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
a0f332
algebra_quadratic_discriminant_v1_1918700295_2798
Let $a = 3$ and $b = 5$. Define $c$ to be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 5$, and $\gcd(i, j) = 1$. Let $r = b^2 - 4ac$. Compute $73441 - r$.
73,560
graphs = [ Graph( let={ "a": Const(3), "b": Const(5), "c": 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(3)), right=IntegerRa...
NT
null
COMPUTE
sympy
COUNT_COPRIME_GRID
[ "COUNT_COPRIME_GRID" ]
20ec03
algebra_quadratic_discriminant_v1
null
3
0
[ "COUNT_COPRIME_GRID" ]
1
0.001
2026-02-08T08:13:03.836559Z
{ "verified": true, "answer": 73560, "timestamp": "2026-02-08T08:13:03.837916Z" }
9f024b
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 132, "completion_tokens": 639 }, "timestamp": "2026-02-13T16:36:52.596Z", "answer": 73560 }, {...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -5.55, "mid": -3.01, "hi": 0.32 }
379f8f
modular_modexp_compute_v1_1125832087_1607
Let $a$ be the largest prime number at most $29$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. Define $e$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the remainder when $a^e$ is divided by $16384$.
3,233
graphs = [ Graph( let={ "_n": Const(29), "a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditi...
NT
null
COMPUTE
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW", "B3" ]
78ed98
modular_modexp_compute_v1
null
6
0
[ "B3", "MAX_PRIME_BELOW" ]
2
0.003
2026-02-08T03:50:11.026586Z
{ "verified": true, "answer": 3233, "timestamp": "2026-02-08T03:50:11.029140Z" }
5cbed9
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 195, "completion_tokens": 7233 }, "timestamp": "2026-02-10T14:35:55.117Z", "answer": 4825 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "V3", "status": "no" }, { "lem...
{ "lo": 1.96, "mid": 5.23, "hi": 8.52 }
778b61
comb_sum_binomial_mod_v1_798873815_376
Let $n = 10141$. Let $m$ be the largest prime number between 2 and 25. Compute the sum $$\sum_{k=m}^{173} \binom{218}{k},$$ and let $r$ be the remainder when this sum is divided by $n$. Determine the value of $$\sum_{j=1}^{|r|} \tau(j),$$ where $\tau(j)$ denotes the number of positive divisors of $j$.
25,555
graphs = [ Graph( let={ "_n": Const(10141), "sum": Summation(var="k", start=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(25)), IsPrime(Var("n"))))), end=Const(173), expr=Binom(n=Const(218), k=Var("k"))), "result": Mo...
NT
null
COMPUTE
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
comb_sum_binomial_mod_v1
null
7
0
[ "MAX_PRIME_BELOW" ]
1
0.014
2026-02-08T02:37:07.980734Z
{ "verified": true, "answer": 25555, "timestamp": "2026-02-08T02:37:07.994531Z" }
89aaad
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 209, "completion_tokens": 32768 }, "timestamp": "2026-02-23T15:20:59.796Z", "answer": null }, { ...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": 3.94, "mid": 5.6, "hi": 7.62 }
fe17c1
comb_count_surjections_v1_865884756_5725
Let $m = 7$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = m$, where $1 \leq i \leq 5$ and $1 \leq j \leq 6$. Let $n$ be the number of such pairs. Now let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = n$. Compute the ...
5,796
graphs = [ Graph( let={ "_m": Const(7), "_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Cons...
COMB
null
COUNT
sympy
LIN_FORM
[ "COUNT_SUM_EQUALS/COMB1" ]
5b2e59
comb_count_surjections_v1
null
6
0
[ "COMB1", "COUNT_SUM_EQUALS", "LIN_FORM" ]
3
0.036
2026-02-08T18:45:52.712812Z
{ "verified": true, "answer": 5796, "timestamp": "2026-02-08T18:45:52.748636Z" }
eb6544
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 188, "completion_tokens": 1518 }, "timestamp": "2026-02-18T19:23:44.421Z", "answer": 5796 }, {...
1
[ { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma...
{ "lo": -3.12, "mid": 1.47, "hi": 6.57 }
24a489
comb_count_surjections_v1_1218484723_4063
Let $k = 3$ and $n = \sum_{i=0}^{2} 2^i$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind.
1,806
graphs = [ Graph( let={ "_n": Const(2), "n": Summation(var="k1", start=Const(0), end=Ref("_n"), expr=Pow(Const(2), Var("k1"))), "k": Const(3), "result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))), }, goal=Ref("result"...
COMB
null
COUNT
sympy
SUM_GEOM
[ "SUM_GEOM" ]
04214c
comb_count_surjections_v1
null
3
0
[ "SUM_GEOM" ]
1
0.002
2026-02-25T05:42:49.809452Z
{ "verified": true, "answer": 1806, "timestamp": "2026-02-25T05:42:49.811222Z" }
e39ad1
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 165, "completion_tokens": 606 }, "timestamp": "2026-03-29T13:35:28.176Z", "answer": 1806 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "SUM_GEOM", "status": "ok" }, { "lemma": "V8", "st...
{ "lo": -6.5, "mid": -3.34, "hi": -0.88 }
caf186
geo_visible_lattice_v1_1742523217_4968
Let $n = 90$. Define $\text{result}$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $Q = 47089 - \text{result}$. Compute $Q$.
42,130
graphs = [ Graph( let={ "n": Const(90), "result": VisibleLatticePoints(n=Ref(name='n')), "Q": Sub(Const(47089), Ref("result")), }, goal=Ref("Q"), ) ]
GEOM
null
COUNT
sympy
[]
geo_visible_lattice_v1
null
5
0
null
null
1.984
2026-02-08T10:41:36.475784Z
{ "verified": true, "answer": 42130, "timestamp": "2026-02-08T10:41:38.459658Z" }
705e5b
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 183, "completion_tokens": 7419 }, "timestamp": "2026-02-24T12:14:36.149Z", "answer": 42130 }, { "...
1
[]
{ "lo": 1.15, "mid": 4.18, "hi": 6.61 }
934e5e
antilemma_k3_v1_1520064083_4806
Compute the sum of $\phi(d)$ over all positive divisors $d$ of 74445, where $\phi$ denotes Euler's totient function.
74,445
graphs = [ Graph( let={ "_n": Const(74445), "x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), }, goal=Ref("x"), ) ]
NT
COMB
COMPUTE
sympy
K3
[ "K3" ]
54c41e
antilemma_k3_v1
null
3
0
[ "K3" ]
1
0
2026-02-08T06:26:26.913923Z
{ "verified": true, "answer": 74445, "timestamp": "2026-02-08T06:26:26.914364Z" }
7b5c07
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 77, "completion_tokens": 599 }, "timestamp": "2026-02-13T00:18:34.168Z", "answer": 74445 }, { ...
1
[ { "lemma": "K3", "status": "ok" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" } ]
{ "lo": -3.51, "mid": 1.33, "hi": 6.56 }
4bc56a
sequence_count_fib_divisible_v1_677425708_1820
Let $ n = 5 $ and $ u = 438 $. Define $ d $ to be the largest integer such that $ 41^d $ divides $ 41^5 $. Determine the number of positive integers $ m $ such that $ 1 \leq m \leq 438 $ and $ d $ divides $ F_m $, where $ F_m $ denotes the $ m $-th Fibonacci number.
87
graphs = [ Graph( let={ "_n": Const(5), "upper": Const(438), "d": MaxKDivides(target=Pow(Const(41), Ref("_n")), base=Const(41)), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(d...
NT
null
COUNT
sympy
K14
[ "K14" ]
a49bcb
sequence_count_fib_divisible_v1
null
5
0
[ "K14" ]
1
0.02
2026-02-08T04:28:54.293842Z
{ "verified": true, "answer": 87, "timestamp": "2026-02-08T04:28:54.313836Z" }
cfd637
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 196, "completion_tokens": 980 }, "timestamp": "2026-02-10T01:28:25.498Z", "answer": 87 }, { "id":...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "ok" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -6.5, "mid": -0.2, "hi": 6.11 }
1df4f9
nt_num_divisors_compute_v1_865884756_3955
Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $$pq=54,\qquad \gcd(p,q)=1,\qquad p<q.$$ Let $S$ be the set of all integers $n_1$ such that $n_1\ge m$, $n_1\le U$, and $n_1$ is prime, where $U$ is defined as follows. First, let $T$ be the set of all integers $t$ ...
88,242
graphs = [ Graph( let={ "_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/COMB1/MAX_PRIME_BELOW", "LIN_FORM/COMB1/MAX_PRIME_BELOW" ]
b98bc8
nt_num_divisors_compute_v1
null
6
0
[ "COMB1", "COPRIME_PAIRS", "LIN_FORM", "MAX_PRIME_BELOW" ]
4
0.019
2026-02-08T17:40:46.547492Z
{ "verified": true, "answer": 88242, "timestamp": "2026-02-08T17:40:46.566812Z" }
a42c3e
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 341, "completion_tokens": 3114 }, "timestamp": "2026-02-18T06:36:37.492Z", "answer": 88242 }, ...
1
[ { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "statu...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
a1e775
lin_form_endings_v1_677425708_783
Let $a = 28$ and $b = 98$. Compute the least common multiple of $a$ and $b$, multiply it by $14621$, and then compute the remainder when this product is divided by $55440$.
38,276
graphs = [ Graph( let={ "a_coeff": Const(28), "b_coeff": Const(98), "_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")), "_scale_k": Const(14621), "_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")), "_mod_M": Const(55440), ...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
2
null
[ "LIN_FORM" ]
1
0.001
2026-02-08T03:43:49.585807Z
{ "verified": true, "answer": 38276, "timestamp": "2026-02-08T03:43:49.586431Z" }
3863fb
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 163, "completion_tokens": 336 }, "timestamp": "2026-02-09T11:48:20.417Z", "answer": 38276 }, { "i...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -3.46, "mid": 1.03, "hi": 5.49 }
1cc01e
geo_visible_lattice_v1_1520064083_6504
Let $n = 100$. Define $r$ 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 value of the Bell number $B_m$, where $m$ is the remainder when $r$ is divided by 11.
15
graphs = [ Graph( let={ "n": Const(100), "result": VisibleLatticePoints(n=Ref(name='n')), "Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), }, goal=Ref("Q"), ) ]
GEOM
COMB
COUNT
sympy
[]
geo_visible_lattice_v1
null
6
0
null
null
0.435
2026-02-08T08:08:02.940417Z
{ "verified": true, "answer": 15, "timestamp": "2026-02-08T08:08:03.375129Z" }
652c03
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": 8636 }, "timestamp": "2026-02-24T08:56:20.676Z", "answer": 15 }, { "id"...
1
[]
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
1bfb51_l
comb_bell_compute_v1_124444284_6170
Let $n$ be the number of nonnegative integers $j$ with $0\le j\le580$ such that $$\binom{580}{j}\equiv1\pmod{2}.$$ Let $B_n$ denote the $n$th Bell number, and let $$Q=47961-B_n.$$ Compute $Q$.
0
COMB
null
COMPUTE
sympy
V8
[ "V8" ]
86348e
comb_bell_compute_v1
null
8
0
[ "V8" ]
1
0.001
2026-02-08T08:10:47.200932Z
{ "verified": false, "answer": 43821, "timestamp": "2026-02-08T08:10:47.201879Z" }
379eec
1bfb51
legacy_text
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": 1095 }, "timestamp": "2026-02-24T08:58:04.583Z", "answer": 43821 }, { "...
1
[ { "lemma": "K16", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V8", "status": "ok" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
d51f2c
antilemma_k3_v1_1520064083_6444
Let $n = 35749$. Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $n$, where $\varphi$ denotes Euler's totient function.
