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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
966206 | nt_sum_divisors_compute_v1_865884756_785 | Let $n = 43681$. Compute the sum of all positive divisors of $n$. | 50,673 | graphs = [
Graph(
let={
"n": Const(43681),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3/MOBIUS_COPRIME/MOBIUS_SUM"
] | d7d237 | nt_sum_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"MOBIUS_COPRIME",
"MOBIUS_SUM"
] | 3 | 0.01 | 2026-02-08T15:36:36.942351Z | {
"verified": true,
"answer": 50673,
"timestamp": "2026-02-08T15:36:36.952400Z"
} | 6b92e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 66,
"completion_tokens": 948
},
"timestamp": "2026-02-16T09:24:50.996Z",
"answer": 50673
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5b3c9d | nt_count_divisible_v1_784195855_1734 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 80000$ and $n$ is divisible by $12$. Let $p$ be the largest prime number less than or equal to $11$. Compute the Bell number $B_r$, where $r$ is the remainder when $|A|$ is divided by $p$. | 1 | graphs = [
Graph(
let={
"upper": Const(80000),
"divisor": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"Q": Be... | NT | COMB | COUNT | sympy | B1 | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_count_divisible_v1 | bell_mod | 3 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 33.873 | 2026-02-08T05:15:33.720376Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T05:16:07.593682Z"
} | 9653e5 | 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": 413
},
"timestamp": "2026-02-12T06:10:50.278Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
612cad | antilemma_k3_v1_865884756_3388 | Let $n = 11453$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 11,453 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=11453), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:20:02.820598Z | {
"verified": true,
"answer": 11453,
"timestamp": "2026-02-08T17:20:02.821248Z"
} | 7de827 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 364
},
"timestamp": "2026-02-16T09:26:20.895Z",
"answer": 12141
},
{
"id": 11,... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
0bdc17 | antilemma_sum_equals_v1_2051736721_2576 | Let $n = 79$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 78$, and $1 \leq j \leq 79$. | 78 | graphs = [
Graph(
let={
"_n": Const(79),
"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(78)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.079 | 2026-02-08T16:47:34.427934Z | {
"verified": true,
"answer": 78,
"timestamp": "2026-02-08T16:47:34.506450Z"
} | d4ced3 | 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": 989
},
"timestamp": "2026-02-24T21:51:33.572Z",
"answer": 78
},
{
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
706232 | nt_count_divisible_and_v1_865884756_5771 | Let $n$ be a positive integer. Define
$$
d_2 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $d_1 = 4$. Determine the number of positive integers $n \leq 52692$ such that $n$ is divisible by both $d_1$ and $d_2$. Compute this number. | 4,391 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(52692),
"d1": Const(4),
"d2": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 5 | 0 | [
"K2"
] | 1 | 1.701 | 2026-02-08T18:46:40.290105Z | {
"verified": true,
"answer": 4391,
"timestamp": "2026-02-08T18:46:41.991374Z"
} | 346313 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 475
},
"timestamp": "2026-02-16T16:06:13.444Z",
"answer": 4391
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ad09f9 | nt_sum_divisors_mod_v1_1918700295_1088 | Let $ T $ be the set of all integers $ t $ such that $ 5 \leq t \leq 2526 $ and there exist positive integers $ a \leq 196 $, $ b \leq 969 $ satisfying $ t = 3a + 2b $. Let $ n $ be the number of elements in $ T $. Let $ \sigma $ be the sum of all positive divisors of $ n $. Let $ M = 11831 $. Compute the remainder whe... | 65,122 | 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=196)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T05:33:25.912655Z | {
"verified": true,
"answer": 65122,
"timestamp": "2026-02-08T05:33:25.920442Z"
} | 807317 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 4714
},
"timestamp": "2026-02-12T11:01:21.570Z",
"answer": 65122
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
070c6d | sequence_lucas_compute_v1_153355830_1610 | Let $p$ and $q$ be positive integers such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of such values of $p$. Let $n$ be the smallest integer that is at least $N$ and divides 10232447. Compute the $n$-th Lucas number. | 64,079 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T06:31:37.569115Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T06:31:37.572405Z"
} | 7b429c | 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": 2166
},
"timestamp": "2026-02-13T01:39:34.088Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e79216 | geo_visible_lattice_v1_151522320_306 | Let $n = 105$. A lattice point $(x, y)$ is called visible from the origin if $\gcd(x, y) = 1$. Compute the number of visible lattice points $(x, y)$ such that $1 \leq x, y \leq n$. | 6,747 | graphs = [
Graph(
let={
"n": Const(105),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.288 | 2026-02-08T03:08:53.169063Z | {
"verified": true,
"answer": 6747,
"timestamp": "2026-02-08T03:08:53.456731Z"
} | 9ead4b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 7344
},
"timestamp": "2026-02-23T21:41:39.658Z",
"answer": 6747
},
{
"i... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
29d8f4 | nt_num_divisors_compute_v1_898971024_120 | Let $c = 14$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = c$. Let $m$ be the maximum value of $xy$ over all such pairs. Now consider the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = m$. Let $n$ be the minimum value of $x_1 + y_1$ over all suc... | 8 | graphs = [
Graph(
let={
"_c": Const(14),
"_m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_c")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"B1/B3/B1"
] | 644515 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B1",
"B3",
"MOBIUS_COPRIME"
] | 3 | 0.025 | 2026-02-08T15:12:03.572553Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T15:12:03.597687Z"
} | b99b82 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 835
},
"timestamp": "2026-02-16T02:38:44.594Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eec44a | geo_count_lattice_triangle_v1_2051736721_2265 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(128,4)$, and $(30,101)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle. Define $C$ to be the number of unordered pairs of distinct positive integers $(p, q)$ such that $pq = 12$ and $\gcd(p, q) = 1$. Compute $\frac... | 6,402 | graphs = [
Graph(
let={
"_n": Const(30),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=101)), Mul(Const(value=30), Sub(left=Const(value=0), right=Const(value=4))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=4))), GCD(a=Abs(arg=Sub(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.009 | 2026-02-08T16:33:10.145431Z | {
"verified": true,
"answer": 6402,
"timestamp": "2026-02-08T16:33:10.154547Z"
} | b29cce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1651
},
"timestamp": "2026-02-17T06:31:41.596Z",
"answer": 6402
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
664b09 | lin_form_endings_v1_151522320_247 | Let $a = 20$ and $b = 25$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 42$ and $B = 11$. Define $s = a'A + b'B - a'b'$. Let $k = 10364$ and $M = 79525$. Compute the remainder when $k \cdot s$ is d... | 36,242 | graphs = [
Graph(
let={
"a_coeff": Const(20),
"b_coeff": Const(25),
"A_val": Const(42),
"B_val": Const(11),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:06:06.788239Z | {
"verified": true,
"answer": 36242,
"timestamp": "2026-02-08T03:06:06.788858Z"
} | ec4141 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 896
},
"timestamp": "2026-02-10T13:06:00.021Z",
"answer": 36242
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
c9b6bf | sequence_count_fib_divisible_v1_865884756_4247 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 139129$. Let $\text{sums}$ be the set of all values $x + y$ where $(x, y) \in S$. Let $u$ be the minimum element of $\text{sums}$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $6$ divides $F_n$, the $n$t... | 17,270 | graphs = [
Graph(
let={
"_n": Const(70381),
"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(139129)))), expr=Sum(Var("x"), Var("... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.091 | 2026-02-08T17:49:40.136872Z | {
"verified": true,
"answer": 17270,
"timestamp": "2026-02-08T17:49:40.228269Z"
} | e41743 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1611
},
"timestamp": "2026-02-18T09:01:52.462Z",
"answer": 17270
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bd018f | antilemma_k3_v1_151522320_1631 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $43873$. Let $Q$ be the remainder when $31547x$ is divided by $68574$. Find the value of $Q$. | 32,489 | graphs = [
Graph(
let={
"_n": Const(43873),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(31547), Ref("x")), modulus=Const(68574)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:08:50.339152Z | {
"verified": true,
"answer": 32489,
"timestamp": "2026-02-08T04:08:50.339586Z"
} | c34a9f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 2976
},
"timestamp": "2026-02-10T15:37:41.861Z",
"answer": 32489
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4da4c5 | algebra_poly_eval_v1_168721529_1076 | Let $n = 6145$. Define $t$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq n$ and $\binom{n}{j}$ is odd. Compute $3t^2 - t + 2$. | 186 | graphs = [
Graph(
let={
"_n": Const(6145),
"t": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(6145)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | algebra_poly_eval_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T13:27:39.183478Z | {
"verified": true,
"answer": 186,
"timestamp": "2026-02-08T13:27:39.186452Z"
} | 55cb3a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 752
},
"timestamp": "2026-02-09T13:36:48.728Z",
"answer": 186
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -1.2,
"mid": 1.93,
"hi": 4.95
} | ||
1a9577 | lin_form_endings_v1_1915831931_3648 | Let $a = 4$ and $b = 6$. Let $A = 25$ and $B = 26$. Compute $g = \gcd(a, b)$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $r = a' \cdot A + b' \cdot B - a' \cdot b'$. Multiply $r$ by $14482$ to obtain a value $s$. Compute the remainder when $s$ is divided ... | 19,272 | graphs = [
Graph(
let={
"a_coeff": Const(4),
"b_coeff": Const(6),
"A_val": Const(25),
"B_val": Const(26),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": Fl... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:47:50.236074Z | {
"verified": true,
"answer": 19272,
"timestamp": "2026-02-08T17:47:50.236828Z"
} | 393768 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 786
},
"timestamp": "2026-02-18T08:04:29.011Z",
"answer": 19272
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69dbe8 | modular_sum_quadratic_residues_v1_1520064083_137 | Let $p$ be the largest prime number less than or equal to $270$. Compute the remainder when $\frac{p(p-1)}{4} \cdot 91841$ is divided by $55430$. | 55,113 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(270)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"_c": Const(91841),... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T03:06:22.415894Z | {
