Determine the smallest positive integer $d$ such that $4 \le d \le u$, $d$ divides $k$, and $\frac{k}{d} \ge 5$. Compute this value of $d$. | 4 | graphs = [
Graph(
let={
"k": Const(180),
"a": Const(3),
"b": Const(4),
"upper": Const(190),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"COPRIME_PAIRS",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.069 | 2026-02-08T16:40:45.069453Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T16:40:45.138036Z"
} | 88391e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 367
},
"timestamp": "2026-02-16T07:42:54.208Z",
"answer": 36
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
bdad39 | antilemma_sum_equals_v1_1431428450_472 | Let $m = 180$. Define $n$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 89$, and $1 \leq j \leq 90$. Compute $$
x + \varphi(|x| + 1) + \tau(|x| + 1),
$$where $\... | 125 | graphs = [
Graph(
let={
"_m": Const(180),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.086 | 2026-02-08T13:28:37.774388Z | {
"verified": true,
"answer": 125,
"timestamp": "2026-02-08T13:28:37.860394Z"
} | 11cd60 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1649
},
"timestamp": "2026-02-24T18:27:17.533Z",
"answer": 125
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
36b180 | alg_qf_psd_min_v1_1218484723_719 | Let $Q$ be the minimum value of the expression $$126280bc + 104181a^2 - 195734ab + 119966b^2 - 119966ac + 59983c^2$$ over all positive integers $a, b, c$ with $1 \leq a, c \leq 41$ and $1 \leq b \leq \left| \left\{ v \in [16,1936] : \exists\, a,b \in [1,11]^2 \text{ such that } 9b^2 + 6ab + a^2 = v \right\} \right|$. F... | 91,553 | graphs = [
Graph(
let={
"_n": Const(2),
"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"), Const(41)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=V... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_min_v1 | null | 6 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.161 | 2026-02-25T02:27:50.711589Z | {
"verified": true,
"answer": 91553,
"timestamp": "2026-02-25T02:27:50.872139Z"
} | 4e61c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T01:04:01.908Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 2.74,
"mid": 4.78,
"hi": 6.68
} | ||
6cd066 | nt_sum_totient_over_divisors_v1_1439011603_2024 | Let $n$ be the number of integers $t$ such that $18 \leq t \leq 11822$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 455$, $1 \leq b \leq 909$, and $t = 10a + 8b$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 5,891 | 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=455)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T16:28:11.895946Z | {
"verified": true,
"answer": 5891,
"timestamp": "2026-02-08T16:28:11.903739Z"
} | 1a9ea0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 5610
},
"timestamp": "2026-02-17T04:05:24.117Z",
"answer": 5891
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dec326 | nt_count_gcd_equals_v1_971394319_1097 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 2601$. Compute the number of positive integers $n$ with $1 \leq n \leq 32041$ such that $\gcd(n, k) = 3$. | 5,026 | graphs = [
Graph(
let={
"_n": Const(2601),
"upper": Const(32041),
"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")), Ref("_n"))))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 3.041 | 2026-02-08T13:29:52.837418Z | {
"verified": true,
"answer": 5026,
"timestamp": "2026-02-08T13:29:55.878363Z"
} | d291e5 | 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": 1264
},
"timestamp": "2026-02-15T16:31:53.146Z",
"answer": 5026
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
05a3ec | alg_poly_orbit_hensel_v1_601307018_3464 | For a non-negative integer $a$, define $N = (2a^4 + 3a^3 + a^2) \bmod 961$, $M = (2N^4 + 3N^3 + N^2) \bmod 961$, and $R = (2M^4 + 3M^3 + M^2) \bmod 961$. Find the number of integers $a$ with $0 \le a \le 1897013$ such that $R = a$, $N \ne a$, and $M \ne a$. | 5,922 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(4))), Mul(Const(3), Pow(Var("a"), Const(3))), Pow(Var("a"), Const(2))), modulus=Const(961)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(4))), Mul(Const(3), Pow(Ref("p1"), Const(3))), Pow(Ref("p1... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.097 | 2026-03-10T04:04:44.981986Z | {
"verified": true,
"answer": 5922,
"timestamp": "2026-03-10T04:04:45.079236Z"
} | 06e750 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 8053
},
"timestamp": "2026-03-29T08:47:31.893Z",
"answer": 3
},
{
"i... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
26e8a8 | nt_sum_divisors_mod_v1_124444284_6158 | Let $S$ be the set of all integers $t$ such that $28 \leq t \leq 1725$ and there exist positive integers $a \leq 112$ and $b \leq 180$ satisfying $t = 4a + 7b + 17$. Let $n$ be the number of elements in $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $1144... | 40,680 | 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=112)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T08:10:38.966653Z | {