35,749
graphs = [ Graph( let={ "_n": Const(35749), "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
2
0
[ "K3" ]
1
0.001
2026-02-08T08:04:25.582713Z
{ "verified": true, "answer": 35749, "timestamp": "2026-02-08T08:04:25.583404Z" }
55d9e0
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": 1183 }, "timestamp": "2026-02-13T15:03:39.309Z", "answer": 35749 }, {...
1
[ { "lemma": "K3", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V3", "status":...
{ "lo": -3.51, "mid": 1.33, "hi": 6.56 }
4ba8d5
antilemma_k3_v1_1440796553_652
Let $n = 52736$. Define $$ x = \sum_{d \mid n} \phi(d), $$ where the sum is over all positive divisors $d$ of $n$, and $\phi(d)$ is the number of positive integers less than or equal to $d$ that are relatively prime to $d$. Let $A$ be the set of all integers $x$ such that $x^2 - 1009x + 60480 = 0$. Let $B$ be the sum ...
24,430
graphs = [ Graph( let={ "_n": Const(52736), "x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), "Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(199)), Mul(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)),...
NT
COMB
COMPUTE
sympy
VIETA_SUM
[ "VIETA_SUM", "K3" ]
4765cd
antilemma_k3_v1
two_moduli
6
0
[ "K3", "VIETA_SUM" ]
2
0.001
2026-02-08T11:55:03.942409Z
{ "verified": true, "answer": 24430, "timestamp": "2026-02-08T11:55:03.943588Z" }
098736
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 199, "completion_tokens": 1114 }, "timestamp": "2026-02-14T20:38:01.191Z", "answer": 24430 }, ...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V8_SUM", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" }...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
e19c5d
lin_form_endings_v1_168721529_312
Let $a = 24$, $b = 60$, $A = 47$, and $B = 18$. Let $g = \gcd(a, b)$, and define $s = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1$. Compute the remainder when $13866 \cdot s$ is divided by $57299$.
4,291
graphs = [ Graph( let={ "a_coeff": Const(24), "b_coeff": Const(60), "A_val": Const(47), "B_val": Const(18), "g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")), "numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
3
null
[ "LIN_FORM" ]
1
0.004
2026-02-08T12:59:23.499970Z
{ "verified": true, "answer": 4291, "timestamp": "2026-02-08T12:59:23.503553Z" }
08d462
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 205, "completion_tokens": 681 }, "timestamp": "2026-02-09T03:33:38.185Z", "answer": 4291 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "status": "no...
{ "lo": -2, "mid": 1.85, "hi": 5.2 }
1d0678
nt_count_with_divisor_count_v1_784195855_7242
Let $t$ be an integer. Consider the set of all integers $t$ such that $5 \leq t \leq 15$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $d$ be the number of elements in this set. Let $S$ be the set of all positive integers $n \leq 55225$ such that the number of ...
100
graphs = [ Graph( let={ "upper": Const(55225), "div_count": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), ...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
nt_count_with_divisor_count_v1
null
4
0
[ "LIN_FORM" ]
1
3.872
2026-02-08T09:09:48.535654Z
{ "verified": true, "answer": 100, "timestamp": "2026-02-08T09:09:52.407627Z" }
d48329
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 262, "completion_tokens": 2481 }, "timestamp": "2026-02-14T00:59:48.300Z", "answer": 100 }, { ...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
26a6a7
antilemma_sum_factor_cartesian_v1_151522320_383
Let $S$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 8$. Let $T$ be the set of all products $i \cdot j$ where $(i,j) \in S$. Compute the sum of all elements in $T$.
1,296
graphs = [ Graph( let={ "x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=Const(2)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(8)))), expr=Mul(Var("i"), Var("j...
NT
null
COMPUTE
sympy
SUM_FACTOR_CARTESIAN
[ "SUM_FACTOR_CARTESIAN", "ONE_PHI_2" ]
09bd3b
antilemma_sum_factor_cartesian_v1
null
2
0
[ "ONE_PHI_2", "SUM_FACTOR_CARTESIAN" ]
2
0.001
2026-02-08T03:12:42.575718Z
{ "verified": true, "answer": 1296, "timestamp": "2026-02-08T03:12:42.576459Z" }
148b96
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 193, "completion_tokens": 2200 }, "timestamp": "2026-02-09T02:06:35.735Z", "answer": 680 }, { ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "ONE_PHI_2", "status":...
{ "lo": -6.49, "mid": 0.51, "hi": 7.52 }
39cb70
alg_poly_preperiod_count_v1_1218484723_5399
Let $S = R^3 + 3R \bmod 37$, where $R = M^3 + 3M \bmod 37$, $M = N^3 + 3N \bmod 37$, and $N = a^3 + 3a \bmod 37$. Find the number of non-negative integers $a$ with $0 \le a \le 14281$ such that $S = M$ and $R \neq M$.
3,860
graphs = [ Graph( let={ "p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(3), Var("a"))), modulus=Const(37)), "p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(3), Ref("p1"))), modulus=Const(37)), "p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(3), Ref(...
ALG
null
COUNT
sympy
POLY_ORBIT_COUNT
[ "POLY_ORBIT_COUNT" ]
4ad965
alg_poly_preperiod_count_v1
null
6
null
[ "POLY_ORBIT_COUNT" ]
1
0.016
2026-02-25T06:58:02.269592Z
{ "verified": true, "answer": 3860, "timestamp": "2026-02-25T06:58:02.285683Z" }
f16502
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 213, "completion_tokens": 6220 }, "timestamp": "2026-03-29T20:55:17.855Z", "answer": 3860 }, { "i...
1
[ { "lemma": "POLY_ORBIT_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -3.33, "mid": 1.03, "hi": 5.26 }
75d16e
nt_count_divisible_v1_1978505735_1407
Let $n = 73303$ and $U = 51529$. Let $d$ be the number of integers $j$ with $0 \leq j \leq 20740$ such that $\binom{20740}{j}$ is odd. Let $R$ be the number of positive integers $m$ with $1 \leq m \leq U$ such that $m$ is divisible by $d$. Let $c = 66389$, and define $Q$ as the remainder when $c \cdot R$ is divided by ...
21,032
graphs = [ Graph( let={ "_n": Const(73303), "upper": Const(51529), "divisor": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(20740)), Eq(Mod(value=Binom(n=Const(20740), k=Var("j")), modulus=Const(2)), Const(1))), dom...
ALG
COMB
COUNT
sympy
V8
[ "V8" ]
86348e
nt_count_divisible_v1
null
5
0
[ "V8" ]
1
1.828
2026-02-08T16:08:08.203109Z
{ "verified": true, "answer": 21032, "timestamp": "2026-02-08T16:08:10.031590Z" }
cd77a6
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 239, "completion_tokens": 1120 }, "timestamp": "2026-02-24T20:02:06.793Z", "answer": 21032 }, { ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V8", "status": "ok" } ]
{ "lo": -2.4, "mid": 1.57, "hi": 5.75 }
c59563
nt_count_divisible_and_v1_151522320_1357
Let $n$ be a positive integer. Determine the value of the number of positive integers $n$ such that $n \leq 35520$, $n$ is divisible by 6, and $n$ is divisible by 10.
1,184
graphs = [ Graph( let={ "upper": Const(35520), "d1": Const(6), "d2": Const(10), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Con...
NT
null
COUNT
sympy
ONE_PHI_1
[ "ONE_PHI_1" ]
f6b5a5
nt_count_divisible_and_v1
null
3
0
[ "ONE_PHI_1" ]
1
1.248
2026-02-08T03:53:35.616860Z
{ "verified": true, "answer": 1184, "timestamp": "2026-02-08T03:53:36.864993Z" }
acdf4f
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 149, "completion_tokens": 337 }, "timestamp": "2026-02-18T07:18:36.179Z", "answer": 1184 } ]
2
[ { "lemma": "DS2", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "ONE_PHI_1", "status": "ok" }, { "lemma": "V5", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -10, "mid": -6.47, "hi": -2.95 }
4d07e7
algebra_vieta_sum_v1_1742523217_3357
Let $m=2$ and $N=99828$. For each positive integer $k$, let $\varphi(k)$ denote the number of positive integers not exceeding $k$ that are relatively prime to $k$. Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $$pq=216,\quad \gcd(p,q)=1,\quad p<q.$$Let $r$ be the nu...
26,094
graphs = [ Graph( let={ "_m": Const(2), "_n": Const(99828), "result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Ref(name='_m'), Pow(base=Var(name='x'), exp=Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=CountOverSet(set...
NT
null
COMPUTE
sympy
LIN_FORM
[ "COUNT_CARTESIAN", "COPRIME_PAIRS/K2" ]
59e2bd
algebra_vieta_sum_v1
affine_mod
8
0
[ "COPRIME_PAIRS", "COUNT_CARTESIAN", "K2", "LIN_FORM" ]
4
0.082
2026-02-08T05:48:53.695652Z
{ "verified": true, "answer": 26094, "timestamp": "2026-02-08T05:48:53.778097Z" }
6e5e02
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 301, "completion_tokens": 2119 }, "timestamp": "2026-02-12T14:54:34.666Z", "answer": 26094 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "K2", "status": "ok_later" }, { "lemma": "L3b", "status": "no"...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
4b382c
comb_catalan_compute_v1_784195855_7471
Let $n_2 = 8$ and define $$ t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}. $$ Let $a = 3$ and $b = 2 + t$. Define $n_1 = a + b$ and $$ f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}. $$ Let $n = 11 + f$. Compute the $n$-th Catalan number, and let $m = |n\text{-th Catalan number}| + 2$. Find the remainder when the Fibonacci se...
840
graphs = [ Graph( let={ "n2": Const(8), "t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))), "a": Const(3), "b": Sum(Const(2), Ref("t")), "n1": Sum(Ref("a"), Ref("b")), ...
COMB
NT
COMPUTE
sympy
BINOMIAL_ALTERNATING
[ "BINOMIAL_ALTERNATING" ]
c21569
comb_catalan_compute_v1
null
4
2
[ "BINOMIAL_ALTERNATING" ]
1
0.002
2026-02-08T09:20:18.787266Z
{ "verified": true, "answer": 840, "timestamp": "2026-02-08T09:20:18.788954Z" }
17245b
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 292, "completion_tokens": 32768 }, "timestamp": "2026-02-24T11:12:33.649Z", "answer": null }, { ...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8"...
{ "lo": 1.15, "mid": 4.18, "hi": 6.61 }
9d9d4d
diophantine_fbi2_count_v1_784195855_579
Let $k = 60$. Consider the set of all integers $d$ such that $3 \leq d \leq 52$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 51$. Let $r$ be the number of such integers $d$. Compute the remainder when $80461 \cdot r$ is divided by $76914$.
31,923
graphs = [ Graph( let={ "_n": Const(3), "k": Const(60), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(52)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(Re...
NT
null
COUNT
sympy
MAX_DIVISOR
[ "MAX_DIVISOR" ]
51757e
diophantine_fbi2_count_v1
null
3
0
[ "MAX_DIVISOR" ]
1
0.006
2026-02-08T04:28:37.963742Z
{ "verified": true, "answer": 31923, "timestamp": "2026-02-08T04:28:37.970229Z" }
ad10db
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 197, "completion_tokens": 720 }, "timestamp": "2026-02-10T16:51:10.097Z", "answer": 31923 }, { "...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_MUL", "sta...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
18e3b4
antilemma_product_of_sums_v1_168721529_1187
Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 7$ and $1 \le j \le 3$. Define $S_1$ to be the sum of $i \cdot j$ over all pairs $(i,j)$ in $S$. Let $T$ be the set of all ordered pairs $(k,\ell)$ of positive integers such that $1 \le k \le 6$ and $1 \le \ell \le 8$. Define $...
11,432
graphs = [ Graph( let={ "S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(3)))), expr=Mul(Var("i"), Var("j")))), ...