"verified": true,
"answer": 55113,
"timestamp": "2026-02-08T03:06:22.417991Z"
} | e909ef | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1513
},
"timestamp": "2026-02-10T12:40:50.683Z",
"answer": 55113
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
a65bc3 | antilemma_k2_v1_1978505735_6426 | Let $n = 137$. Compute $x = \sum_{k=1}^{137} \phi(k) \left\lfloor \frac{137}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $Q = x + \phi(|x| + 1) + \tau(|x| + 1)$, where $\tau(m)$ denotes the number of positive divisors of $m$. Find the value of $Q$. | 13,997 | graphs = [
Graph(
let={
"_n": Const(137),
"x": Summation(var="k", start=Const(1), end=Const(137), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x'... | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2"
] | 2 | 0.005 | 2026-02-08T19:35:44.757573Z | {
"verified": true,
"answer": 13997,
"timestamp": "2026-02-08T19:35:44.762323Z"
} | a03f39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1756
},
"timestamp": "2026-02-18T22:56:29.082Z",
"answer": 13997
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bb6e79 | comb_count_derangements_v1_458359167_4490 | Let $n = 7$. Define $d_n$ to be the number of derangements of $n$ elements. Let $p$ be the largest prime number less than or equal to 11. Compute the Bell number $B_k$, where $k$ is the remainder when $|d_n|$ is divided by $p$. | 203 | graphs = [
Graph(
let={
"_n": Const(11),
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_count_derangements_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.008 | 2026-02-08T11:49:15.374725Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T11:49:15.382511Z"
} | 6256c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 519
},
"timestamp": "2026-02-14T20:00:41.575Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d335bc | comb_sum_binomial_row_v1_601307018_8627 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ satisfying
$$
128b^3 + d \cdot a^2 b + 128a^3 + 384a b^2 = 8192000,
$$
where $d = \min\{ |x - y| : x > 0, y > 0,\, xy = 300697 \}$. Let $S = 2^n$. Find the remainder when $84239 \cdot S$ is divided by $74635$. | 39,987 | graphs = [
Graph(
let={
"_m": Const(128),
"_n": Const(25),
"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"), Ref("_n")), Eq(Sum(Mul(Const(128... | COMB | null | SUM | sympy | POLY_ORBIT_LEGENDRE | [
"B3_DIFF/POLY3_COUNT"
] | 18d12f | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B3_DIFF",
"POLY3_COUNT",
"POLY_ORBIT_LEGENDRE"
] | 3 | 0.041 | 2026-03-10T09:05:33.373633Z | {
"verified": true,
"answer": 39987,
"timestamp": "2026-03-10T09:05:33.414506Z"
} | 8047e1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 4815
},
"timestamp": "2026-04-19T09:23:09.234Z",
"answer": 39987
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "V... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
d4eb10 | geo_count_lattice_triangle_v1_865884756_1066 | Let $A$ be the absolute value of the expression $120 \cdot 120 + 50 \cdot (0 - 100)$. Let $B$ be the sum
\[
\gcd(|120|, |100|) + \gcd(|50 - 120|, |120 - 100|) + \gcd(|0 - 50|, |0 - 120|).
\]
Define $R = \frac{A + 2 - B}{2}$. Compute the remainder when $80665 \cdot R$ is divided by $63743$. | 43,076 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=120)), Mul(Const(value=50), Sub(left=Const(value=0), right=Const(value=100))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=100))), GCD(a=Abs(arg=Sub(left=Const(value=50), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.012 | 2026-02-08T15:45:43.095690Z | {
"verified": true,
"answer": 43076,
"timestamp": "2026-02-08T15:45:43.107717Z"
} | b7f839 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1166
},
"timestamp": "2026-02-16T13:28:30.140Z",
"answer": 43076
},
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
3ad740 | sequence_fibonacci_compute_v1_458359167_1018 | Let $m = 9$ and $k_0 = 1 + 2 + 3$. For each positive integer $k \leq k_0$, let $s_k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Define $n = \sum_{k=1}^{k_0} \phi(k) \left\lfloor \frac{s_k}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Com... | 10,946 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Va... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2",
"B3/K2"
] | 04224a | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B3",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.004 | 2026-02-08T04:13:47.466479Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T04:13:47.470703Z"
} | b91fba | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1512
},
"timestamp": "2026-02-10T15:53:17.797Z",
"answer": 10946
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lem... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
73520d | algebra_poly_eval_v1_1520064083_4543 | Let $k = 5$ and $n = 3$. Define $S$ as the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of
$$
5^4 + 3 \cdot 5^3 - 2 \cdot 5^{|S|} - 5 - 3.
$$ | 942 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(5),
"result": Sum(Pow(Ref("k"), Const(4)), Mul(Const(3), Pow(Ref("k"), Ref("_n"))), Mul(Const(-2), Pow(Ref("k"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T06:19:05.109018Z | {
"verified": true,
"answer": 942,
"timestamp": "2026-02-08T06:19:05.111329Z"
} | be0f23 | 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": 1141
},
"timestamp": "2026-02-12T22:20:07.629Z",
"answer": 942
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4fd9d6 | nt_count_coprime_v1_1918700295_1080 | Let $x$ and $y$ be positive integers such that $xy = 289$. Let $s$ be the sum $x + y$. Define $k$ to be the minimum value of $s$ over all such pairs $(x, y)$. Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 10946$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 5,151 | graphs = [
Graph(
let={
"upper": Const(10946),
"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(289)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 4.611 | 2026-02-08T05:33:09.548545Z | {
"verified": true,
"answer": 5151,
"timestamp": "2026-02-08T05:33:14.159982Z"
} | fb9f37 | 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": 1198
},
"timestamp": "2026-02-12T10:59:55.432Z",
"answer": 5151
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
99bfcd | comb_binomial_compute_v1_1742523217_77 | Let $n = 13$. Let $k$ be the largest prime number less than or equal to 7. Compute $\binom{n}{k}$, and then find the remainder when $31301$ times this binomial coefficient is divided by $67448$. | 23,908 | graphs = [
Graph(
let={
"n": Const(13),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Const(31301),
"Q": Mod(value... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.012 | 2026-02-08T02:52:14.231953Z | {
"verified": true,
"answer": 23908,
"timestamp": "2026-02-08T02:52:14.244105Z"
} | 08b960 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1870
},
"timestamp": "2026-02-09T13:38:26.094Z",
"answer": 23908
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": 0.01,
"mid": 1.71,
"hi": 3.25
} | ||
ecb1ac | geo_count_lattice_rect_v1_971394319_1038 | Let $a = 120$ and $b = 65$. Define $\text{result}$ to be the number of lattice points $(x,y)$ with $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the remainder when $46125 \cdot \text{result}$ is divided by $60376$. | 274 | graphs = [
Graph(
let={
"a": Const(120),
"b": Const(65),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(46125), Ref("result")), modulus=Const(60376)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T13:27:04.847214Z | {
"verified": true,
"answer": 274,
"timestamp": "2026-02-08T13:27:04.849233Z"
} | 39e269 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1130
},
"timestamp": "2026-02-24T18:21:37.699Z",
"answer": 274
},
{
"id... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
1fb0ea | nt_count_intersection_v1_784195855_5354 | Let $a = 5$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 36$. Let $N = 50000$. Compute the number of positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. Let $c = 73342$ and $m = 67319$. Find the remainder when $c$ times this count is divi... | 13,597 | graphs = [
Graph(
let={
"_n": Const(67319),
"N": Const(50000),
"a": Const(5),
"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"),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 6 | 0 | [
"B3"
] | 1 | 1.944 | 2026-02-08T07:50:10.868932Z | {
"verified": true,
"answer": 13597,
"timestamp": "2026-02-08T07:50:12.813285Z"
} | 1a208e | 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": 1592
},
"timestamp": "2026-02-13T12:36:54.860Z",
"answer": 13597
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
bd4486 | diophantine_sum_product_min_v1_717093673_2177 | Let $S = 139$ and $P = 4074$. Determine the value of $x$ such that $1 \leq x \leq 138$ and $x(S - x) = P$. | 42 | graphs = [
Graph(
let={
"S": Const(139),
"P": Const(4074),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(138)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),... | NT | null | EXTREMUM | sympy | LTE_DIFF_P2 | [
"LTE_DIFF_P2",
"B3"
] | 853b4c | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"B3",
"LTE_DIFF_P2"
] | 2 | 0.052 | 2026-02-08T16:36:07.048425Z | {
"verified": true,
"answer": 42,
"timestamp": "2026-02-08T16:36:07.099933Z"
} | 075d70 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 1336
},
"timestamp": "2026-02-17T08:15:54.447Z",
"answer": 42
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
629740 | nt_count_coprime_and_v1_784195855_9485 | Let $k_1$ be the smallest divisor of $2695$ that is at least $2$, and let $k_2 = 11$. Determine the number of positive integers $n \leq 11288$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Let $r$ be this number. Find the remainder when $80131 \cdot r$ is divided by $77342$. | 4,458 | graphs = [
Graph(
let={
"upper": Const(11288),
"k1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2695))))),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), con... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.335 | 2026-02-08T16:51:55.150683Z | {
"verified": true,
"answer": 4458,
"timestamp": "2026-02-08T16:51:57.485802Z"
} | ccd559 | 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": 1179
},
"timestamp": "2026-02-17T13:46:46.002Z",
"answer": 4458
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fe8fc3_n | comb_count_permutations_fixed_v1_1218484723_1173 | A theater has 7 actors, each assigned a unique costume. A prankster redistributes the costumes so that no actor receives their own. Meanwhile, the director selects a single costume (out of $\binom{7}{1}$ choices, since $0! = 1$) to display on stage, separate from the prank. In how many ways can the display costume be c... | 1,855 | COMB | null | COUNT | sympy | ONE_FACTORIAL_0 | [
"ONE_FACTORIAL_0"
] | 7064c7 | comb_count_permutations_fixed_v1 | null | 3 | null | [
"ONE_FACTORIAL_0"
] | 1 | 0.001 | 2026-02-25T02:56:05.882047Z | null | 2afe9c | fe8fc3 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 5986
},
"timestamp": "2026-03-30T16:27:09.961Z",
"answer": 1855
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
8498de | nt_count_divisible_and_v1_677425708_4040 | Let $n = 4$ and $u = 149970$. Define
$$
d_2 = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor,
$$
where $\phi(k)$ is Euler's totient function. Let $d_1 = 6$.