"verified": true,
"answer": 40680,
"timestamp": "2026-02-08T08:10:38.968643Z"
} | 7db66f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 6154
},
"timestamp": "2026-02-13T15:33:24.348Z",
"answer": 40680
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
46f129_n | alg_sym_quad_system_v1_1218484723_1792 | Three types of solar panels generate power levels $a$, $b$, and $c$, each a positive integer. Their efficiency is maximized when $a^2 + b^2 + c^2 = ab + bc + ca$, and their combined installation cost is fixed at $4a + 7b + 9c = 9200$ dollars. The total energy output is $a^3 + b^3 + c^3$. The system must also route data... | 1,536 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sym_quad_system_v1 | null | 6 | null | [
"B3"
] | 1 | 0.026 | 2026-02-25T03:26:44.920887Z | null | 7732c0 | 46f129 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1554
},
"timestamp": "2026-03-30T17:18:20.990Z",
"answer": 1536
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
520afb | diophantine_fbi2_min_v1_1439011603_1773 | Let $m = 190$. Let $A$ be the set of all positive integers $k_1$ such that $1 \le k_1 \le 45600$ and $m$ divides $k_1$. Let $B$ be the set of all positive integers $d$ such that $1 \le d \le |A|$ and $d$ divides $61680$. Let $d_{\text{max}}$ be the largest element of $B$. Let $C$ be the set of all positive integers $n$... | 4 | graphs = [
Graph(
let={
"_m": Const(190),
"_n": Const(3),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), CountOverSet(set=... | NT | null | EXTREMUM | sympy | C4 | [
"C2/MAX_DIVISOR/COUNT_FIB_DIVISIBLE"
] | cb7cd5 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"C2",
"C4",
"COUNT_FIB_DIVISIBLE",
"MAX_DIVISOR"
] | 4 | 0.032 | 2026-02-08T16:16:51.074743Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T16:16:51.106685Z"
} | fcc6a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 1739
},
"timestamp": "2026-02-17T00:38:44.248Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5e28a8 | modular_sum_quadratic_residues_v1_1874849503_761 | Let $p$ be the largest prime number less than or equal to 520. Define $c = 13924$ and let
$$
Q = (c - \frac{p(p-1)}{4}) \mod 50500.
$$
Find the value of $Q$. | 50,281 | graphs = [
Graph(
let={
"_n": Const(520),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": Const(13924),... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:18:14.993569Z | {
"verified": true,
"answer": 50281,
"timestamp": "2026-02-08T13:18:14.995069Z"
} | 70b9b3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 2597
},
"timestamp": "2026-02-09T20:40:27.983Z",
"answer": 50281
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -5.15,
"mid": 0.12,
"hi": 6.12
} | ||
8c8605 | algebra_vieta_sum_v1_124444284_911 | Let $S$ be the set of all real numbers $x$ such that $$
2x^3 + 16x^2 - 38x + 20 = 0.
$$
Let $P$ be the product of all elements of $S$. Compute the remainder when $44121 \cdot P$ is divided by 66166. | 21,952 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=2), Pow(base=Var(name='x'), exp=Const(value=3))), Mul(Const(value=16), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=-38), Var(name='x')), Const(value=20)), ... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.023 | 2026-02-08T03:35:50.254035Z | {
"verified": true,
"answer": 21952,
"timestamp": "2026-02-08T03:35:50.276928Z"
} | 748f49 | 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": 922
},
"timestamp": "2026-02-09T23:47:44.216Z",
"answer": 21952
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
2e7858 | comb_sum_binomial_row_v1_1440796553_528 | Let $n$ be the number of positive integers $k$ not exceeding $390$ such that $20$ divides the $k$-th Fibonacci number. Compute $2^n$. Let $c = 76433$ and $m = 58876$. Find the remainder when $c \cdot 2^n$ is divided by $m$. | 51,752 | graphs = [
Graph(
let={
"_n": Const(58876),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(390)), Divides(divisor=Const(20), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Pow(Const(2), Ref("n")),
... | ALG | NT | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T11:50:43.244942Z | {
"verified": true,
"answer": 51752,
"timestamp": "2026-02-08T11:50:43.246084Z"
} | 8fc015 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1937
},
"timestamp": "2026-02-14T19:25:23.795Z",
"answer": 51752
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
15b71e | nt_num_divisors_compute_v1_1742523217_3184 | Let $n = 2304$. Compute the number of positive divisors of $n$. | 27 | graphs = [
Graph(
let={
"n": Const(2304),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"B3/VIETA_SUM/B3/MAX_PRIME_BELOW"
] | c36cfc | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME",
"VIETA_SUM"
] | 4 | 0.036 | 2026-02-08T05:42:45.467813Z | {
"verified": true,
"answer": 27,
"timestamp": "2026-02-08T05:42:45.504084Z"
} | e7e6f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 387
},
"timestamp": "2026-02-12T12:36:48.566Z",
"answer": 27
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