NT
null
COMPUTE
sympy
PRODUCT_OF_SUMS
[ "PRODUCT_OF_SUMS" ]
f2b2b0
antilemma_product_of_sums_v1
null
3
0
[ "PRODUCT_OF_SUMS" ]
1
0.001
2026-02-08T13:31:22.305082Z
{ "verified": true, "answer": 11432, "timestamp": "2026-02-08T13:31:22.305975Z" }
65a4d8
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 288, "completion_tokens": 4157 }, "timestamp": "2026-02-09T14:26:35.802Z", "answer": 11432 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "PRODUCT_OF_SUMS", "status": "ok" ...
{ "lo": -1.99, "mid": 2.14, "hi": 6.33 }
0a19cb
antilemma_cartesian_v1_898971024_2455
Compute the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 23$ and $1 \leq j \leq 28$.
644
graphs = [ Graph( let={ "x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Const(28)))), "Q": Ref("x"), }, goal=Ref("Q"), ) ]
COMB
GEOM
COMPUTE
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
antilemma_cartesian_v1
null
2
0
[ "COUNT_CARTESIAN" ]
1
0.001
2026-02-08T16:46:19.813669Z
{ "verified": true, "answer": 644, "timestamp": "2026-02-08T16:46:19.814495Z" }
385888
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 81, "completion_tokens": 354 }, "timestamp": "2026-02-24T21:48:59.133Z", "answer": 644 }, { ...
2
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -10, "mid": -7.42, "hi": -4.85 }
aec6ad
nt_gcd_compute_v1_153355830_1954
Let $n$ be a positive integer such that $1 \leq n \leq 57973$ and $$n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}.$$ Let $c$ be the number of such integers $n$. Compute the value of $$c - \gcd(557697, 1035723) \pmod{78011}.$$
6,621
graphs = [ Graph( let={ "_n": Const(57973), "a": Const(557697), "b": Const(1035723), "result": GCD(a=Ref("a"), b=Ref("b")), "_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent...
NT
null
COMPUTE
sympy
L3C
[ "L3C" ]
fba717
nt_gcd_compute_v1
negation_mod
6
0
[ "L3C" ]
1
0.002
2026-02-08T06:48:13.596997Z
{ "verified": true, "answer": 6621, "timestamp": "2026-02-08T06:48:13.598767Z" }
f432e0
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 133, "completion_tokens": 1544 }, "timestamp": "2026-02-13T05:11:49.311Z", "answer": 6621 }, {...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "L3C", "status": "ok" }, { "lemma": "L3c", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
cc63d4
nt_lcm_compute_v1_677425708_3797
Let $a$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 31$ and $1 \leq j \leq 46$. Let $b = 1903$. Let $L$ be the least common multiple of $a$ and $b$. Compute the remainder when $64820 \times L$ is divided by $76969$. Find the value of this remainder.
42,593
graphs = [ Graph( let={ "a": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(31)), right=IntegerRange(start=Const(1), end=Const(46)))), "b": Const(1903), "result": LCM(a=Ref("a"), b=Ref("b")), "Q": Mod(value=Mul(Const(64820), Ref(...
NT
null
COMPUTE
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
nt_lcm_compute_v1
null
3
0
[ "COUNT_CARTESIAN" ]
1
0.001
2026-02-08T05:56:37.847511Z
{ "verified": true, "answer": 42593, "timestamp": "2026-02-08T05:56:37.848257Z" }
b179fc
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 134, "completion_tokens": 2278 }, "timestamp": "2026-02-12T16:53:52.253Z", "answer": 42593 }, ...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
024f93
diophantine_product_count_v1_124444284_8637
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1982464$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Define $n_0$ to be the minimum element of $T$. Let $U$ be the set of all integers $n$ such that $1 \leq n \leq n_0$ and $n \equiv \left\lfloor \frac{n}{2} \right...
22
graphs = [ Graph( let={ "_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1982464)))), expr=Sum(Var("x"), Var("y")))), "k": Const(420...
NT
null
COUNT
sympy
MAX_PRIME_BELOW
[ "B3/L3C" ]
345f3b
diophantine_product_count_v1
null
7
0
[ "B3", "L3C", "MAX_PRIME_BELOW" ]
3
0.091
2026-02-08T11:51:15.862828Z
{ "verified": true, "answer": 22, "timestamp": "2026-02-08T11:51:15.953346Z" }
3ac402
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 228, "completion_tokens": 2570 }, "timestamp": "2026-02-14T19:42:17.143Z", "answer": 22 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "L3C", "status": "ok_later" }, { "lemma": "V7", "status": "no" }, ...
{ "lo": -6.96, "mid": -4.56, "hi": -1.46 }
b651ef
nt_count_primes_v1_151522320_87
Let $p$ be the number of prime numbers $n$ such that $2 \leq n \leq 33856$. Let $S$ be the set of all positive integers $t$ such that $32 \leq t \leq 10847$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 434$, $1 \leq b \leq 288$, and $$ t = 21a + 6b + 5. $$ Let $q$ be the number of elements in $S$....
80,706
graphs = [ Graph( let={ "_n": Const(80731), "upper": Const(33856), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))), "Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
324ba4
nt_count_primes_v1
negation_mod
5
0
[ "LIN_FORM" ]
1
0.881
2026-02-08T02:58:05.754202Z
{ "verified": true, "answer": 80706, "timestamp": "2026-02-08T02:58:06.634772Z" }
d68835
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 254, "completion_tokens": 32768 }, "timestamp": "2026-02-23T20:10:45.182Z", "answer": null }, { ...
0
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status": "no"...
{ "lo": 4.68, "mid": 6.57, "hi": 9.55 }
994ccd
diophantine_fbi2_count_v1_168721529_29
Let $k$ be the sum of all nonnegative integers $j$ with $0 \leq j \leq 60$ such that $$ \binom{60}{j} \equiv 1 \pmod{2}. $$ Let $r$ be the number of integers $d$ such that $5 \leq d \leq 204$, $d$ divides $k$, and $$ 2 \leq \frac{k}{d} \leq 201. $$ Find the value of $r$.
18
graphs = [ Graph( let={ "k": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(60)), Eq(Mod(value=Binom(n=Const(60), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), "result": CountOverSet(set=SolutionsSet...
NT
null
COUNT
sympy
MIN_PRIME_FACTOR
[ "V8" ]
86348e
diophantine_fbi2_count_v1
null
5
0
[ "MIN_PRIME_FACTOR", "V8" ]
2
0.115
2026-02-08T12:46:17.061564Z
{ "verified": true, "answer": 18, "timestamp": "2026-02-08T12:46:17.176414Z" }
a20705
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 230, "completion_tokens": 3581 }, "timestamp": "2026-02-08T20:57:40.331Z", "answer": 18 }, { "id"...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V8", "status": "ok" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -2, "mid": 1.85, "hi": 5.2 }
9cc061
nt_sum_gcd_range_mod_v1_397696148_185
Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1000000$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 57600$. Let $M = 10613$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remain...
10,225
graphs = [ Graph( let={ "N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1000000)))), expr=Sum(Var("x"), Var("y")))), "k": MinOverSet...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_sum_gcd_range_mod_v1
null
6
0
[ "B3" ]
1
0.123
2026-02-08T11:21:20.569504Z
{ "verified": true, "answer": 10225, "timestamp": "2026-02-08T11:21:20.692953Z" }
a658e1
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 163, "completion_tokens": 3273 }, "timestamp": "2026-02-14T12:23:43.279Z", "answer": 10225 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V8", "status": "no" ...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
dbf05b
comb_count_partitions_v1_1918700295_2794
Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all positive integers $t$ that can be expressed as $t = 5a + 4b$ for integers $a$ and $b$ with $1 \leq a \leq ...
63,261
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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ...
NT
COMB
COUNT
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MAX_PRIME_BELOW", "LIN_FORM/MAX_PRIME_BELOW" ]
d6bd1c
comb_count_partitions_v1
null
6
0
[ "COPRIME_PAIRS", "LIN_FORM", "MAX_PRIME_BELOW" ]
3
0.006
2026-02-08T08:12:35.075374Z
{ "verified": true, "answer": 63261, "timestamp": "2026-02-08T08:12:35.081760Z" }
9b38fc
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 213, "completion_tokens": 2241 }, "timestamp": "2026-02-13T16:39:23.154Z", "answer": 63261 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "POLY_PADIC_VAL_CON...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
823fcb
modular_min_linear_v1_1470522791_1351
Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1157776$. Determine the smallest positive integer $x$ such that $1 \leq x \leq m$ and $$ 1665x \equiv 2115 \pmod{m}. $$
1,339
graphs = [ Graph( let={ "a": Const(1665), "b": Const(2115), "m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1157776)))),...
NT
null
EXTREMUM
sympy
B3
[ "B3" ]
0cd20d
modular_min_linear_v1
null
4
0
[ "B3" ]
1
8.976
2026-02-08T13:35:37.589427Z
{ "verified": true, "answer": 1339, "timestamp": "2026-02-08T13:35:46.565063Z" }
30554b
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 118, "completion_tokens": 2323 }, "timestamp": "2026-02-15T18:19:18.552Z", "answer": 1339 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
ba8fdf
diophantine_product_count_v1_717093673_3206
Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 900$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $k$ be the minimum element of $T$. Let $N$ be the number of positive integers $x_1$ such that $1 \leq x_1 \leq 36$, $x_1$ divides $k$, and $\frac{k}{x_1} \leq 3...
17,714
graphs = [ Graph( let={ "_n": Const(900), "k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))), ...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
diophantine_product_count_v1
null
5
0
[ "B3" ]
1
0.007
2026-02-08T17:25:34.821725Z
{ "verified": true, "answer": 17714, "timestamp": "2026-02-08T17:25:34.828333Z" }
086a1e
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 181, "completion_tokens": 911 }, "timestamp": "2026-02-18T01:54:29.531Z", "answer": 17714 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
2deb61
nt_min_coprime_above_v1_1439011603_1716
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 8340544$. Define $\alpha$ to be the minimum value of $x + y$ over all such pairs. Let $\beta$ be the smallest integer $n$ such that $\alpha < n \leq 5823$ and $\gcd(n, 37) = 1$. Compute the remainder when $$\n\beta \bmod 293 + 3001 \cd...
23,116
graphs = [ Graph( let={ "start": 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(8340544)))), expr=Sum(Var("x"), Var("y")))), "upper": Co...
NT
null
EXTREMUM
sympy
B3
[ "B3" ]
0cd20d
nt_min_coprime_above_v1
null
5
0
[ "B3" ]
1
0.015
2026-02-08T16:14:05.828123Z
{ "verified": true, "answer": 23116, "timestamp": "2026-02-08T16:14:05.842805Z" }
532f34
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": 1137 }, "timestamp": "2026-02-16T23:00:43.315Z", "answer": 23116 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
01d89f
antilemma_sum_equals_v1_784195855_7212
Compute the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 101$, $1 \leq j \leq 101$, and $i + j = 103$.
100
graphs = [ Graph( let={ "x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(103)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(101)), right=IntegerRange(start=Const(1), end=Const(101))))), }, ...
COMB
GEOM
COMPUTE
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS" ]
75ab0f
antilemma_sum_equals_v1
null
3
0
[ "COUNT_SUM_EQUALS" ]
1
0.003
2026-02-08T09:08:49.528381Z
{ "verified": true, "answer": 100, "timestamp": "2026-02-08T09:08:49.531347Z" }
e01e13
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 158, "completion_tokens": 243 }, "timestamp": "2026-02-24T10:34:47.605Z", "answer": 100 }, { "id"...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V8_SU...
{ "lo": -5.97, "mid": -3.97, "hi": -1.93 }
d3d71d
comb_factorial_compute_v1_784195855_1660
Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 147000$. Compute $n!$.
40,320
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=147000)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
comb_factorial_compute_v1
null
6
0
[ "COPRIME_PAIRS" ]
1
0.001
2026-02-08T05:12:11.698434Z
{ "verified": true, "answer": 40320, "timestamp": "2026-02-08T05:12:11.699328Z" }
a2a36f
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 164, "completion_tokens": 916 }, "timestamp": "2026-02-11T23:03:20.871Z", "answer": 40320 }, { "...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -3.49, "mid": 1.84, "hi": 7.55 }
6dfc58
diophantine_fbi2_count_v1_349078426_500
Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 1069$. Determine the number of positive integers $d$ with $4 \leq d \leq 103$ such that $d$ divides $k$, and $\frac{k}{d}$ is an integer between $6$ and $105$, inclusive.