Compute the number of positive integers $n$ with $1 \leq n \leq u$ such that $n$ is divisible by both $d_1$ and $d_2$. | 4,999 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(149970),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 5 | 0 | [
"K2"
] | 1 | 5.378 | 2026-02-08T06:24:32.307894Z | {
"verified": true,
"answer": 4999,
"timestamp": "2026-02-08T06:24:37.686335Z"
} | dfba7c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 587
},
"timestamp": "2026-02-15T17:28:15.539Z",
"answer": 4999
},
{
"id": 11,
... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
4d295f | modular_inverse_v1_153355830_950 | Let $a$ be the sum of all positive integers $n$ such that $1 \leq n \leq 390$ and $n$ is divisible by 195. Let $m = 907$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq 906$ and $a \cdot x \equiv 1 \pmod{m}$. Compute the remainder when $44121$ times this value is divided by $69515$. | 32,483 | graphs = [
Graph(
let={
"a": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(390)), Eq(Mod(value=Var("n"), modulus=Const(195)), Const(0))))),
"m": Const(907),
"upper": Const(906),
"result": MinOverSet(set=So... | NT | null | EXTREMUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | modular_inverse_v1 | null | 5 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.04 | 2026-02-08T04:18:41.095122Z | {
"verified": true,
"answer": 32483,
"timestamp": "2026-02-08T04:18:41.134935Z"
} | dc9713 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1711
},
"timestamp": "2026-02-10T16:08:36.264Z",
"answer": 32483
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
14b305 | lin_form_endings_v1_1874849503_677 | Let $S$ be the set of all positive integers $t$ such that $105 \leq t \leq 1620$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 20$, $1 \leq b \leq 12$, and $t = 45a + 60b$. Let $c$ be the number of elements in $S$. Compute the remainder when $17746 \cdot c$ is divided by $92643$. | 36,042 | graphs = [
Graph(
let={
"_inner_result": 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=20)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:15:11.341930Z | {
"verified": true,
"answer": 36042,
"timestamp": "2026-02-08T13:15:11.344085Z"
} | 749976 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T17:40:13.114Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
8b5116 | modular_sum_quadratic_residues_v1_1520064083_433 | Let $p$ be the smallest prime divisor of $14662648678309$. Define $r = \frac{p(p-1)}{4}$. Let $n = 11$. Compute the Bell number $B_{|r| \bmod n}$. | 877 | graphs = [
Graph(
let={
"_n": Const(11),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(14662648678309))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": B... | NT | COMB | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T03:21:29.113618Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T03:21:29.115213Z"
} | 31677d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 25248
},
"timestamp": "2026-02-23T19:23:12.892Z",
"answer": 877
},
{
"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
a1933f | antilemma_k2_v1_458359167_4179 | Let $n = \sum_{d \mid 249} \phi(d)$, where $\phi$ denotes Euler's totient function. Define $x = \sum_{k=1}^{249} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$. Compute the remainder when $47503 \cdot x$ is divided by $91966$. | 85,459 | graphs = [
Graph(
let={
"_m": Const(91966),
"_n": SumOverDivisors(n=Const(value=249), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Const(249), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(v... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.002 | 2026-02-08T11:36:02.604308Z | {
"verified": true,
"answer": 85459,
"timestamp": "2026-02-08T11:36:02.606288Z"
} | c9df0c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1388
},
"timestamp": "2026-02-14T16:36:16.335Z",
"answer": 85459
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
331ac2 | comb_count_derangements_v1_2051736721_3919 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 2054$ such that $\binom{2054}{j}$ is odd. Let $c = 73067$. Compute the remainder when $c \cdot !n$ is divided by $82450$, where $!n$ denotes the subfactorial of $n$. | 80,011 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2054)), Eq(Mod(value=Binom(n=Const(2054), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T17:37:22.419422Z | {
"verified": true,
"answer": 80011,
"timestamp": "2026-02-08T17:37:22.422376Z"
} | 5798fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 2080
},
"timestamp": "2026-02-18T05:02:45.627Z",
"answer": 80011
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
f6ca5f | sequence_fibonacci_compute_v1_655260480_5819 | Let $n$ be the number of integers $t$ such that $16 \leq t \leq 94$ and there exist integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 5$, and $t = 6a + 9b + 1$. Let $F_n$ denote the $n$th Fibonacci number. Find the remainder when $38617 \cdot F_n$ is divided by $92354$. | 3,091 | graphs = [
Graph(
let={
"_n": Const(38617),
"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=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:40:11.322299Z | {
"verified": true,
"answer": 3091,
"timestamp": "2026-02-08T18:40:11.324649Z"
} | 9ad832 | 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": 4338
},
"timestamp": "2026-02-18T18:31:01.612Z",
"answer": 3091
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
08d6a3 | comb_count_permutations_fixed_v1_1218484723_3109 | Let $D_n$ denote the number of derangements of $n$ elements. Let $n = 6$ and $k = 0$. Compute $\binom{n}{k} \cdot D_{n - k}$. | 265 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(4),
"n3": Sum(Ref("a"), Ref("b")),
"e": Summation(var="k1", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n3"), k=Var("k1")))),
"n2": Const(0),
"s": Div... | COMB | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/BINOMIAL_ALTERNATING"
] | e40483 | comb_count_permutations_fixed_v1 | null | 2 | 3 | [
"BINOMIAL_ALTERNATING",
"SUM_INDEPENDENT"
] | 2 | 0.003 | 2026-02-25T04:50:34.593156Z | {
"verified": true,
"answer": 265,
"timestamp": "2026-02-25T04:50:34.595815Z"
} | 335781 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 675
},
"timestamp": "2026-03-29T08:24:32.320Z",
"answer": 265
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemm... | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.88
} | ||
2bba5e | antilemma_k2_v1_2051736721_2546 | For each integer $k$ from $1$ to $62$ and each integer $j$ from $1$ to $4$, compute $\phi(k) \cdot \left\lfloor \frac{62}{k} \right\rfloor$. Let $S$ be the set of all such values. Compute the sum of the elements in $S$, multiply the result by $4$, and then divide by $16$. Find the value of this expression. | 1,953 | graphs = [
Graph(
let={
"_m": Const(62),
"x": Div(Mul(Const(4), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(62)), right=IntegerRange(start=Const(1), end=C... | NT | COMB | COMPUTE | sympy | K13 | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"SUM_INDEPENDENT"
] | 3 | 0.002 | 2026-02-08T16:47:11.422180Z | {
"verified": true,
"answer": 1953,
"timestamp": "2026-02-08T16:47:11.423882Z"
} | 4d7bc9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1024
},
"timestamp": "2026-02-17T11:55:02.435Z",
"answer": 1953
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": ... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
3f5b57 | comb_count_surjections_v1_1915831931_345 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Compute $k! \cdot S(4, k)$, where $S(4, k)$ denotes the Stirling number of the second kind. Multiply this result by $56531$ and find the remainder when divided by $57934$. | 24,262 | graphs = [
Graph(
let={
"_n": Const(57934),
"n": Const(4),
"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... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T15:22:22.471489Z | {
"verified": true,
"answer": 24262,
"timestamp": "2026-02-08T15:22:22.474407Z"
} | 83b384 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 919
},
"timestamp": "2026-02-24T20:42:03.934Z",
"answer": 24262
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
509b80 | modular_sum_quadratic_residues_v1_898971024_3000 | Let $p$ be the largest prime number less than or equal to $277$. Compute $\frac{p(p-1)}{4}$. | 19,113 | graphs = [
Graph(
let={
"_n": Const(277),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | C3 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"C3",
"MAX_PRIME_BELOW"
] | 2 | 0.021 | 2026-02-08T17:06:12.179472Z | {
"verified": true,
"answer": 19113,
"timestamp": "2026-02-08T17:06:12.200864Z"
} | 3a41e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 627
},
"timestamp": "2026-02-17T18:45:04.500Z",
"answer": 19113
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1cd880 | sequence_count_fib_divisible_v1_2051736721_1219 | Let $n = 83521$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. For each such pair, compute $x + y$, and let $S$ be the set of all such sums. Let $u$ be the minimum value in $S$.