3a0334 | antilemma_k3_v1_458359167_1890 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $49452$, where $\phi$ denotes Euler's totient function. Compute the remainder when $77159 \cdot x$ is divided by $75627$. | 57,837 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=49452), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(77159), Ref("x")), modulus=Const(75627)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:55:28.657977Z | {
"verified": true,
"answer": 57837,
"timestamp": "2026-02-08T04:55:28.658494Z"
} | 304148 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 2083
},
"timestamp": "2026-02-11T22:27:16.996Z",
"answer": 57837
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
b1f3b2 | geo_count_lattice_rect_v1_2051736721_5128 | Compute the number of lattice points in the rectangle $[0, 300] \times [0, 134]$, including the boundary. Find the value of $70000$ minus this number. | 29,365 | graphs = [
Graph(
let={
"a": Const(300),
"b": Const(134),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Sub(Const(70000), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:22:47.292332Z | {
"verified": true,
"answer": 29365,
"timestamp": "2026-02-08T18:22:47.293658Z"
} | 0444a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 491
},
"timestamp": "2026-02-24T23:50:42.547Z",
"answer": 29365
},
{
... | 1 | [] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||||
b33e0a | sequence_count_fib_divisible_v1_784195855_3404 | Let $d$ be the largest prime number $n$ such that $2 \leq n \leq 18$. Compute the number of positive integers $n \leq 497$ for which $d$ divides the $n$-th Fibonacci number. Let $Q = 512$ minus this number. Find the value of $Q$. | 457 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(497),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(18)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.023 | 2026-02-08T06:24:47.488006Z | {
"verified": true,
"answer": 457,
"timestamp": "2026-02-08T06:24:47.510738Z"
} | a97b7e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 2100
},
"timestamp": "2026-02-13T00:01:20.347Z",
"answer": 457
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1b7da8 | lin_form_endings_v1_1742523217_5704 | Let $a = 36$ and $b = 48$. Compute the greatest common divisor of $a$ and $b$, multiply it by $14977$, and find the remainder when the result is divided by $96129$. Compute the value of this remainder. | 83,595 | graphs = [
Graph(
let={
"a_coeff": Const(36),
"b_coeff": Const(48),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(14977),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(96129),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:11:38.042650Z | {
"verified": true,
"answer": 83595,
"timestamp": "2026-02-08T11:11:38.043173Z"
} | d76bb3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 348
},
"timestamp": "2026-02-15T21:09:19.587Z",
"answer": 83595
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
aa38b9 | nt_count_squarefree_v1_1248542787_108 | Let $d(n)$ denote the number of positive divisors of $n$. The M\"obius function $\mu(n)$ is defined as follows: $\mu(n) = 0$ if $n$ has a squared prime factor; otherwise, $\mu(n) = (-1)^k$ where $k$ is the number of distinct prime factors of $n$. Let $g = \gcd(12, 25)$. Compute the number of integers $n$ such that $\mu... | 43,993 | graphs = [
Graph(
let={
"upper": Const(72361),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=12), b=Const(value=25)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Ref("upper")), Eq(Mul(MoebiusMu(n=Va... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_squarefree_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 17.506 | 2026-02-08T02:57:16.314478Z | {
"verified": true,
"answer": 43993,
"timestamp": "2026-02-08T02:57:33.820151Z"
} | 4cbe16 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 4363
},
"timestamp": "2026-02-09T12:42:43.367Z",
"answer": 43990
},
{
... | 0 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 3.31,
"mid": 6.77,
"hi": 10
} | ||
20e1ff | algebra_poly_eval_v1_601307018_8951 | Let $t$ be the number of integers $v$ in the range $16 \leq v \leq S$ such that $v = 32a^2 + b^2 - 8ab$ for some integers $a, b$ with $1 \leq a, b \leq 5$, where $$S = \left|\{ (a, b) \in \mathbb{Z}^2 : 1 \leq a, b \leq 40,\ 25b^2 - 18ab + 10a^2 \leq 9370 \}\right|.$$ Let $R = 9t^2 + 7t + 7$. Find the remainder when $4... | 49,151 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": Const(44121),
"t": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(16)), Leq(Var("v"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_DISTINCT"
] | 0cf842 | algebra_poly_eval_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 2 | 0.006 | 2026-03-10T09:23:13.179813Z | {
"verified": true,
"answer": 49151,
"timestamp": "2026-03-10T09:23:13.185697Z"
} | f1fcda | 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": 9579
},
"timestamp": "2026-04-19T10:14:34.887Z",
"answer": 49151
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