10
graphs = [ Graph( let={ "_n": Const(1069), "k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), ...
NT
null
COUNT
sympy
COUNT_COPRIME_GRID
[ "COUNT_PRIMES" ]
07c874
diophantine_fbi2_count_v1
null
4
0
[ "COUNT_COPRIME_GRID", "COUNT_PRIMES" ]
2
0.033
2026-02-08T13:06:11.550409Z
{ "verified": true, "answer": 10, "timestamp": "2026-02-08T13:06:11.583505Z" }
a890d0
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 122, "completion_tokens": 1202 }, "timestamp": "2026-02-15T09:26:47.310Z", "answer": 10 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
1b53d8
v1_endings_v1_601307018_433
Let $L = 58260!$. Let $U$ be the largest integer $k$ such that $5^k$ divides $L$. Let $V = 2U$. Let $A_1$ be the largest integer $k$ such that $2^k$ divides $L$, and let $A_2 = 5A_1$. Let $A_3$ be the largest integer $k$ such that $3^k$ divides $L$, and let $A_4 = 2A_3$. Define $A_5 = V + A_2 + A_4 + 965$. Find the rem...
79,595
graphs = [ Graph( let={ "n_val": Const(58260), "p1_val": Const(5), "p2_val": Const(2), "p3_val": Const(3), "n_fact": Factorial(Ref("n_val")), "vp1": MaxKDivides(target=Ref("n_fact"), base=Ref("p1_val")), "vp2": MaxKDivides(t...
NT
null
COMPUTE
sympy
V1
[ "V1" ]
dae96f
v1_endings_v1
null
5
null
[ "V1" ]
1
0.001
2026-03-10T00:57:35.242296Z
{ "verified": true, "answer": 79595, "timestamp": "2026-03-10T00:57:35.243748Z" }
508489
CC BY 4.0
null
null
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K5", "status": "same_pattern_wrong" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V1", "status": "...
{ "lo": -10, "mid": 0, "hi": 10 }
a7be96
antilemma_sum_equals_v1_1742523217_474
Let $m = 55246$. Let $n$ be the number of integers $t$ such that $30 \leq t \leq 315$ and there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 12$, and $t = 9a + 21b$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 83$ and $1 \leq j \leq 83$ such that $i + j = n$. Let...
33,413
graphs = [ Graph( let={ "_m": Const(55246), "_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=V...
COMB
GEOM
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/COUNT_SUM_EQUALS", "COUNT_SUM_EQUALS" ]
ada383
antilemma_sum_equals_v1
null
5
0
[ "COUNT_SUM_EQUALS", "LIN_FORM" ]
2
0.008
2026-02-08T03:04:36.469722Z
{ "verified": true, "answer": 33413, "timestamp": "2026-02-08T03:04:36.477997Z" }
d1e91b
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 273, "completion_tokens": 4721 }, "timestamp": "2026-02-23T21:29:11.092Z", "answer": 33413 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" }, ...
{ "lo": -0.05, "mid": 2.89, "hi": 5.27 }
b8e0ae
alg_poly3_min_v1_1218484723_3825
Let $A = \left|\{ t : \exists\, a,b \in \mathbb{Z},\ 1 \leq a \leq 155,\ 1 \leq b \leq 600,\ t = 14a + 10b,\ 24 \leq t \leq 8170 \}\right|$ and $B = \left|\{ t_1 : \exists\, a,b \in \mathbb{Z},\ 1 \leq a \leq 1950,\ 1 \leq b \leq 32,\ t_1 = 2a + 5b + 13,\ 20 \leq t_1 \leq 4073 \}\right|$. Find the minimum value of $A a...
15,552
graphs = [ Graph( let={ "_m": Const(6750), "_n": Const(2), "result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(346)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(346))))...
ALG
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
alg_poly3_min_v1
null
6
0
[ "LIN_FORM" ]
1
0.225
2026-02-25T05:28:30.956945Z
{ "verified": true, "answer": 15552, "timestamp": "2026-02-25T05:28:31.182353Z" }
c30b82
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 325, "completion_tokens": 32768 }, "timestamp": "2026-03-29T12:31:57.114Z", "answer": null }, { ...
1
[ { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": 3.81, "mid": 6.33, "hi": 9.49 }
5aae0c
nt_sum_gcd_range_mod_v1_655260480_740
Let $\mathcal{R}$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 166$. Let $N$ be the maximum value of $xy$ as $(x, y)$ ranges over $\mathcal{R}$. Define $k = 84$. Let $s = \sum_{n=1}^{N} \gcd(n, k)$. Let $r$ be the remainder when $s$ is divided by 10853. Find the remainder when $44121...
29,008
graphs = [ Graph( let={ "_n": Const(166), "N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))), ...
NT
null
COMPUTE
sympy
B1
[ "B1" ]
5b950e
nt_sum_gcd_range_mod_v1
null
5
0
[ "B1" ]
1
0.326
2026-02-08T15:33:12.144514Z
{ "verified": true, "answer": 29008, "timestamp": "2026-02-08T15:33:12.470850Z" }
f8e335
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 163, "completion_tokens": 2389 }, "timestamp": "2026-02-16T08:38:07.207Z", "answer": 29008 }, ...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V5", "status": "no" } ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
966cc3
comb_sum_binomial_row_v1_601307018_9483
Let $M$ be the minimum value of $-28ab + 41a^2 + 5b^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 11$. Let $n$ be the number of integers $t$ in the range $19 \leq t \leq 36$ that can be expressed as $t = 3a + 2b + 14$ for some positive integers $a, b$ with $1 \leq a \leq 4$, $1 \leq b \...
65,536
graphs = [ Graph( let={ "_m": Const(2), "_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(11)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(11)))), expr=Sum(Mul(Const(-28), Var("a"), ...
COMB
null
SUM
sympy
QF_PSD_MIN
[ "QF_PSD_MIN/LIN_FORM" ]
8ce6bc
comb_sum_binomial_row_v1
null
5
0
[ "LIN_FORM", "QF_PSD_MIN" ]
2
0.005
2026-03-10T09:54:31.579229Z
{ "verified": true, "answer": 65536, "timestamp": "2026-03-10T09:54:31.584307Z" }
9bc7b5
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 249, "completion_tokens": 3175 }, "timestamp": "2026-04-19T11:25:55.499Z", "answer": 65536 }, { ...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok_later" }, { "lemma": "QF_PSD_MIN", "status": "ok" }, { "lemma": "V...
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
f6633c
comb_binomial_compute_v1_601307018_9264
Let $n = \sum_{k=1}^{5} \varphi(k) \cdot \left\lfloor \frac{5}{k} \right\rfloor$, and let $M = \binom{n}{7}$. Find the remainder when $40574M$ is divided by $52359$.
31,716
graphs = [ Graph( let={ "_n": Const(5), "n": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(5), Var("k1"))))), "k": Const(7), "result": Binom(n=Ref("n"), k=Ref("k")), "Q": Mod(value=Mul(Const(4057...
COMB
NT
COMPUTE
sympy
K2
[ "K2" ]
6897ab
comb_binomial_compute_v1
null
4
0
[ "K2" ]
1
0.003
2026-03-10T09:39:27.521014Z
{ "verified": true, "answer": 31716, "timestamp": "2026-03-10T09:39:27.523772Z" }
6ba27d
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 179, "completion_tokens": 1584 }, "timestamp": "2026-04-19T11:01:12.000Z", "answer": 31716 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
234740
nt_num_divisors_compute_v1_458359167_20
Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 97558461000$, $\gcd(p, q) = 1$, and $p < q$. Let $n = |S|$. Determine the value of $\tau(n)$, the number of positive divisors of $n$.
7
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=97558461000)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(val...
NT
null
COMPUTE
sympy
L3C
[ "COPRIME_PAIRS" ]
2bb3aa
nt_num_divisors_compute_v1
null
5
0
[ "COPRIME_PAIRS", "L3C" ]
2
0.012
2026-02-08T02:57:08.095257Z
{ "verified": true, "answer": 7, "timestamp": "2026-02-08T02:57:08.107593Z" }
a04951
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 194, "completion_tokens": 2832 }, "timestamp": "2026-02-23T20:27:42.426Z", "answer": 6 }, { "id...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ...
{ "lo": 1.1, "mid": 4.17, "hi": 6.61 }
495238
lin_form_endings_v1_458359167_3630
Let $a = 48$, $b = 36$, $A = 42$, and $B = 52$. Let $g = \gcd(a, b)$, and define $$ a' = \left\lfloor \frac{a}{g} \right\rfloor, \quad b' = \left\lfloor \frac{b}{g} \right\rfloor. $$ Compute the value of $$ (7407 \cdot (a' \cdot A + b' \cdot B - a' \cdot b')) \bmod 85019. $$
15,471
graphs = [ Graph( let={ "a_coeff": Const(48), "b_coeff": Const(36), "A_val": Const(42), "B_val": Const(52), "g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")), "ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))), "bp_node": ...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
3
null
[ "LIN_FORM" ]
1
0.002
2026-02-08T11:12:26.028195Z
{ "verified": true, "answer": 15471, "timestamp": "2026-02-08T11:12:26.029726Z" }
bad609
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 164, "completion_tokens": 650 }, "timestamp": "2026-02-14T11:12:39.401Z", "answer": 15471 }, {...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "status": "no...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
cd3ff4
antilemma_k3_v1_124444284_6
Let $n = 39840$. Define $$ x = \sum_{d \mid n} \phi(d), $$ where $\phi$ denotes Euler's totient function. Compute the value of $$ \left( x \bmod 199 \right) + 2003 \cdot \left( x \bmod 499 \right), $$ and then take the result modulo $59700$. Find the value of this final quantity.
3,497
graphs = [ Graph( let={ "_n": Const(39840), "x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), "_c": Const(2003), "Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(199)), Mul(Ref("_c"), Mod(value=Ref("x"), modulus=Const(499))))...
NT
COMB
COMPUTE
sympy
K13
[ "K3" ]
54c41e
antilemma_k3_v1
null
4
0
[ "K13", "K3" ]
2
0.002
2026-02-08T02:52:53.825958Z
{ "verified": true, "answer": 3497, "timestamp": "2026-02-08T02:52:53.827613Z" }
14d217
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 211, "completion_tokens": 561 }, "timestamp": "2026-02-08T19:57:37.569Z", "answer": 4497 }, { ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "V3", "status": "no" } ]
{ "lo": 1.96, "mid": 3.41, "hi": 4.8 }
563517
nt_count_divisible_v1_458359167_2147
Let $A$ be the set of positive integers $n$ such that $n \leq 44850$ and $n$ is divisible by $8$. Let $r$ be the number of elements in $A$. Let $S$ be the Cartesian product of the sets $\{1, 2, 3, 4\}$ and $\{1, 2, \dots, 827\}$. Compute the remainder when the product of the number of elements in $S$ and $r$ is divided...
46,093
graphs = [ Graph( let={ "upper": Const(44850), "divisor": Const(8), "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": Mod...
NT
null
COUNT
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
27a9f8
nt_count_divisible_v1
affine_mod
2
0
[ "COUNT_CARTESIAN" ]
1
3.399
2026-02-08T05:09:25.483501Z
{ "verified": true, "answer": 46093, "timestamp": "2026-02-08T05:09:28.882619Z" }
3dd732
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 224, "completion_tokens": 1180 }, "timestamp": "2026-02-11T23:00:07.858Z", "answer": 46093 }, { "...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V8", "status": "no" } ...