Define $d = \sum_{k=1}^{m} k$, where
$$
m = \sum_{k_1=1}^{2} \varphi(k_1) \left\lfloor \frac{2}{k_1}... | 48 | graphs = [
Graph(
let={
"_n": Const(83521),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"K2/SUM_ARITHMETIC",
"B3"
] | 8bf53a | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B3",
"K2",
"SUM_ARITHMETIC"
] | 3 | 0.175 | 2026-02-08T15:54:18.582424Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T15:54:18.756946Z"
} | 714935 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1973
},
"timestamp": "2026-02-16T16:01:11.156Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8ae9fa | nt_sum_totient_over_divisors_v1_1915831931_679 | Let $n = 57806$. Define $s = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. Let $m = \max\{ p \mid 2 \leq p \leq 12,\ p\ \text{is prime} \}$. Compute the Bell number $B_k$, where $k$ is the remainder when $|s|$ is divided by $m$. Find the va... | 1 | graphs = [
Graph(
let={
"n": Const(57806),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_totient_over_divisors_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.012 | 2026-02-08T15:36:58.062795Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T15:36:58.074613Z"
} | d45ffb | 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": 555
},
"timestamp": "2026-02-16T10:16:43.480Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4758c6 | antilemma_v1_legendre_1116507919_450 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 19360000$. For each such pair, compute $x + y$, and let $T$ be the set of all such sums. Let $m$ be the minimum value in $T$. Determine the largest integer $k$ such that $11^k$ divides $m!$. Let $Q = (80356 \times k) \bmod 98659$. Fin... | 11,383 | graphs = [
Graph(
let={
"_n": Const(11),
"x": MaxKDivides(target=Factorial(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(19360000)))), ... | NT | null | COMPUTE | sympy | B3 | [
"B3/V1",
"V1"
] | 25e8f3 | antilemma_v1_legendre | null | 6 | 0 | [
"B3",
"V1"
] | 2 | 0.001 | 2026-02-08T02:34:22.661211Z | {
"verified": true,
"answer": 11383,
"timestamp": "2026-02-08T02:34:22.662089Z"
} | a60f1b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 2566
},
"timestamp": "2026-02-08T19:34:14.684Z",
"answer": 11383
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "V1",
"status": "ok"
},
... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
9a8995 | antilemma_k3_v1_124444284_5801 | Let $n = 71443$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 71,443 | graphs = [
Graph(
let={
"_n": Const(71443),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T06:51:43.992456Z | {
"verified": true,
"answer": 71443,
"timestamp": "2026-02-08T06:51:43.992819Z"
} | cc58af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 3387
},
"timestamp": "2026-02-13T05:12:37.723Z",
"answer": 71443
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
1cb179 | comb_count_surjections_v1_1978505735_230 | Let $S(5, 5)$ denote the Stirling number of the second kind, which counts the number of ways to partition a set of 5 elements into 5 nonempty subsets. Let $Q$ be the remainder when $44121 \cdot 5! \cdot S(5, 5)$ is divided by $60668$. Find the value of $Q$. | 16,404 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(60668)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | COMB1 | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS"
] | eb862e | comb_count_surjections_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.084 | 2026-02-08T15:14:09.006704Z | {
"verified": true,
"answer": 16404,
"timestamp": "2026-02-08T15:14:09.090226Z"
} | 43bc42 | 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": 847
},
"timestamp": "2026-02-24T20:12:51.088Z",
"answer": 16404
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
6a1480 | comb_catalan_compute_v1_1918700295_270 | Let $n = 11$. Compute the $n$th Catalan number, denoted $C_n$. Let $Q$ be the remainder when $8 - C_n$ is divided by $91567$, where $8$ is the number of elements in the Cartesian product $\{1, 2\} \times \{1, 2, 3, 4\}$. Find the value of $Q$. | 32,789 | graphs = [
Graph(
let={
"_n": Const(91567),
"n": Const(11),
"result": Catalan(Ref("n")),
"Q": Mod(value=Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))), Ref("result")), m... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | comb_catalan_compute_v1 | negation_mod | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T03:08:11.089510Z | {
"verified": true,
"answer": 32789,
"timestamp": "2026-02-08T03:08:11.091074Z"
} | bc437d | 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": 766
},
"timestamp": "2026-02-10T13:11:03.872Z",
"answer": 32789
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
6d7e69 | nt_sum_divisors_range_v1_798873815_37 | Let $n = 65479$. Let $u$ be the number of nonnegative integers $j \leq n$ for which $\binom{n}{j}$ is odd. Compute the sum of the number of positive divisors of each integer from $1$ to $u$. | 75,108 | graphs = [
Graph(
let={
"_n": Const(65479),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65479)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | SUM | sympy | V8 | [
"V8"
] | 86348e | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.278 | 2026-02-08T02:24:41.667614Z | {
"verified": true,
"answer": 75108,
"timestamp": "2026-02-08T02:24:41.945224Z"
} | 4585e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 15173
},
"timestamp": "2026-02-23T13:34:08.045Z",
"answer": 75112
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": 4.35,
"mid": 5.74,
"hi": 7.35
} | ||
84a77b | nt_num_divisors_compute_v1_1520064083_9910 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 26$, $1 \leq j \leq 188$, and $\gcd(i, j) = 1$. Compute the number of positive divisors of $n$. | 9 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(26)), right=IntegerRange(start=Const(1), end=Const(188))))),
"... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T11:02:40.132131Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T11:02:40.132955Z"
} | ea508d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 3037
},
"timestamp": "2026-02-14T10:10:40.434Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d1ecda | nt_count_intersection_v1_971394319_65 | Let $b$ be the number of integers $t$ such that $7 \le t \le 28$ and there exist positive integers $a$ and $b$ with $1 \le a \le 4$, $1 \le b \le 4$, and $t = 4a + 3b$. Let $a = 9$. Define $N = 100000$. Let $r$ be the number of positive integers $n \le N$ such that $9$ divides $n$ and $\gcd(n, b) = 1$. Find the smalles... | 4,776 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(9),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=C... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.376 | 2026-02-08T12:49:04.300867Z | {
"verified": true,
"answer": 4776,
"timestamp": "2026-02-08T12:49:07.676539Z"
} | d3e9e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 3475
},
"timestamp": "2026-02-15T05:40:42.554Z",
"answer": 4776
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
19ca79 | geo_count_lattice_rect_v1_124444284_340 | Let $a = 351$ and $b = 90$. Define the rectangle $R$ as the set of all lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $N$ be the number of lattice points in $R$. Compute the remainder when $12749 \cdot N$ is divided by $94680$. | 21,128 | graphs = [
Graph(
let={
"a": Const(351),
"b": Const(90),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(12749),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(94680)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T03:13:13.836051Z | {
"verified": true,
"answer": 21128,
"timestamp": "2026-02-08T03:13:13.838535Z"
} | ce9a9b | 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": 2750
},
"timestamp": "2026-02-09T16:20:08.238Z",
"answer": 21128
},
{
"... | 1 | [] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||||
71f959 | nt_min_coprime_above_v1_153355830_715 | Let $n = 137$. Define $s = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 24196561$. Define $u$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Let $A$ be the set of all integers $n$ such that $n > s$,... | 9,454 | graphs = [
Graph(
let={
"_n": Const(137),