fd40d6 | nt_count_digit_sum_v1_124444284_4333 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 10009$ and there exist positive integers $a \leq 1333$ and $b \leq 1672$ satisfying $t = 5a + 2b$. Let $u$ be the number of positive integers $n \leq |T|$ such that the sum of the decimal digits of $n$ is 19. Let $d$ be the number of digits in $u$. Compute... | 13,074 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1333)), Geq(left=Var(name='b'), right=Const(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.537 | 2026-02-08T05:55:23.528449Z | {
"verified": true,
"answer": 13074,
"timestamp": "2026-02-08T05:55:24.064987Z"
} | 61761f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T04:57:01.506Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
a58e8b | nt_count_divisors_in_range_v1_865884756_3032 | Let $n = 1680$, $a = 5$, and $b = 86$. Define $r$ to be the number of positive divisors of $n$ that are at least $a$ and at most $b$. Let $s$ be the sum of all real solutions $x$ to the equation $x^2 - 3001x + 202308 = 0$. Compute the value of $$
mod{r}{307} + s \cdot \left(\nmod{r}{317}\right).$$ | 69,046 | graphs = [
Graph(
let={
"_n": Const(317),
"n": Const(1680),
"a": Const(5),
"b": Const(86),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref(... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 805c31 | nt_count_divisors_in_range_v1 | two_moduli | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.007 | 2026-02-08T17:07:36.163084Z | {
"verified": true,
"answer": 69046,
"timestamp": "2026-02-08T17:07:36.170369Z"
} | 98641a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1375
},
"timestamp": "2026-02-17T19:52:20.685Z",
"answer": 69046
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
71cc91 | modular_sum_quadratic_residues_v1_153355830_1744 | Let $p = 373$ and define $r = \frac{p(p-1)}{4}$. Let $c$ be the number of positive integers $n$ such that $1 \leq n \leq 23312$, $4$ divides $n$, and $\gcd(n, 35) = 1$.
Compute the remainder when $c \cdot r$ is divided by $93236$. | 10,001 | graphs = [
Graph(
let={
"_n": Const(4),
"p": Const(373),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(23312)), Divides(divisor=Ref(... | NT | null | SUM | sympy | C5 | [
"C5"
] | 833638 | modular_sum_quadratic_residues_v1 | affine_mod | 4 | 0 | [
"C5"
] | 1 | 0.003 | 2026-02-08T06:35:44.915039Z | {
"verified": true,
"answer": 10001,
"timestamp": "2026-02-08T06:35:44.917569Z"
} | e2b820 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1317
},
"timestamp": "2026-02-13T02:26:52.657Z",
"answer": 10001
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d4beb6 | nt_count_gcd_equals_v1_1440796553_1476 | Let $u = 23716$. Define $k$ to be the number of positive integers $n$ such that $1 \leq n \leq 889$ and $\gcd(n, 6) = 1$. Compute $20000$ minus the number of positive integers $n$ such that $1 \leq n \leq u$ and $\gcd(n, k) = 1$. | 5,627 | graphs = [
Graph(
let={
"upper": Const(23716),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(889)), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"d": Const(1),
"result": CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"C4"
] | 1 | 2.372 | 2026-02-08T14:01:45.181906Z | {
"verified": true,
"answer": 5627,
"timestamp": "2026-02-08T14:01:47.554315Z"
} | 4dd0ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1133
},
"timestamp": "2026-02-15T23:00:45.756Z",
"answer": 5627
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
3e86c7 | nt_count_divisible_v1_971394319_1649 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 160083000$ and $\gcd(p, q) = 1$. Let $d$ be the number of elements in $S$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 67600$ and $n$ is divisible by $d$. Find the remainder when... | 75,102 | graphs = [
Graph(
let={
"upper": Const(67600),
"divisor": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=160083000)), Eq(left=GCD(a=Var(name=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 4.982 | 2026-02-08T13:47:28.212052Z | {
"verified": true,
"answer": 75102,
"timestamp": "2026-02-08T13:47:33.194070Z"
} | 8a32fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1905
},
"timestamp": "2026-02-15T21:05:15.898Z",
"answer": 75102
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
790151 | nt_max_prime_below_v1_1918700295_2877 | Let $S$ be the set of all positive integers $p$ for which there exist positive integers $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Define $T$ to be the set of all prime numbers $n$ such that $m \leq n \leq 76176$. Determine the value of the largest element in $T$. | 76,163 | graphs = [
Graph(
let={
"upper": Const(76176),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.881 | 2026-02-08T08:16:38.303324Z | {
"verified": true,
"answer": 76163,
"timestamp": "2026-02-08T08:16:40.184367Z"
} | 34866d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2257
},
"timestamp": "2026-02-13T16:47:32.807Z",
"answer": 76163
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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