{ "lo": -3.45, "mid": 1.15, "hi": 6.18 }
98155f
algebra_vieta_sum_v1_2051736721_5395
Let $P(x) = x^4 - 5x^3 - 23x^2 + 45x + m$, where $m$ is the largest positive divisor of $16002$ that is at most $126$. Find the sum of all real roots of the equation $P(x) = 0$.
5
graphs = [ Graph( let={ "_n": Const(16002), "result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(4)), Mul(Const(-5), Pow(Var("x"), Const(3))), Mul(Const(-23), Pow(Var("x"), Const(2))), Mul(Const(45), Var("x")), MaxOverSet(set=SolutionsSet(var=Var("...
NT
null
COMPUTE
sympy
B1
[ "MAX_DIVISOR" ]
51757e
algebra_vieta_sum_v1
null
4
0
[ "B1", "MAX_DIVISOR" ]
2
0.085
2026-02-08T18:31:45.046466Z
{ "verified": true, "answer": 5, "timestamp": "2026-02-08T18:31:45.131439Z" }
9d0803
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 131, "completion_tokens": 285 }, "timestamp": "2026-02-16T12:24:31.703Z", "answer": 5 }, { "id": 11, "...
2
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -10, "mid": -7.27, "hi": -4.54 }
5e51bb
comb_count_derangements_v1_124444284_2711
Let $m = 4$ and $n_0 = 2$. Define $N$ to be the largest prime number $n$ such that $$ n \le \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor. $$ Compute the subfactorial of $N$, denoted $!N$.
1,854
graphs = [ Graph( let={ "_m": Const(4), "_n": Const(2), "n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k")))))),...
NT
COMB
COUNT
sympy
SUM_ARITHMETIC
[ "K2/MAX_PRIME_BELOW" ]
f058da
comb_count_derangements_v1
null
5
0
[ "K2", "MAX_PRIME_BELOW", "SUM_ARITHMETIC" ]
3
0.011
2026-02-08T04:53:57.640076Z
{ "verified": true, "answer": 1854, "timestamp": "2026-02-08T04:53:57.651225Z" }
20c897
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 192, "completion_tokens": 1471 }, "timestamp": "2026-02-11T22:42:06.454Z", "answer": 1854 }, { "...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "V8", "status": "no" ...
{ "lo": -5.55, "mid": -3.01, "hi": 0.33 }
e82c4f
modular_sum_quadratic_residues_v1_397696148_1556
Let $p$ be the largest prime number at most $433$. Let $r = \frac{p(p-1)}{4}$. Compute the remainder when $14147r$ is divided by $63349$.
16,701
graphs = [ Graph( let={ "_n": Const(433), "p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)), "_c": Const(14147),...
NT
null
SUM
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
modular_sum_quadratic_residues_v1
null
4
0
[ "MAX_PRIME_BELOW" ]
1
0.001
2026-02-08T12:38:50.671063Z
{ "verified": true, "answer": 16701, "timestamp": "2026-02-08T12:38:50.672189Z" }
c23929
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 90, "completion_tokens": 1336 }, "timestamp": "2026-02-15T03:05:31.996Z", "answer": 16701 }, {...
1
[ { "lemma": "K16", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
c80d25
modular_mod_compute_v1_1742523217_5018
Let $a = 180$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1234321$. Define $m$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Compute the remainder when $a$ is divided by $m$.
180
graphs = [ Graph( let={ "a": Const(180), "m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1234321)))), expr=Sum(Var("x"), Var("y"))))...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
modular_mod_compute_v1
null
5
0
[ "B3" ]
1
0.001
2026-02-08T10:45:29.671981Z
{ "verified": true, "answer": 180, "timestamp": "2026-02-08T10:45:29.672891Z" }
271b52
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 137, "completion_tokens": 723 }, "timestamp": "2026-02-15T21:02:56.012Z", "answer": 180 }, { "id": 11, ...
2
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -10, "mid": -7.27, "hi": -4.54 }
3f86a2
algebra_quadratic_discriminant_v1_168721529_73
Let $a = -2$, $b = -10$, and $n = 2$. Let $c$ be the sum of all real solutions $x$ to the equation $x^n - 72x - 3193 = 0$. Compute $b^2 - 4ac$.
676
graphs = [ Graph( let={ "_n": Const(2), "a": Const(-2), "b": Const(-10), "c": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-72), Var("x")), Const(-3193)), Const(0)))), "result": Sub(Pow(Ref("b"), Co...
NT
null
COMPUTE
sympy
VIETA_SUM
[ "VIETA_SUM" ]
b33a7a
algebra_quadratic_discriminant_v1
null
6
0
[ "VIETA_SUM" ]
1
0.002
2026-02-08T12:48:00.100682Z
{ "verified": true, "answer": 676, "timestamp": "2026-02-08T12:48:00.102479Z" }
eb0536
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 177, "completion_tokens": 532 }, "timestamp": "2026-02-08T20:59:38.982Z", "answer": 676 }, { "id"...
1
[ { "lemma": "K14", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "VIETA_SUM", "status": "ok" } ]
{ "lo": -5.3, "mid": -2.05, "hi": 1.82 }
7c98e8
nt_lcm_compute_v1_971394319_1517
Let $a = 1579$ and $b = 1533$. Define $L = \mathrm{lcm}(a, b)$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1028196$. Compute the remainder when $s - L$ is divided by $92658$.
83,187
graphs = [ Graph( let={ "a": Const(1579), "b": Const(1533), "result": LCM(a=Ref("a"), b=Ref("b")), "Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(a...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
fc629c
nt_lcm_compute_v1
negation_mod
4
0
[ "B3" ]
1
0.002
2026-02-08T13:43:11.150859Z
{ "verified": true, "answer": 83187, "timestamp": "2026-02-08T13:43:11.153205Z" }
7f6c9f
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": 1488 }, "timestamp": "2026-02-15T20:17:19.371Z", "answer": 83187 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }...
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
dddec4
comb_bell_compute_v1_1125832087_587
Let $S$ be the set of all positive integers $d$ such that $d \leq 8$ and $d$ divides $\sum_{d' \mid 88} \phi(d')$, where $\phi$ denotes Euler's totient function. Let $n$ be the maximum element of $S$. Define $B_n$ to be the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Let $Q = 4536...
41,220
graphs = [ Graph( let={ "_n": Const(8), "n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=SumOverDivisors(n=Const(value=88), var='d', expr=EulerPhi(n=Var(name='d'))))))), "res...
NT
COMB
COMPUTE
sympy
K3
[ "K3/MAX_DIVISOR" ]
43ff77
comb_bell_compute_v1
null
5
0
[ "K3", "MAX_DIVISOR" ]
2
0.002
2026-02-08T03:09:36.695008Z
{ "verified": true, "answer": 41220, "timestamp": "2026-02-08T03:09:36.696953Z" }
39800a
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 225, "completion_tokens": 1538 }, "timestamp": "2026-02-10T13:14:54.883Z", "answer": 41220 }, { "...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": ...
{ "lo": -5.55, "mid": -3.02, "hi": 0.31 }
5c514a
nt_min_phi_inverse_v1_809748730_468
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 59$ and the sum of the decimal digits of $n$ leaves a remainder of 1 when divided by 2. Let $u = |S|$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = 10$. Compute the minimum value of $T$.
11
graphs = [ Graph( let={ "_n": Const(2), "upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(59)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))), "k": Const(10), "result": MinOverSe...
NT
null
EXTREMUM
sympy
LIN_FORM
[ "L3B" ]
cc148f
nt_min_phi_inverse_v1
null
7
0
[ "L3B", "LIN_FORM" ]
2
0.149
2026-02-08T11:32:25.024334Z
{ "verified": true, "answer": 11, "timestamp": "2026-02-08T11:32:25.173554Z" }
5261f9
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": 2167 }, "timestamp": "2026-02-14T15:33:52.219Z", "answer": 11 }, { ...
1
[ { "lemma": "K17", "status": "no" }, { "lemma": "L3B", "status": "ok" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
f9f2eb
nt_min_coprime_above_v1_2051736721_5599
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 72$. Let $P$ be the maximum value of $xy$ over all such pairs. Let $n$ be the smallest integer greater than $P$ and at most $1328$ such that $\gcd(n, 22) = 1$. Compute $n$.
1,297
graphs = [ Graph( let={ "start": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(72)))), expr=Mul(Var("x"), Var("y")))), "upper": Const(1...
NT
null
EXTREMUM
sympy
B1
[ "B1" ]
5b950e
nt_min_coprime_above_v1
null
4
0
[ "B1" ]
1
0.01
2026-02-08T18:40:59.921417Z
{ "verified": true, "answer": 1297, "timestamp": "2026-02-08T18:40:59.931620Z" }
a525df
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 130, "completion_tokens": 814 }, "timestamp": "2026-02-18T18:36:39.676Z", "answer": 1297 }, { ...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
6d5e03
comb_catalan_compute_v1_458359167_606
Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 20$. Determine the value of the $n$-th Catalan number.
16,796
graphs = [ Graph( let={ "_n": Const(20), "n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re...
COMB
null
COMPUTE
sympy
COMB1
[ "COMB1" ]
567f58
comb_catalan_compute_v1
null
4
0
[ "COMB1" ]
1
0.002
2026-02-08T03:26:18.534872Z
{ "verified": true, "answer": 16796, "timestamp": "2026-02-08T03:26:18.537269Z" }
2b19d8
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": 606 }, "timestamp": "2026-02-10T14:22:07.020Z", "answer": 16796 }, { "i...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -9.23, "mid": -6.18, "hi": -4.06 }
b1fe68
geo_count_lattice_rect_v1_865884756_6341
Let $a = 64$ and $b = 101$. Define the set of lattice points in the rectangle $[0, a] \times [0, b]$ as the set of all ordered pairs $(x, y)$ of nonnegative integers such that $0 \le x \le a$ and $0 \le y \le b$. Compute the number of such lattice points.
6,630
graphs = [ Graph( let={ "a": Const(64), "b": Const(101), "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
2026-02-08T19:09:49.657018Z
{ "verified": true, "answer": 6630, "timestamp": "2026-02-08T19:09:49.657509Z" }
439b62
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": 383 }, "timestamp": "2026-02-25T01:00:23.658Z", "answer": 6630 }, { ...
1
[]
{ "lo": -8.48, "mid": -5.37, "hi": -3.03 }
80885b
modular_min_modexp_v1_1918700295_1833
Let $a = 3$, $b = 3$, and let $m$ be the smallest divisor of $467821919$ that is at least $2$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 48$ and $a^x \equiv b \pmod{m}$. Compute this value of $x$.
1
graphs = [ Graph( let={ "a": Const(3), "b": Const(3), "m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(467821919))))), "upper": Const(48), "result": MinOverSet(set=Soluti...
NT
null
EXTREMUM
sympy
C4
[ "MIN_PRIME_FACTOR" ]
bc3776
modular_min_modexp_v1
null
5
0
[ "C4", "MIN_PRIME_FACTOR" ]
2
0.141
2026-02-08T06:04:32.072015Z
{ "verified": true, "answer": 1, "timestamp": "2026-02-08T06:04:32.212664Z" }
5aea88
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 140, "completion_tokens": 505 }, "timestamp": "2026-02-15T17:06:46.990Z", "answer": null }, { "id": 11, ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V8", "status": "no...
{ "lo": -9.14, "mid": -6.05, "hi": -3.73 }
e1544f
modular_sum_quadratic_residues_v1_601307018_645
Let $p$ be the smallest positive divisor of $70325205721$ greater than $1$. Let $M = \frac{p(p - 1)}{4}$. Find the remainder when $44121M$ is divided by $83374$.
56,011
graphs = [ Graph( let={ "_n": Const(2), "p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(70325205721))))), "result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)), "Q": Mod(...