"start": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(137), Var("k"))))),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"K2"
] | f1ea07 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.041 | 2026-02-08T04:08:31.277189Z | {
"verified": true,
"answer": 9454,
"timestamp": "2026-02-08T04:08:31.318205Z"
} | 8280d4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 1164
},
"timestamp": "2026-02-10T15:30:56.653Z",
"answer": 9454
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
bedd83 | comb_sum_binomial_mod_v1_1918700295_48 | Let $m$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Define $s = \sum_{k=t}^{232} \binom{256}{k}$, where $t = \sum_{k=1}^{m} k$. Compute the remainder when $s$ is divided by $10247$. | 9,782 | graphs = [
Graph(
let={
"_m": Const(256),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var("y")))),
... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1/SUM_ARITHMETIC"
] | 8e3bd4 | comb_sum_binomial_mod_v1 | null | 7 | 0 | [
"B1",
"SUM_ARITHMETIC"
] | 2 | 0.018 | 2026-02-08T02:57:40.550633Z | {
"verified": true,
"answer": 9782,
"timestamp": "2026-02-08T02:57:40.568832Z"
} | 8bb7bf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T20:49:18.494Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
}
] | {
"lo": 5.91,
"mid": 7.63,
"hi": 10
} | ||
3e1e88_n | alg_sum_powers_v1_1419126231_1331 | A treasure hunter collects gold coins on 840 consecutive days, taking $k^3$ coins on day $k$. At the end, they deposit all coins into a vault that requires a keycode equal to the sum of numbers from 758 to 813 in steps of 5. What is the remainder when the total coins collected is divided by the keycode? | 3,756 | ALG | null | COMPUTE | sympy | SUM_AP | [
"SUM_AP"
] | ff6f57 | alg_sum_powers_v1 | null | 2 | null | [
"SUM_AP"
] | 1 | 0.029 | 2026-02-25T10:45:00.024995Z | null | aa0ae1 | 3e1e88 | narrative | 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": 29490
},
"timestamp": "2026-03-31T04:36:44.141Z",
"answer": 3756
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
1e1e47 | antilemma_k3_v1_809748730_1110 | Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $45387$, where $\phi$ denotes Euler's totient function. Compute $x$. | 45,387 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=45387), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T12:11:01.162565Z | {
"verified": true,
"answer": 45387,
"timestamp": "2026-02-08T12:11:01.162792Z"
} | 28020d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 485
},
"timestamp": "2026-02-16T03:32:40.313Z",
"answer": 60527
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
0e4f05 | diophantine_product_count_v1_1742523217_2041 | Let $ k $ be the sum of all real solutions $ x $ to the equation $ x^2 - 360x - 15561 = 0 $. Let $ S $ be the set of all positive integers $ x $ such that $ 1 \leq x \leq 278 $, $ x $ divides $ k $, and $ \frac{k}{x} \leq 278 $. Compute the number of elements in $ S $. | 22 | graphs = [
Graph(
let={
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-360), Var("x")), Const(-15561)), Const(0)))),
"upper": Const(278),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"),... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"VIETA_SUM"
] | b33a7a | diophantine_product_count_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 2 | 0.065 | 2026-02-08T04:25:51.104397Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T04:25:51.169640Z"
} | 502b26 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 956
},
"timestamp": "2026-02-10T16:41:06.546Z",
"answer": 22
},
{
"id"... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
10de03 | nt_min_coprime_above_v1_784195855_10367 | Let $\mathcal{P}$ be the set of all ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 25$, $1 \leq j \leq 26$, and $\gcd(i, j) = 1$. Let $m$ be the number of elements in $\mathcal{P}$. Find the smallest integer $n$ such that $55225 < n \leq 55646$ and $\gcd(n, m) = 1$. | 55,226 | graphs = [
Graph(
let={
"start": Const(55225),
"upper": Const(55646),
"modulus": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Cons... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.037 | 2026-02-08T17:48:31.823785Z | {
"verified": true,
"answer": 55226,
"timestamp": "2026-02-08T17:48:31.860705Z"
} | 379fdc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 2763
},
"timestamp": "2026-02-18T13:34:20.868Z",
"answer": 55226
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
91a391 | modular_min_linear_v1_898971024_1948 | Let $N = 64176$. Define $a$ as the number of positive integers $n \le N$ such that the $n$-th Fibonacci number is divisible by 12. Let $b = 38624$ and $m = 39044$. Find the smallest positive integer $x \le m$ such that $a \cdot x \equiv b \pmod{m}$. | 7,359 | graphs = [
Graph(
let={
"_n": Const(64176),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(12), dividend=Fibonacci(arg=Var(name='n')))))),
"b": Const(38624),
"m": Const(39... | ALG | NT | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_min_linear_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 1.553 | 2026-02-08T16:26:11.785365Z | {
"verified": true,
"answer": 7359,
"timestamp": "2026-02-08T16:26:13.338430Z"
} | 052a8d | 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": 2987
},
"timestamp": "2026-02-17T04:19:51.389Z",
"answer": 7359
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f8a3e4 | nt_max_prime_below_v1_168721529_1573 | Let $n$ be the largest prime number less than or equal to $84681$. Compute the remainder when $n^2 + d \cdot n + 16$ is divided by $83101$, where $d$ is the smallest divisor of $1517$ that is at least $2$. | 36,334 | graphs = [
Graph(
let={
"upper": Const(84681),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(MinOverSet(set=SolutionsSet(va... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 76121b | nt_max_prime_below_v1 | quadratic_mod | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 4.226 | 2026-02-08T13:47:15.421060Z | {
"verified": true,
"answer": 36334,
"timestamp": "2026-02-08T13:47:19.647514Z"
} | 719cfa | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 4985
},
"timestamp": "2026-02-11T07:58:46.766Z",
"answer": 36334
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
5fad58 | comb_count_surjections_v1_1218484723_5274 | Let $N$ be the number of positive integers $t$ with $30 \leq t \leq 2324$ such that $t = 14a + 8b + 8$ for some integers $a, b$ satisfying $1 \leq a \leq 74$, $1 \leq b \leq 160$. Let $M = 5! \cdot S(5,5)$, where $S(n,k)$ denotes the Stirling number of the second kind. Find the remainder when $N \cdot M$ is divided by ... | 36,339 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), con... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | comb_count_surjections_v1 | affine_mod | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-25T06:55:13.091217Z | {
"verified": true,
"answer": 36339,
"timestamp": "2026-02-25T06:55:13.092550Z"
} | 2f997f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T20:20:04.785Z",
"answer": 37419
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
170fde | geo_visible_lattice_v1_717093673_2077 | Let $n = 88$. A lattice point $(x, y)$ is called visible if $\gcd(x, y) = 1$. Define $\mathcal{P}$ as the set of all ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $58469$ multiplied by the number of elements in $\mathcal{P}$ is divided by $72... | 54,215 | graphs = [
Graph(
let={
"n": Const(88),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(58469),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(72650)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 1.038 | 2026-02-08T16:29:41.775241Z | {
"verified": true,
"answer": 54215,
"timestamp": "2026-02-08T16:29:42.812935Z"
} | 780510 | 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": 4548
},
"timestamp": "2026-02-17T05:43:55.896Z",
"answer": 54215
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
0dfc6b | nt_min_coprime_above_v1_1978505735_8194 | Let $ S $ be the set of all integers $ t $ such that there exist integers $ a $ and $ b $ satisfying $ 1 \leq a \leq 913 $, $ 1 \leq b \leq 878 $, $ 17 \leq t \leq 4507 $, and
$$
t = 3a + 2b + 12.
$$
Let $ s $ be the number of elements in $ S $.