NT
null
SUM
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
modular_sum_quadratic_residues_v1
null
3
0
[ "MIN_PRIME_FACTOR" ]
1
0.004
2026-03-10T01:11:27.961078Z
{ "verified": true, "answer": 56011, "timestamp": "2026-03-10T01:11:27.965412Z" }
198dc3
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 164, "completion_tokens": 32768 }, "timestamp": "2026-03-28T23:43:57.137Z", "answer": null }, { ...
1
[ { "lemma": "K17", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V1", "status": "no" } ]
{ "lo": 4.01, "mid": 6.11, "hi": 9.15 }
b50d2e
sequence_fibonacci_compute_v1_784195855_561
Let $n$ be the number of integers $t$ such that $18 \leq t \leq 78$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 9$, and $t = 14a + 4b$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq...
75,025
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
sequence_fibonacci_compute_v1
null
4
0
[ "LIN_FORM" ]
1
0.002
2026-02-08T04:27:30.226270Z
{ "verified": true, "answer": 75025, "timestamp": "2026-02-08T04:27:30.228420Z" }
e66ec2
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 252, "completion_tokens": 1199 }, "timestamp": "2026-02-10T16:50:45.869Z", "answer": 75025 }, { ...
1
[ { "lemma": "K15", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V1", "status": "no" } ]
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
7f2ff0
sequence_fibonacci_compute_v1_1520064083_1427
Let $n$ be the largest integer such that $2^n \leq 26863683$. Let $F_n$ denote the $n$th Fibonacci number, where $F_0 = 0$, $F_1 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 2$. Compute the remainder when $65938 \cdot F_n$ is divided by 87669.
44,478
graphs = [ Graph( let={ "_n": Const(2), "n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(26863683)))), "result": Fibonacci(arg=Ref(name='n')), "Q": Mod(value=Mul(Const(65938), Ref("result")), modulus=Const(87669)), ...
NT
null
COMPUTE
sympy
MAX_VAL
[ "MAX_VAL" ]
1da621
sequence_fibonacci_compute_v1
null
4
0
[ "MAX_VAL" ]
1
0.002
2026-02-08T03:59:34.282037Z
{ "verified": true, "answer": 44478, "timestamp": "2026-02-08T03:59:34.284343Z" }
e256ae
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 210, "completion_tokens": 3339 }, "timestamp": "2026-02-10T16:31:40.334Z", "answer": 44478 }, { "...
1
[ { "lemma": "K14", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K16", "status": "same_pattern_wrong" }, { "lemma": "MAX_VAL", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V1", "status": "no" }, ...
{ "lo": -3.46, "mid": 1.03, "hi": 5.49 }
0eee10
nt_count_intersection_v1_1125832087_1066
Let $a$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 10$. Let $N$ be the number of positive integers $n \leq 100000$ such that $a$ divides $n$ and $\gcd(n, 12) = 1$. Compute $N$.
6,667
graphs = [ Graph( let={ "N": Const(100000), "a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),...
NT
null
COUNT
sympy
COMB1
[ "COMB1" ]
567f58
nt_count_intersection_v1
null
4
0
[ "COMB1" ]
1
9.469
2026-02-08T03:29:46.379745Z
{ "verified": true, "answer": 6667, "timestamp": "2026-02-08T03:29:55.848655Z" }
ea2d5a
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 193, "completion_tokens": 1859 }, "timestamp": "2026-02-10T14:50:36.670Z", "answer": 6667 }, { "i...
1
[ { "lemma": "COMB1", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -3.46, "mid": 1.03, "hi": 5.49 }
9c9a19
geo_count_lattice_rect_v1_865884756_2703
Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 233$ and $0 \leq y \leq 257$.
60,372
graphs = [ Graph( let={ "a": Const(233), "b": Const(257), "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
0.002
2026-02-08T16:53:37.427036Z
{ "verified": true, "answer": 60372, "timestamp": "2026-02-08T16:53:37.429012Z" }
3f09d9
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 81, "completion_tokens": 460 }, "timestamp": "2026-02-17T14:40:00.735Z", "answer": 60372 }, { ...
1
[]
{ "lo": -5.64, "mid": -3.17, "hi": -0.81 }
07ed35
antilemma_sum_equals_v1_971394319_631
Let $m$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying \begin{itemize} \item $1\le a\le 21$, \item $1\le b\le 30$, \item $7\le t\le 174$, and \item $t=4a+3b$. \end{itemize} Let $n=43$. Let $x$ be the number of ordered pairs $(i,j)$ of integers such that $1\le i\le 41$, $1\le j\le 4...
41
graphs = [ Graph( let={ "_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=21)), Geq(left=Var(name='b'), right=Const(value...
COMB
GEOM
COMPUTE
sympy
COMB1
[ "LIN_FORM/COMB1", "COUNT_SUM_EQUALS" ]
b9178b
antilemma_sum_equals_v1
negation_mod
5
0
[ "COMB1", "COUNT_SUM_EQUALS", "LIN_FORM" ]
3
0.025
2026-02-08T13:13:46.355097Z
{ "verified": true, "answer": 41, "timestamp": "2026-02-08T13:13:46.379697Z" }
c7f54c
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 302, "completion_tokens": 14485 }, "timestamp": "2026-02-24T17:29:22.769Z", "answer": 41 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no"...
{ "lo": 1.15, "mid": 4.18, "hi": 6.61 }
2078fb
algebra_poly_eval_v1_1125832087_1170
Let $x = 27$. Define $y$ to be the smallest integer $d \geq 2$ such that $d$ divides the number of integers $t$ in the interval $[20, 1736]$ that can be expressed as $6a + 14b$ for some positive integers $a \leq 7$ and $b \leq 121$. Let $z = x^3 + y \cdot x^2 - 2x - 7$. Determine the value of the smallest positive inte...
12,246
graphs = [ Graph( let={ "_m": Const(2), "_n": Const(3), "x": Const(27), "result": Sum(Pow(Ref("x"), Ref("_n")), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSe...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/MIN_PRIME_FACTOR" ]
bb1a13
algebra_poly_eval_v1
null
6
0
[ "LIN_FORM", "MIN_PRIME_FACTOR" ]
2
0.008
2026-02-08T03:34:18.421389Z
{ "verified": true, "answer": 12246, "timestamp": "2026-02-08T03:34:18.429239Z" }
deb4c8
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 248, "completion_tokens": 9594 }, "timestamp": "2026-02-23T20:57:29.452Z", "answer": 12246 }, { ...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma":...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
86baff
diophantine_product_count_v1_1125832087_542
Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 176400$. Let $u$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14884$. Determine the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\fra...
69,284
graphs = [ Graph( let={ "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(176400)))), expr=Sum(Var("x"), Var("y")))), "upper": MinOver...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
diophantine_product_count_v1
null
6
0
[ "B3" ]
1
0.015
2026-02-08T03:09:01.507114Z
{ "verified": true, "answer": 69284, "timestamp": "2026-02-08T03:09:01.522266Z" }
5ecc49
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 246, "completion_tokens": 4637 }, "timestamp": "2026-02-10T12:54:39.582Z", "answer": 69284 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
44b050
sequence_lucas_compute_v1_898971024_1203
Let $n$ be the number of positive integers $k$ such that $1 \le k \le 296$, $8$ divides $k$, and $\gcd(k, 15) = 1$. Compute the $n$th Lucas number. Determine the value of this Lucas number.
15,127
graphs = [ Graph( let={ "_n": Const(15), "n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(296)), Divides(divisor=Const(8), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Ref("_n")), Const(1))))), "result": Lucas(ar...
NT
null
COMPUTE
sympy
C5
[ "C5" ]
1d9668
sequence_lucas_compute_v1
null
4
0
[ "C5" ]
1
0.002
2026-02-08T15:59:48.727706Z
{ "verified": true, "answer": 15127, "timestamp": "2026-02-08T15:59:48.729739Z" }
7eacd9
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": 1018 }, "timestamp": "2026-02-16T18:44:13.998Z", "answer": 15127 }, ...
1
[ { "lemma": "C5", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
c68e12
algebra_poly_eval_v1_1742523217_4972
Let $z = 6$. Compute the value of $5z^4 - 10z^3 + z^2 + dz - 1$, where $d$ is the smallest divisor of 1225 that is at least 2.
4,385
graphs = [ Graph( let={ "z": Const(6), "result": Sum(Mul(Const(5), Pow(Ref("z"), Const(4))), Mul(Const(-10), Pow(Ref("z"), Const(3))), Pow(Ref("z"), Const(2)), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Cons...
NT
null
COMPUTE
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
algebra_poly_eval_v1
null
3
0
[ "MIN_PRIME_FACTOR" ]
1
0.003
2026-02-08T10:41:39.010223Z
{ "verified": true, "answer": 4385, "timestamp": "2026-02-08T10:41:39.012815Z" }
7121ac
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 110, "completion_tokens": 433 }, "timestamp": "2026-02-15T21:02:01.416Z", "answer": 4355 }, { "id": 11,...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY_PADIC_...
{ "lo": -6.96, "mid": -4.56, "hi": -1.46 }
aee871
antilemma_cartesian_v1_168721529_2086
Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 27, inclusive, and $b$ is an integer from 1 to 29, inclusive. Define $S = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$. Compute the sum of the number of positive divisors of $n$, as $n$ ranges from $|S|$ to $x$, inclusive. Find the value of this ...
5,345
graphs = [ Graph( let={ "x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(27)), right=IntegerRange(start=Const(1), end=Const(29)))), "Q": Summation(var="n", start=Factorial(Summation(var="k", start=Const(0), end=Const(10), expr=Mul(Pow(Const(-1), Var(...
COMB
GEOM
COMPUTE
sympy
BINOMIAL_ALTERNATING
[ "BINOMIAL_ALTERNATING", "COUNT_CARTESIAN", "ONE_FACTORIAL_0" ]
12185f
antilemma_cartesian_v1
null
5
0
[ "BINOMIAL_ALTERNATING", "COUNT_CARTESIAN", "ONE_FACTORIAL_0" ]
3
0.001
2026-02-08T14:07:00.584568Z
{ "verified": true, "answer": 5345, "timestamp": "2026-02-08T14:07:00.585989Z" }
c94fa6
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 220, "completion_tokens": 3716 }, "timestamp": "2026-02-10T01:52:43.115Z", "answer": 5345 }, { "i...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { ...
{ "lo": -2.43, "mid": 1.2, "hi": 4.84 }
e8238b
nt_sum_totient_over_divisors_v1_655260480_1140
Let $n$ be the number of positive integers $n_1$ with $1 \le n_1 \le 59256$ such that $7$ divides the $n_1$-th Fibonacci number. Compute the remainder when $89363$ times the sum of $\phi(d)$ over all positive divisors $d$ of $n$ is divided by 58899.
4,779
graphs = [ Graph( let={ "_n": Const(7), "n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(59256)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n1')))))), "result": SumOverDivisors(n=Ref(name='n')...
NT
null
COMPUTE
sympy
COUNT_FIB_DIVISIBLE
[ "COUNT_FIB_DIVISIBLE" ]
66de3c
nt_sum_totient_over_divisors_v1
null
5
0
[ "COUNT_FIB_DIVISIBLE" ]
1
0.008
2026-02-08T15:55:40.621555Z
{ "verified": true, "answer": 4779, "timestamp": "2026-02-08T15:55:40.629560Z" }
b737b1
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 126, "completion_tokens": 2680 }, "timestamp": "2026-02-16T17:08:35.892Z", "answer": 4779 }, {...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "VAL_SUM_EQ", ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
12e7aa
comb_count_partitions_v1_151522320_567
Let $m = 42$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $P$ be the set of all values of $xy$ over these pairs. Define $n$ to be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy$ equals the maximum element of $P$. Let $r$ b...
1,224
graphs = [ Graph( let={ "_m": Const(42), "_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))), ...
NT
COMB
COUNT
sympy
B1
[ "B1/B3" ]
80b49d
comb_count_partitions_v1
null
7
0
[ "B1", "B3" ]
2
0.002
2026-02-08T03:22:41.870415Z
{ "verified": true, "answer": 1224, "timestamp": "2026-02-08T03:22:41.872397Z" }
1ec7e0
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 238, "completion_tokens": 4695 }, "timestamp": "2026-02-10T14:16:35.638Z", "answer": 1224 }, { "i...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "B3", "status": "ok_later" }, { "lemma": "K13", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "...
{ "lo": -3.46, "mid": 1.03, "hi": 5.49 }
ec1470
nt_sum_totient_over_divisors_v1_458359167_1940
Let $n = 62059$. Define $R$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Define $T$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $R^2 +...
1,775
graphs = [ Graph( let={ "n": Const(62059), "result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))), "Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(5), Ref("result")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Va...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
d720b5
nt_sum_totient_over_divisors_v1
quadratic_mod
4
0
[ "B3" ]
1
0.001
2026-02-08T04:56:20.231403Z
{ "verified": true, "answer": 1775, "timestamp": "2026-02-08T04:56:20.232814Z" }
03ff10
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 234, "completion_tokens": 1922 }, "timestamp": "2026-02-11T22:31:06.126Z", "answer": 1775 }, { "...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V1", "status": "no" } ]
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
17611f
nt_count_coprime_and_v1_168721529_1403
Let $n$ be a positive integer. Define $k_1 = 3$ and let $k_2$ be the largest prime number satisfying $2 \leq n \leq 12$. Determine the number of positive integers $n$ with $1 \leq n \leq 47904$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = \phi(2)$. Compute this number.
29,033
graphs = [ Graph( let={ "_n": Const(2), "upper": Const(47904), "k1": Const(3), "k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))), "result": CountOverSet(set=Soluti...
NT
null
COUNT
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW", "ONE_PHI_2" ]
256a94
nt_count_coprime_and_v1
null
4
0
[ "MAX_PRIME_BELOW", "ONE_PHI_2" ]
2
10.283
2026-02-08T13:40:54.573242Z
{ "verified": true, "answer": 29033, "timestamp": "2026-02-08T13:41:04.856570Z" }
fe9c35
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 212, "completion_tokens": 1127 }, "timestamp": "2026-02-09T16:32:47.862Z", "answer": 29033 }, { "...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" },...
{ "lo": -1.99, "mid": 2.14, "hi": 6.33 }
748a52
modular_sum_quadratic_residues_v1_784195855_8743
Let $p$ be the largest prime number $n$ such that $2 \leq n \leq 521$. Compute $\frac{p(p-1)}{4}$.
67,730
graphs = [ Graph( let={ "_n": Const(2), "p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(521)), IsPrime(Var("n"))))), "result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)), }, goal=Ref("re...
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
2026-02-08T16:17:58.738396Z
{ "verified": true, "answer": 67730, "timestamp": "2026-02-08T16:17:58.740046Z" }
8d187a
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 81, "completion_tokens": 787 }, "timestamp": "2026-02-17T01:07:24.089Z", "answer": 67730 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
104caa
geo_count_lattice_triangle_v1_717093673_525
Let $t$ be an integer. Determine the number of values of $t$ in the range $14 \le t \le 204$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 6$, $1 \le b \le 21$, such that $t = 6a + 8b$. Let this number be $n$. Define $A = |100 \cdot 128 - 121n|$. Let $B$ be the sum of the greatest common divisor...
954
graphs = [ Graph( let={ "_m": Const(121), "_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=6)), Geq(left=Var...
ALG
NT
COUNT
sympy
LIN_FORM
[ "LIN_FORM/COMB1" ]
268a62
geo_count_lattice_triangle_v1
null
7
0
[ "COMB1", "LIN_FORM" ]
2
0.018
2026-02-08T15:29:57.027246Z
{ "verified": true, "answer": 954, "timestamp": "2026-02-08T15:29:57.044991Z" }
fc4968
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": 5666 }, "timestamp": "2026-02-16T07:00:42.359Z", "answer": 954 }, { ...
1
[ { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
91a6de
comb_count_derangements_v1_1918700295_222
Let $n$ be the largest prime number satisfying $2 \leq n \leq \sum_{k=1}^4 k$. Compute the number of derangements of $n$ elements.
1,854
graphs = [ Graph( let={ "_n": Const(2), "n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(4), expr=Var("k"))), IsPrime(Var("n"))))), "result": Subfactorial(arg=Ref(name='n')), ...
NT
COMB
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC/MAX_PRIME_BELOW" ]
bde608
comb_count_derangements_v1
null
3
0
[ "MAX_PRIME_BELOW", "SUM_ARITHMETIC" ]
2
0.002
2026-02-08T03:06:18.990620Z
{ "verified": true, "answer": 1854, "timestamp": "2026-02-08T03:06:18.992665Z" }
131a51
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 152, "completion_tokens": 986 }, "timestamp": "2026-02-10T13:09:22.721Z", "answer": 1854 }, { "id...
1
[ { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status...
{ "lo": -5.55, "mid": -3.02, "hi": 0.31 }
606933
nt_count_divisors_in_range_v1_151522320_1870
Let $n = 840$, $a = 4$, and $b = 169$. Define $r$ to be the number of positive divisors of $n$ that are at least $a$ and at most $b$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 23059204$. Define $c$ to be the minimum value of $x + y$ over all such pairs in $S$. Compute ...
9,579
graphs = [ Graph( let={ "n": Const(840), "a": Const(4), "b": Const(169), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))), "_c": Mi...
NT
null
COUNT
sympy
B3
[ "B3" ]
fc629c
nt_count_divisors_in_range_v1
negation_mod
6
0
[ "B3" ]
1
0.012
2026-02-08T04:26:27.996289Z
{ "verified": true, "answer": 9579, "timestamp": "2026-02-08T04:26:28.007932Z" }
36bced
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": 1794 }, "timestamp": "2026-02-10T16:35:08.550Z", "answer": 9579 }, { "...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" } ]
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
cdeb78
alg_qf_psd_sum_v1_1218484723_3147
Find the remainder when $$ \sum_{\substack{a=1 \\ b=1}}^{p \leq 59} \left(2a^2 - 6ab + 9b^2\right) $$ is divided by $55644$, where $p$ is the largest prime less than or equal to $59$.
4,126
graphs = [ Graph( let={ "_n": Const(9), "result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(V...
NT
null
COMPUTE
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
alg_qf_psd_sum_v1
null
4
0
[ "MAX_PRIME_BELOW" ]
1
0.016
2026-02-25T04:51:22.109336Z
{ "verified": true, "answer": 4126, "timestamp": "2026-02-25T04:51:22.125482Z" }
2d834b
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": 2523 }, "timestamp": "2026-03-29T08:40:14.753Z", "answer": 4126 }, { "i...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" ...
{ "lo": -2.45, "mid": 1.37, "hi": 5.29 }
685442
alg_sum_powers_v1_1218484723_376
Find the remainder when $\sum_{k=1}^{1090} k^3$ is divided by $\left|\left\{ (a, b) : 1 \le a \le 40,\ 1 \le b \le \left|\left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 40,\ 16b_1^2 = 16 \right\}\right|,\ 2a^2 + 41b^2 - 2ab \le 31994 \right\}\right|.$
569
graphs = [ Graph( let={ "_m": Const(40), "_n": Const(2), "result": Mod(value=Summation(var="k", start=Const(1), end=Const(1090), expr=Pow(Var("k"), Const(3))), modulus=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Cons...
ALG
null
COMPUTE
sympy
QF_PSD_COUNT
[ "QF_PSD_COUNT/QF_PSD_COUNT_LEQ" ]
89ab91
alg_sum_powers_v1
null
5
0
[ "QF_PSD_COUNT", "QF_PSD_COUNT_LEQ" ]
2
0.135
2026-02-25T02:04:35.008227Z
{ "verified": true, "answer": 569, "timestamp": "2026-02-25T02:04:35.143334Z" }
d6450a
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 236, "completion_tokens": 6246 }, "timestamp": "2026-03-28T22:25:40.018Z", "answer": 569 }, { "id...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT", "status": "ok" }, { "lemma": "QF_PSD_COUNT_LEQ", "status": "ok_later" } ]
{ "lo": 1.22, "mid": 3.76, "hi": 5.73 }
1baa4c
comb_sum_binomial_row_v1_458359167_1064
Let $n = \sum_{k=1}^{5} k$. Define $\text{result} = 2^n$. Find the value of $\text{result}$.
32,768
graphs = [ Graph( let={ "_n": Const(5), "n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), "result": Pow(Const(2), Ref("n")), }, goal=Ref("result"), ) ]
NT
null
SUM
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
comb_sum_binomial_row_v1
null
2
0
[ "SUM_ARITHMETIC" ]
1
0.002
2026-02-08T04:15:41.039523Z
{ "verified": true, "answer": 32768, "timestamp": "2026-02-08T04:15:41.041185Z" }
160aaa
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 147, "completion_tokens": 130 }, "timestamp": "2026-02-10T16:26:22.673Z", "answer": 32768 }, { "...
2
[ { "lemma": "K13", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V3", "statu...
{ "lo": -10, "mid": -7.73, "hi": -5.46 }
75c5c8
diophantine_fbi2_min_v1_48377204_333
Let $T$ be the set of all integers $t$ such that $10 \le t \le 1070$ and $t = 4a + 6b$ for some integers $a, b$ with $1 \le a \le 197$ and $1 \le b \le 47$. Let $k = 36$. Define $u$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy$ equals the number of elements in $T...
11,054
graphs = [ Graph( let={ "_m": Const(2), "_n": Const(2), "k": Const(36), "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"), V...
NT
null
EXTREMUM
sympy
LIN_FORM
[ "LIN_FORM/B3" ]
05313e
diophantine_fbi2_min_v1
null
7
0
[ "B3", "LIN_FORM" ]
2
0.007
2026-02-08T15:20:41.351125Z
{ "verified": true, "answer": 11054, "timestamp": "2026-02-08T15:20:41.357855Z" }
d69e5b
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 232, "completion_tokens": 3785 }, "timestamp": "2026-02-16T05:46:42.031Z", "answer": 11054 }, ...
1
[ { "lemma": "B3", "status": "ok_later" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONS...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
5102d9
algebra_poly_eval_v1_601307018_2397
Let $a = 19$. Compute $$ \left|\left\{ (a_1, b) : 1 \le a_1, b \le 25,\ 64a_1^3 + 27b^3 + 144a_1^2b + 108a_1b^2 = 456533 \right\}\right| \cdot a^3 - 3a - 10. $$
41,087
graphs = [ Graph( let={ "a": Const(19), "result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(64), Pow(Var("a1")...
ALG
null
COMPUTE
sympy
POLY3_COUNT
[ "POLY3_COUNT" ]
355dbe
algebra_poly_eval_v1
null
3
0
[ "POLY3_COUNT" ]
1
0.003
2026-03-10T03:05:26.827641Z
{ "verified": true, "answer": 41087, "timestamp": "2026-03-10T03:05:26.830279Z" }
877bec
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 205, "completion_tokens": 1480 }, "timestamp": "2026-03-29T05:15:57.395Z", "answer": 41087 }, { "...
1
[ { "lemma": "POLY3_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -4.26, "mid": -1.81, "hi": 1.24 }
f6d928
modular_modexp_compute_v1_601307018_8573
Let $M$ be the number of positive integers $t$ with $14 \le t \le 242$ that can be expressed as $t = 4c + 10b$ for some integers $c, b$ satisfying $1 \le c \le 38$, $1 \le b \le 9$. Let $R$ be the largest prime number $n$ such that $2 \le n \le 41$. Let $e$ be the number of positive integers $k$ with $1 \le k \le 55944...
35,149
graphs = [ Graph( let={ "_m": Const(44121), "_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=38)), Geq(left=...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/C2", "MAX_PRIME_BELOW" ]
7c9620
modular_modexp_compute_v1
null
5
0
[ "C2", "LIN_FORM", "MAX_PRIME_BELOW" ]
3
0.007
2026-03-10T09:04:35.450955Z
{ "verified": true, "answer": 35149, "timestamp": "2026-03-10T09:04:35.458254Z" }
7e18f4
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 269, "completion_tokens": 7698 }, "timestamp": "2026-04-19T09:16:49.587Z", "answer": 35149 }, { ...