Let $ T $ be the set of all integers $ t_1 $ such that there exist integ... | 13,963 | graphs = [
Graph(
let={
"_n": Const(77557),
"start": 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=913)), Geq(l... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-08T20:42:58.271565Z | {
"verified": true,
"answer": 13963,
"timestamp": "2026-02-08T20:42:58.287502Z"
} | 860b1a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 7935
},
"timestamp": "2026-02-19T00:59:38.159Z",
"answer": 13963
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0d2e39 | diophantine_product_count_v1_397696148_1026 | Let $k = 720$ and let $U = 409$. Compute the number of positive integers $x$ such that $1 \leq x \leq U$, $x$ divides $k$, and $\frac{k}{x} \leq U$. | 28 | graphs = [
Graph(
let={
"k": Const(720),
"upper": Const(409),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | C3 | [
"LIN_FORM",
"V8"
] | a2d4b4 | diophantine_product_count_v1 | null | 4 | 0 | [
"C3",
"LIN_FORM",
"V8"
] | 3 | 0.364 | 2026-02-08T12:18:30.942615Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T12:18:31.306794Z"
} | 3e1b4b | 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": 1837
},
"timestamp": "2026-02-14T23:51:20.765Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6c054f | comb_count_derangements_v1_1218484723_526 | Let $n = \sum_{k=0}^{2} 2^k$ and let $M$ be the number of derangements of $n$ elements. Find the remainder when $93926M$ is divided by $94383$. | 2,169 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(0), end=Ref("_n"), expr=Pow(Const(2), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(93926), Ref("result")), modulus=Const(94383)),
},
... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T02:11:30.948753Z | {
"verified": true,
"answer": 2169,
"timestamp": "2026-02-25T02:11:30.949763Z"
} | acd60c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1631
},
"timestamp": "2026-03-28T22:58:16.006Z",
"answer": 2169
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
21901d | comb_count_partitions_v1_1915831931_649 | Let $m = 441$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $S$ be the set of all values of $x + y$ for such pairs. Let $n$ be the minimum value in $S$. Compute the number of integer partitions of $\sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ o... | 53,174 | graphs = [
Graph(
let={
"_m": Const(441),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | B3 | [
"B3/K3"
] | 4a4ef2 | comb_count_partitions_v1 | null | 6 | 0 | [
"B3",
"K3"
] | 2 | 0.002 | 2026-02-08T15:35:50.532367Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T15:35:50.534620Z"
} | 10e865 | 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": 862
},
"timestamp": "2026-02-16T10:15:00.430Z",
"answer": 53174
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd92e9 | modular_modexp_compute_v1_1978505735_2146 | Let $a = 17$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 66$. Define $e$ to be the maximum value of $xy$ over all pairs $(x,y) \in S$. Let $m = 25200$. Compute the value of $a^e \bmod m$. | 2,897 | graphs = [
Graph(
let={
"a": Const(17),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(66)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T16:40:34.301967Z | {
"verified": true,
"answer": 2897,
"timestamp": "2026-02-08T16:40:34.303713Z"
} | 14b12d | 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": 2588
},
"timestamp": "2026-02-17T11:10:41.154Z",
"answer": 2897
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c5c6fb | antilemma_k3_v1_1248542787_682 | Let $n = \sum_{d \mid 55214} \phi(d)$, where the sum is taken over all positive divisors $d$ of $55214$, and $\phi$ denotes Euler's totient function. Let $k$ be the number of decimal digits of $|n|$. Compute
$$
\sum_{i=0}^{k-1} \left( \text{the } i\text{-th digit of } |n| \right) \cdot (i+1)^2 + 77841,
$$
determining t... | 78,072 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=55214), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='x')), k=Var(name='i'), base=N... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:19:42.928404Z | {
"verified": true,
"answer": 78072,
"timestamp": "2026-02-08T03:19:42.928993Z"
} | faa275 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 6646
},
"timestamp": "2026-02-09T07:00:29.900Z",
"answer": 78072
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
44ea5a | comb_factorial_compute_v1_1218484723_3015 | Let $n$ be the number of non-negative integers $v$ with $0 \leq v \leq 2009$ such that there exist integers $a, b$ with $1 \leq a, b \leq 8$ satisfying $v = 41a^2 + 41b^2 - 82ab$. Let $Q = n!$. Compute $Q$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(2009),
"n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(0)), Leq(Var("v"), Ref("_n")), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(lef... | COMB | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | comb_factorial_compute_v1 | null | 4 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.002 | 2026-02-25T04:45:10.139736Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T04:45:10.141286Z"
} | 6dabd2 | 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": 680
},
"timestamp": "2026-03-29T07:51:32.239Z",
"answer": 40320
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"l... | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
e6bf9a | nt_sum_divisors_range_v1_717093673_3332 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 188$. Let $T$ be the set of all products $xy$ where $(x, y) \in S$. Let $m$ be the maximum element of $T$. Let $U$ be the set of all positive integers $n$ such that $1 \leq n \leq m$. For each $n \in U$, let $d(n)$ denote the numbe... | 56,402 | graphs = [
Graph(
let={
"_n": Const(60132),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(188)))), expr=Mul(Var("x"), Var("y")... | NT | null | SUM | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.461 | 2026-02-08T17:30:01.470821Z | {
"verified": true,
"answer": 56402,
"timestamp": "2026-02-08T17:30:01.932229Z"
} | 3f74e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 7770
},
"timestamp": "2026-02-18T03:57:25.123Z",
"answer": 56402
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0c7c6d | nt_min_phi_inverse_v1_677425708_63 | Let $k = 16$ and let $\text{upper} = 70$. Define $\text{result}$ to be the smallest positive integer $n$ such that $1 \leq n \leq \text{upper}$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function.
Let $m = 65380$. Define $S$ to be the set of all positive integers $n$ such that $1 \leq n \leq m$ and $15$ d... | 55,403 | graphs = [
Graph(
let={
"_m": Const(65380),
"_n": Const(2),
"upper": Const(70),
"k": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW"
] | 29d498 | nt_min_phi_inverse_v1 | affine_mod | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.013 | 2026-02-08T03:02:18.173151Z | {
"verified": true,
"answer": 55403,
"timestamp": "2026-02-08T03:02:18.186562Z"
} | 7d4bf0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 7720
},
"timestamp": "2026-02-08T20:18:29.726Z",
"answer": 55303
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"st... | {
"lo": 2.8,
"mid": 4.67,
"hi": 6.48
} | ||
85ba24 | geo_count_lattice_rect_v1_717093673_2068 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 361$ and $0 \leq y \leq 162$. | 59,006 | graphs = [
Graph(
let={
"a": Const(361),
"b": Const(162),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T16:29:09.340762Z | {
"verified": true,
"answer": 59006,
"timestamp": "2026-02-08T16:29:09.341654Z"
} | 2602fa | 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": 319
},
"timestamp": "2026-05-03T10:19:15.526Z",
"answer": 59006
},
{
"... | 1 | [] | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||||
3eac92 | comb_factorial_compute_v1_1742523217_3486 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 40961$ such that $\binom{40961}{j} \equiv 1 \pmod{2}$. Let $f = n!$. Compute the remainder when $89409 \cdot f$ is divided by $86677$. | 74,450 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(40961)), Eq(Mod(value=Binom(n=Const(40961), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T05:53:59.522524Z | {
"verified": true,
"answer": 74450,
"timestamp": "2026-02-08T05:53:59.523356Z"
} | 77f783 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1222
},
"timestamp": "2026-02-24T04:51:52.133Z",
"answer": 74450
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
896715 | nt_min_coprime_above_v1_1874849503_1454 | Let $S$ be the set of all integers $t$ such that $7 \le t \le 7797$ and there exist positive integers $a \le 2361$ and $b \le 615$ satisfying $t = 2a + 5b$. Let $u$ be the number of elements in $S$, and let $s = 7569$. Find the smallest integer $n$ such that $s < n \le u$ and $\gcd(n, 208) = 1$. | 7,571 | graphs = [
Graph(
let={
"start": Const(7569),
"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=2361)), Ge... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.037 | 2026-02-08T13:54:35.103217Z | {
"verified": true,
"answer": 7571,
"timestamp": "2026-02-08T13:54:35.140501Z"
} | 05a074 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 6650
},
"timestamp": "2026-02-11T08:03:14.321Z",
"answer": 7571
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
ab47e4 | comb_binomial_compute_v1_1440796553_1288 | Let $ n $ be the number of elements in the Cartesian product of the sets $ \{1, 2, 3\} $ and $ \{1, 2, 3, 4, 5\} $. Let $ T $ be the set of all integers $ t $ such that $ 15 \leq t \leq 42 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 4 $, $ 1 \leq b \leq 2 $, and $ t = 6a + 9b $.
Let $ k $ ... | 75,715 | graphs = [
Graph(
let={
"_n": Const(77203),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(5)))),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), con... | ALG | COMB | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | efa619 | comb_binomial_compute_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T13:38:17.060432Z | {
"verified": true,
"answer": 75715,
"timestamp": "2026-02-08T13:38:17.063522Z"
} | 0fad08 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 310,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T18:53:17.816Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
a838a7 | nt_num_divisors_compute_v1_1874849503_245 | Let $c$ be the number of integers $t$ with $7 \leq t \leq 136$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 53$, $1 \leq b \leq 6$, and $t = 2a + 5b$. Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = c$. Let $s$ be the minimum value of ... | 15 | graphs = [
Graph(
let={
"_c": 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=53)), Geq(left=Var(name='b'), right=Const(value... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B3/B1",
"B1/B3/B1"
] | 3c6640 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.009 | 2026-02-08T12:53:31.461532Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T12:53:31.470819Z"
} | 6c7698 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 340,
"completion_tokens": 2356
},
"timestamp": "2026-02-09T15:01:02.602Z",
"answer": 15
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": ... | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
49c123 | nt_sum_over_divisible_v1_1915831931_2065 | Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 10201$ and $n$ is divisible by $45$. Compute the sum of the elements of $S$. Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 26244$. Find the remainder when $c - \sum S$ is divided by $84995... | 35,959 | graphs = [
Graph(
let={
"upper": Const(10201),
"divisor": Const(45),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": Min... | NT | null | SUM | sympy | B3 | [
"B3"
] | fc629c | nt_sum_over_divisible_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.379 | 2026-02-08T16:36:16.244011Z | {
"verified": true,
"answer": 35959,
"timestamp": "2026-02-08T16:36:16.622598Z"
} | 60f675 | 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": 1179
},
"timestamp": "2026-02-17T07:39:29.906Z",
"answer": 35959
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bc9b6d | geo_visible_lattice_v1_151522320_691 | Let $n = 180$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $44121 \cdot L$ is divided by $60712$. | 23,231 | graphs = [
Graph(
let={
"n": Const(180),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(60712)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 1.812 | 2026-02-08T03:27:37.257902Z | {
"verified": true,
"answer": 23231,
"timestamp": "2026-02-08T03:27:39.069700Z"
} | d7d052 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 27382
},
"timestamp": "2026-02-23T22:24:13.706Z",
"answer": 23231
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
80c345 | sequence_lucas_compute_v1_1978505735_5763 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 121$. For each such pair, compute $x + y$, and let $M$ be the minimum of these sums. Let $n$ be the largest prime number satisfying $2 \leq n \leq M$. Define $L_n$ to be the $n$th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_k = L... | 39,187 | graphs = [
Graph(
let={
"_n": Const(121),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositiv... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T19:12:41.186018Z | {
"verified": true,
"answer": 39187,
"timestamp": "2026-02-08T19:12:41.190027Z"
} | b6e597 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1846
},
"timestamp": "2026-02-18T21:34:32.798Z",
"answer": 39187
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d04308 | nt_min_coprime_above_v1_124444284_5554 | Let $S$ be the set of integers $n$ such that $5184 < n \leq 5212$ and $\gcd(n, 18) = 1$. Let $m$ be the smallest element of $S$. Compute $m^2 + 50m + \sum_{k=1}^{15} \phi(k) \left\lfloor \frac{15}{k} \right\rfloor$, and then find the remainder when this sum is divided by $82082$. Determine the value of this remainder. | 56,535 | graphs = [
Graph(
let={
"start": Const(5184),
"upper": Const(5212),
"modulus": Const(18),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(1))... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 598070 | nt_min_coprime_above_v1 | quadratic_mod | 4 | 0 | [
"K2"
] | 1 | 0.01 | 2026-02-08T06:41:58.102724Z | {
"verified": true,
"answer": 56535,
"timestamp": "2026-02-08T06:41:58.112940Z"
} | 9fe875 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 3201
},
"timestamp": "2026-02-13T03:37:04.120Z",
"answer": 56535
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a13ec5 | nt_min_with_divisor_count_v1_717093673_2410 | Let $n$ be a positive integer such that $1 \leq n \leq 2926$ and the number of positive divisors of $n$ is exactly 8. Let $m$ be the smallest such integer $n$. Compute the remainder when $|m|$ is divided by 84514. | 24 | graphs = [
Graph(
let={
"upper": Const(2926),
"div_count": Const(8),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"Q": Mod(value=Abs(ar... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"LIN_FORM"
] | 7b2633 | nt_min_with_divisor_count_v1 | null | 3 | 0 | [
"LIN_FORM",
"ONE_PHI_1"
] | 2 | 4.739 | 2026-02-08T16:49:41.840161Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T16:49:46.578988Z"
} | 88d2d1 | 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": 1089
},
"timestamp": "2026-02-17T12:31:37.844Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0af625 | nt_gcd_compute_v1_1431428450_600 | Let $a = 296791$ and $b = 512639$. Let $d$ be the greatest common divisor of $a$ and $b$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 202500$. Let $s$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when $s - d$ is divided by $92841$. | 66,760 | graphs = [
Graph(
let={
"_n": Const(92841),
"a": Const(296791),
"b": Const(512639),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_gcd_compute_v1 | negation_mod | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T13:33:15.939374Z | {
"verified": true,
"answer": 66760,
"timestamp": "2026-02-08T13:33:15.941218Z"
} | 9e7d21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1457
},
"timestamp": "2026-02-15T18:04:05.333Z",
"answer": 66760
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1a508f | comb_factorial_compute_v1_1915831931_3494 | Let $m = 44121$ and $n = 78706$. Let $c$ be the number of positive integers $k$ from $1$ to $45$, inclusive, such that the $k$-th Fibonacci number is divisible by $5$. Define $q$ to be the largest prime number $q_1$ such that $2 \leq q_1 \leq c$. Compute the remainder when $m \cdot q!$ is divided by $n$. | 25,390 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(78706),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(1)), Leq(Var("n2"), Const... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW"
] | c3fe6d | comb_factorial_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T17:41:49.206172Z | {
"verified": true,
"answer": 25390,
"timestamp": "2026-02-08T17:41:49.208059Z"
} | a9a23a | 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": 1385
},
"timestamp": "2026-02-18T07:01:54.980Z",
"answer": 25390
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dbfb72 | geo_count_lattice_triangle_v1_601307018_10438 | Let $R = \left|111 \cdot 111 + 80 \cdot (0 - 7)\right|$. Let $S = \gcd\left(\left|\left\{ v : 17 \leq v \leq 3338,\ \exists\text{ integers }a,b\text{ with }1 \leq a,b \leq 11\text{ such that }5a^2 + 29b^2 - 16ab = v \right\}\right|, 7\right) + \gcd(|80 - 111|, |111 - 7|) + \gcd(|0 - 80|, |0 - 111|)$. Let $T = \frac{R +... | 58,760 | graphs = [
Graph(
let={
"_n": Const(111),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=111)), Mul(Const(value=80), Sub(left=Const(value=0), right=Const(value=7))))),
"boundary": Sum(GCD(a=Abs(arg=CountOverSet(set=SolutionsSet(var=Var(name='v'), condition=And(G... | GEOM | NT | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.006 | 2026-03-10T10:55:22.925582Z | {
"verified": true,
"answer": 58760,
"timestamp": "2026-03-10T10:55:22.931804Z"
} | f970d9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 5561
},
"timestamp": "2026-04-19T13:48:02.762Z",
"answer": 58760
},
{
... | 1 | [
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
9190ef | nt_min_coprime_above_v1_1742523217_2227 | Let $S$ be the set of all real numbers $x$ such that $x^2 - 5271x - 239220 = 0$. Let $T$ be the set of all positive integers $n$ at most the sum of the elements of $S$ such that $7$ divides $n$ and $\gcd(n, 10) = 1$. Let $m$ be the number of elements in $T$. Find the smallest integer $n$ such that $13456 < n \leq 13768... | 13,457 | graphs = [
Graph(
let={
"start": Const(13456),
"upper": Const(13768),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM/C5"
] | c4f167 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"C5",
"VIETA_SUM"
] | 2 | 0.028 | 2026-02-08T04:36:48.135984Z | {
"verified": true,
"answer": 13457,
"timestamp": "2026-02-08T04:36:48.164436Z"
} | 4ab888 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 1582
},
"timestamp": "2026-02-10T17:13:50.539Z",
"answer": 13457
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
73ca5d_n | alg_poly4_min_v1_1218484723_5822 | A factory produces a special alloy whose cost depends on inputs $a$ and $b$, each between $1$ and $105$. The total cost is given by $2408a^3b + 4816b^4 + P a^4 + Q a^2b^2 + 9632ab^3$, where $P$ is the minimal sum of two positive integers multiplying to $90601$, and $Q$ is the minimal sum of two positive integers multip... | 24,682 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 6 | null | [
"B3"
] | 1 | 0.039 | 2026-02-25T07:24:20.730372Z | null | f74f86 | 73ca5d | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T00:14:00.305Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
2282c0_n | alg_telescope_v1_601307018_4443 | A game generates scores using the formula $7a + 2b$, where $a$ is the number of actions of type A (from 1 to 164) and $b$ is the number of actions of type B (from 1 to 217). Only scores $t$ between 9 and 1582 inclusive are valid. Let $T$ be the set of all such valid scores. A sequence of $|T|$ levels is designed, and t... | 5 | ALG | COMB | COMPUTE | sympy | COUNT_CARTESIAN | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 6 | null | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.221 | 2026-03-10T05:00:00.505289Z | null | cfdb79 | 2282c0 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 13773
},
"timestamp": "2026-03-29T18:45:09.051Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
74132e | geo_count_lattice_triangle_v1_784195855_5489 | Consider the polygon with vertices $(0,0)$, $(128,0)$, $(128,180)$, and $(0,16)$ listed in this order.
Let $A_2$ be twice the area of this polygon, so that
$$A_2=\left|128\cdot 180+256\cdot(0-16)\right|.$$
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy=802816$, and let $T$ be the s... | 9,461 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(16),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=180)), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=16))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Ref(na... | NT | null | COUNT | sympy | B3 | [
"B3/L3C"
] | 345f3b | geo_count_lattice_triangle_v1 | null | 8 | 0 | [
"B3",
"L3C"
] | 2 | 0.008 | 2026-02-08T07:55:45.014439Z | {
"verified": true,
"answer": 9461,
"timestamp": "2026-02-08T07:55:45.022802Z"
} | 4093a3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 2998
},
"timestamp": "2026-02-13T13:30:24.048Z",
"answer": 9461
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "n... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
539ef1 | algebra_quadratic_discriminant_v1_1978505735_1745 | Let $a = 2$, $b = 2$, $c = 0$, and $n = 2$. Consider the discriminant $D = b^n - 4ac$. Define
$$
r = 2 \cdot [D > 0] + [D = 0],
$$
where $[P]$ denotes the Iverson bracket, equal to 1 if $P$ is true and 0 otherwise. Let $T$ be the set of all positive integers $k$ such that $1 \leq k \leq 210510$ and $30$ divides $k$. Le... | 14,034 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Const(2),
"c": Const(0),
"D": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(... | ALG | NT | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"C2/C3"
] | c72efb | algebra_quadratic_discriminant_v1 | affine_mod | 4 | 0 | [
"C2",
"C3",
"COUNT_COPRIME_GRID"
] | 3 | 0.013 | 2026-02-08T16:23:07.116803Z | {
"verified": true,
"answer": 14034,
"timestamp": "2026-02-08T16:23:07.130244Z"
} | dc0a54 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 1003
},
"timestamp": "2026-02-17T02:20:05.563Z",
"answer": 14034
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ecf3a3 | modular_modexp_compute_v1_1520064083_1581 | Let $m = 26741$. Let $n$ be the smallest divisor of $m$ that is at least $2$. Let $a = 17$. Let $e$ be the number of positive integers $t$ such that $10 \le t \le 4050$ and there exist positive integers $a$ and $b$ with $1 \le a \le 375$, $1 \le b \le 425$, and $t = 4a + 6b$. Define $r = a^e \bmod 10404$. Let $Q$ be th... | 877 | graphs = [
Graph(
let={
"_m": Const(26741),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"a": Const(17),
"e": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exis... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR/LIN_FORM"
] | b86314 | modular_modexp_compute_v1 | bell_mod | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.114 | 2026-02-08T04:07:43.825398Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T04:07:43.938921Z"
} | 129a5f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 3337
},
"timestamp": "2026-02-10T15:25:56.636Z",
"answer": 877
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "o... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
baf381 | antilemma_k2_v1_784195855_4711 | Compute the value of
$$
\sum_{k=1}^{144} \phi(k) \left\lfloor \frac{144}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 10,440 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(144), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(144), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T07:17:45.058464Z | {
"verified": true,
"answer": 10440,
"timestamp": "2026-02-08T07:17:45.058823Z"
} | 23790b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 469
},
"timestamp": "2026-02-13T09:31:19.235Z",
"answer": 10440
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
c72867 | nt_count_intersection_v1_2051736721_1572 | Let $N$ be the number of positive integers $n$ such that $1 \le n \le 30000$ and $4$ divides the $n$th Fibonacci number. Let $a = 9$ and $b = 16$. Compute the number of positive integers $n_1$ such that $1 \le n_1 \le N$, $9$ divides $n_1$, and $\gcd(n_1, 16) = 1$. | 278 | graphs = [
Graph(
let={
"_n": Const(4),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(30000)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"a": Const(9),
"b": Const(16),
... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_intersection_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.711 | 2026-02-08T16:06:34.439733Z | {
"verified": true,
"answer": 278,
"timestamp": "2026-02-08T16:06:35.150343Z"
} | 9fedef | 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": 1226
},
"timestamp": "2026-02-16T20:48:53.575Z",
"answer": 278
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ccbc95 | antilemma_k2_v1_1978505735_4353 | Compute $$\sum_{k=1}^{48} \phi(k) \left\lfloor \frac{48}{k} \right\rfloor,$$ where $\phi(k)$ denotes Euler's totient function. | 1,176 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(48), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(48), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T18:11:43.627587Z | {
"verified": true,
"answer": 1176,
"timestamp": "2026-02-08T18:11:43.629823Z"
} | 92d9ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1072
},
"timestamp": "2026-02-18T14:39:54.083Z",
"answer": 1176
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dee1f2 | algebra_quadratic_discriminant_v1_655260480_2268 | Let $b = \sum_{k=1}^{4} k$. Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1080$, $\gcd(p, q) = 1$, and $p < q$. Let $c = 0$. Compute the remainder when $38570$ times the quantity $b^2 - (-7) \cdot |T| \cdot c$ is divided by $50873$. | 41,525 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(50873),
"a": Const(-7),
"b": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Var("k")),
"c": Const(0),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(CountOverSet(set=SolutionsSet(v... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.004 | 2026-02-08T16:39:19.196877Z | {
"verified": true,
"answer": 41525,
"timestamp": "2026-02-08T16:39:19.200523Z"
} | 9430c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1715
},
"timestamp": "2026-02-17T08:27:45.092Z",
"answer": 41525
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e3807c | sequence_fibonacci_compute_v1_2051736721_2906 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 121$. For each such pair, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. 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 $F_n + \... | 23,511 | graphs = [
Graph(
let={
"_n": Const(121),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | C3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"B3",
"C3"
] | 2 | 0.025 | 2026-02-08T16:59:50.718371Z | {
"verified": true,
"answer": 23511,
"timestamp": "2026-02-08T16:59:50.743309Z"
} | fb8af7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1100
},
"timestamp": "2026-02-17T16:47:30.935Z",
"answer": 23511
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8430fd | antilemma_k3_v1_48377204_2050 | Let $n = 79621$. Compute the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. | 79,621 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=79621), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T16:34:32.047262Z | {
"verified": true,
"answer": 79621,
"timestamp": "2026-02-08T16:34:32.047632Z"
} | d27097 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 2214
},
"timestamp": "2026-02-17T07:18:03.993Z",
"answer": 79621
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cf8511 | nt_count_with_divisor_count_v1_1915831931_2201 | Let $T$ be the set of all positive integers $t$ such that $10 \leq t \leq 7581$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 174$, $1 \leq b \leq 2121$, and $t = 7a + 3b$. Let $U$ be the number of positive integers $n$ with $1 \leq n \leq |T|$ such that the number of positive divisors of $n$ is exa... | 324 | 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=174)), Geq(left=Var(name='b'), right=Const(v... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 2.728 | 2026-02-08T16:40:16.553894Z | {
"verified": true,
"answer": 324,
"timestamp": "2026-02-08T16:40:19.282101Z"
} | 426cb7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 4273
},
"timestamp": "2026-02-17T09:04:51.773Z",
"answer": 324
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5c911d | comb_catalan_compute_v1_717093673_2766 | Let $u = 4$ and define $n_2 = u + 0!$. Let $$
c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$ Define $n_1 = c$. Let $$
w = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$ Let $n$ be the product of $w$ and the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Compute the value o... | 58,786 | graphs = [
Graph(
let={
"u": Const(4),
"n2": Sum(Ref("u"), Factorial(Const(0))),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("c"),
"w": Summation(var="k1", st... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 202ae5 | comb_catalan_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"ONE_FACTORIAL_0"
] | 3 | 0.004 | 2026-02-08T17:09:35.623171Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T17:09:35.627257Z"
} | 1dfb17 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1430
},
"timestamp": "2026-02-17T20:07:45.152Z",
"answer": 58786
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INT... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
8fecbf | nt_count_gcd_equals_v1_865884756_5713 | Let $n$ be a positive integer such that $1 \leq n \leq 457$ and $\gcd(n, 20) = 1$. The number of such integers $n$ is denoted by $k$. Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 28561$ and $\gcd(n_1, k) = 61$. Compute the number of elements in $S$. | 312 | graphs = [
Graph(
let={
"upper": Const(28561),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(457)), Eq(GCD(a=Var("n"), b=Const(20)), Const(1))))),
"d": Const(61),
"result": CountOverSet(set=Solution... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"C4"
] | 1 | 2.065 | 2026-02-08T18:45:40.139929Z | {
"verified": true,
"answer": 312,
"timestamp": "2026-02-08T18:45:42.204720Z"
} | 62e561 | 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": 1405
},
"timestamp": "2026-02-18T19:22:51.583Z",
"answer": 312
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
563901 | comb_factorial_compute_v1_1419126231_1720 | Let $n = \sum_{k=1}^{2} 2^k$, where the lower limit of the sum is $\sum_{k_1=0}^{3} (-1)^{k_1} \binom{3}{k_1}$. Let $M = n!$. Let $T$ be the set of integers $t$ such that $t = 2a + 3b$ for integers $a, b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $5 \leq t \leq 17$. Let $Q = B_{M \bmod |T|}$, where $B_k$ denotes t... | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Summation(var="k1", start=Const(0), end=Const(3), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Const(3), k=Var("k1")))), end=Const(2), expr=Pow(Ref("_n"), Var("k"))),
"result": Factorial(Ref("n")),
... | COMB | null | COMPUTE | sympy | K13 | [
"LIN_FORM",
"BINOMIAL_ALTERNATING",
"SUM_GEOM"
] | a3cc9d | comb_factorial_compute_v1 | bell_mod | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"K13",
"LIN_FORM",
"SUM_GEOM"
] | 4 | 3.715 | 2026-02-25T11:14:33.087702Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-25T11:14:36.803001Z"
} | 508c85 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 1319
},
"timestamp": "2026-03-30T13:34:24.083Z",
"answer": 2
},
{
"id":... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lem... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
145c35 | modular_modexp_compute_v1_1978505735_2654 | Let $a = 13$, $e = 576$, and $m = 55555$. Let $R$ be the remainder when $a^e$ is divided by $m$. Let $P$ be the largest prime number less than or equal to $7009$. Compute the remainder when $\left(R \bmod 307\right) + P \cdot \left(R \bmod 317\right)$ is divided by $90739$. | 48,308 | graphs = [
Graph(
let={
"a": Const(13),
"e": Const(576),
"m": Const(55555),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7009... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | modular_modexp_compute_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T17:03:33.479182Z | {
"verified": true,
"answer": 48308,
"timestamp": "2026-02-08T17:03:33.482176Z"
} | 92e33d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 3688
},
"timestamp": "2026-02-17T18:36:42.794Z",
"answer": 48308
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
04c392 | sequence_count_fib_divisible_v1_1742523217_4097 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 83$ and $\binom{83}{j}$ is odd. Let $u$ be the sum of all elements in $S$. Determine the number of positive integers $n$ such that $n \leq u$ and $16$ divides the $n$th Fibonacci number. Let $r$ be this count. Compute the remainder when $44121 ... | 17,795 | graphs = [
Graph(
let={
"_n": Const(83),
"upper": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(83)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"d": C... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.029 | 2026-02-08T06:59:54.256473Z | {
"verified": true,
"answer": 17795,
"timestamp": "2026-02-08T06:59:54.285502Z"
} | 769f7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 2029
},
"timestamp": "2026-02-13T06:54:14.140Z",
"answer": 17795
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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