1
[ { "lemma": "C2", "status": "ok_later" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, ...
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
5c4f91
nt_sum_gcd_range_mod_v1_798873815_503
Let $ N $ be the smallest integer $ d \geq 2 $ that divides $ 8287306393 $. Compute the sum $ \sum_{n=1}^{N} \gcd(n, 252) $, and let $ M = 11689 $. Find the remainder when this sum is divided by $ M $.
5,784
graphs = [ Graph( let={ "_n": Const(2), "N": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(8287306393))))), "k": Const(252), "M": Const(11689), "sum": Summation(var="n", s...
NT
null
COMPUTE
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
nt_sum_gcd_range_mod_v1
null
5
0
[ "MIN_PRIME_FACTOR" ]
1
0.472
2026-02-08T02:40:21.813813Z
{ "verified": true, "answer": 5784, "timestamp": "2026-02-08T02:40:22.285933Z" }
15ebe1
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 178, "completion_tokens": 32768 }, "timestamp": "2026-02-23T15:42:12.191Z", "answer": null }, { ...
0
[ { "lemma": "C2", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": 4.67, "mid": 6.56, "hi": 9.55 }
254dc9
lte_diff_endings_v1_601307018_45
Let $R = 31 - 3$, $T = 190187$, $K = T!$, and $L = 2$. Let $P$ be the largest integer $k$ such that $2^k$ divides $R$. Let $Q = T \cdot P$. Let $W$ be the largest integer $k$ such that $2^k$ divides $K$. Let $U = Q + W$. Find the remainder when $U$ is divided by $100000$.
70,549
graphs = [ Graph( let={ "a_val": Const(31), "b_val": Const(3), "p_val": Const(2), "n_val": Const(190187), "ab_diff": Sub(Ref("a_val"), Ref("b_val")), "vp_ab": MaxKDivides(target=Ref("ab_diff"), base=Ref("p_val")), "n_times_C...
NT
null
COMPUTE
sympy
LTE_DIFF
[ "LTE_DIFF" ]
cf8260
lte_diff_endings_v1
null
4
null
[ "LTE_DIFF" ]
1
0.001
2026-03-10T00:43:16.108402Z
{ "verified": true, "answer": 70549, "timestamp": "2026-03-10T00:43:16.109725Z" }
e9627f
CC BY 4.0
null
null
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_DIFF", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "V8", "status": "no"...
{ "lo": -10, "mid": 0, "hi": 10 }
e6e7f6
geo_count_lattice_rect_v1_655260480_2467
Let $a = 484$ and $b = 143$. Define a lattice point as a point in the plane with integer coordinates. Consider the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$, including the boundary. Compute the number of lattice points contained in this rectangle.
69,840
graphs = [ Graph( let={ "a": Const(484), "b": Const(143), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), }, goal=Ref("result"), ) ]
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
3
0
null
null
0.001
2026-02-08T16:45:14.094891Z
{ "verified": true, "answer": 69840, "timestamp": "2026-02-08T16:45:14.095999Z" }
82977a
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 115, "completion_tokens": 556 }, "timestamp": "2026-02-17T11:23:04.865Z", "answer": 69840 }, {...
1
[]
{ "lo": -5.64, "mid": -3.17, "hi": -0.81 }
718b2b
lin_form_endings_v1_784195855_1135
Let $a = 21$ and $b = 14$. Define $d = \gcd(a, b)$. Let $r = \left\lfloor \frac{21}{d} \right\rfloor$. Multiply $r$ by $6182$, and let the result be $s$. Compute the remainder when $s$ is divided by $72978$.
18,546
graphs = [ Graph( let={ "a_coeff": Const(21), "b_coeff": Const(14), "_inner_result": Floor(Div(Const(21), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))), "_scale_k": Const(6182), "_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")), "_mod_M...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
2
null
[ "LIN_FORM" ]
1
0
2026-02-08T04:52:29.955000Z
{ "verified": true, "answer": 18546, "timestamp": "2026-02-08T04:52:29.955452Z" }
8da0d0
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 144, "completion_tokens": 265 }, "timestamp": "2026-02-11T21:59:11.739Z", "answer": 18546 }, { "id": 11, ...
2
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" ...
{ "lo": -9.14, "mid": -6.05, "hi": -3.73 }
342ece
comb_count_derangements_v1_1431428450_1349
Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 5880$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be the number of derangements of $n$ elements. Compute the remainder when $30223r$ is divided by $73243$.
50,599
graphs = [ Graph( let={ "_n": Const(73243), "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=5880)), Eq(left=GCD(a=Var(name='p'), b=Var(na...
NT
COMB
COUNT
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
comb_count_derangements_v1
null
4
0
[ "COPRIME_PAIRS" ]
1
0.002
2026-02-08T14:02:53.455091Z
{ "verified": true, "answer": 50599, "timestamp": "2026-02-08T14:02:53.457476Z" }
f8919a
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": 2510 }, "timestamp": "2026-02-15T23:31:37.685Z", "answer": 50599 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V8_SUM", "status": "no"...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
dc4c83
comb_count_partitions_v1_865884756_3003
Let $n = 1 + 2 + 3 + \cdots + 9$. Compute the number of integer partitions of $n$. Then find the remainder when $19321$ minus this number is divided by $64099$.
58,385
graphs = [ Graph( let={ "_n": Const(9), "n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), "result": Partition(arg=Ref(name='n')), "_c": Const(19321), "Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(64099)), ...
COMB
null
COUNT
sympy
COPRIME_PAIRS
[ "SUM_ARITHMETIC" ]
eb34f0
comb_count_partitions_v1
null
3
0
[ "COPRIME_PAIRS", "SUM_ARITHMETIC" ]
2
0.021
2026-02-08T17:05:20.224634Z
{ "verified": true, "answer": 58385, "timestamp": "2026-02-08T17:05:20.245376Z" }
ac2954
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 95, "completion_tokens": 753 }, "timestamp": "2026-02-17T19:50:52.255Z", "answer": 58385 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V7", ...
{ "lo": -2.38, "mid": 1.74, "hi": 6.59 }
e49337
nt_count_divisors_in_range_v1_677425708_913
Let $n = 840$. Compute the number of positive divisors $d$ of $n$ such that $3 \leq d \leq 125$. Let this number be $r$. Find the value of $$ r + 2^{r \bmod 16} \bmod 75125. $$
280
graphs = [ Graph( let={ "n": Const(840), "a": Const(3), "b": Const(125), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))), "Q": Sum...
NT
null
COUNT
sympy
MOBIUS_COPRIME
[ "COPRIME_PAIRS" ]
64a51e
nt_count_divisors_in_range_v1
mod_exp
4
0
[ "COPRIME_PAIRS", "MOBIUS_COPRIME" ]
2
0.158
2026-02-08T03:51:33.081032Z
{ "verified": true, "answer": 280, "timestamp": "2026-02-08T03:51:33.239158Z" }
a8dcd3
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 181, "completion_tokens": 2772 }, "timestamp": "2026-02-09T13:58:31.520Z", "answer": 280 }, { "id...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" } ]
{ "lo": -5.55, "mid": -3.02, "hi": 0.31 }
b6b32d
comb_sum_binomial_row_v1_601307018_4134
Let $M = 0$, $R = \frac{2}{14} \sum_{(k_1, a),\ 1} k_1$, $S = 0$, $h = \sum_{k=0}^{S} (-1)^k \binom{S}{k}$, $n = 11h$, $u = \sum_{k_2=0}^{R} (-1)^{k_2} \binom{R}{k_2}$, and $w = \sum_{k_3=0}^{M} (-1)^{k_3} \binom{M}{k_3}$. Compute $(2 + u) \cdot w)^n$.
2,048
graphs = [ Graph( let={ "_n": Const(2), "n3": Const(0), "h": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))), "n2": Div(Mul(Const(2), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(ele...
COMB
null
SUM
sympy
SUM_INDEPENDENT
[ "SUM_INDEPENDENT/SUM_ARITHMETIC/BINOMIAL_ALTERNATING" ]
610c6e
comb_sum_binomial_row_v1
null
2
3
[ "BINOMIAL_ALTERNATING", "SUM_ARITHMETIC", "SUM_INDEPENDENT" ]
3
0.005
2026-03-10T04:43:43.386100Z
{ "verified": true, "answer": 2048, "timestamp": "2026-03-10T04:43:43.390882Z" }
3973e9
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 263, "completion_tokens": 2139 }, "timestamp": "2026-03-29T11:09:27.541Z", "answer": 2048 }, { "i...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok_later" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok_later" }, { "lemma...
{ "lo": -3.34, "mid": 0.9, "hi": 4.9 }
6062a6
algebra_vieta_sum_v1_1125832087_1121
Let $S$ be the set of all real numbers $x$ such that $$ -x^3 + 12x^2 - 27x - 40 = 0. $$ Compute the sum of all elements of $S$.
12
graphs = [ Graph( let={ "result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(-1), Pow(Var("x"), Const(3))), Mul(Const(12), Pow(Var("x"), Const(2))), Mul(Const(-27), Var("x")), Const(-40)), Const(0)))), }, goal=Ref("result"), ) ]
NT
null
COMPUTE
sympy
V8
[ "V8/K3" ]
0ba015
algebra_vieta_sum_v1
null
3
0
[ "K3", "V8" ]
2
0.033
2026-02-08T03:32:58.625639Z
{ "verified": true, "answer": 12, "timestamp": "2026-02-08T03:32:58.658661Z" }
dc3256
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": 903 }, "timestamp": "2026-02-10T14:53:13.015Z", "answer": 12 }, { "id":...
2
[ { "lemma": "K3", "status": "ok_later" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "ok" }, ...
{ "lo": -10, "mid": -7.73, "hi": -5.46 }
68b455
sequence_count_fib_divisible_v1_397696148_2577
Let $x_1$ and $x_2$ be positive odd integers such that $x_1 + x_2 = 1586$. Let $u$ be the number of such ordered pairs $(x_1, x_2)$. Determine the number of positive integers $n$ with $1 \leq n \leq u$ such that the $n$-th Fibonacci number is divisible by 4. Find the value of this number.
132
graphs = [ Graph( let={ "_n": Const(1586), "upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2"...
NT
null
COUNT
sympy
LIN_FORM
[ "COMB1" ]
567f58
sequence_count_fib_divisible_v1
null
6
0
[ "COMB1", "LIN_FORM" ]
2
0.314
2026-02-08T13:25:30.432613Z
{ "verified": true, "answer": 132, "timestamp": "2026-02-08T13:25:30.746839Z" }
030d5d
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": 860 }, "timestamp": "2026-02-15T15:22:49.969Z", "answer": 132 }, { ...
1
[ { "lemma": "COMB1", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V3", "status": "no" } ]
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
632b13
nt_count_divisible_and_v1_1918700295_2828
Let $d_1 = 10$. Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 15$, $1 \leq j \leq 16$, and $i + j = 17$. Let $d_2 = |S|$. Let $T$ be the set of all positive integers $t$ such that $7 \leq t \leq 20$ and there exist positive integers $a, b$ with $1 \leq a \leq 2$, $1 \leq...
13,956
graphs = [ Graph( let={ "upper": Const(130110), "d1": Const(10), "d2": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(17)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right...
COMB
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM/BINOMIAL_ALTERNATING", "COUNT_SUM_EQUALS" ]
d728f4
nt_count_divisible_and_v1
null
7
0
[ "BINOMIAL_ALTERNATING", "COUNT_SUM_EQUALS", "LIN_FORM" ]
3
4.333
2026-02-08T08:14:33.407694Z
{ "verified": true, "answer": 13956, "timestamp": "2026-02-08T08:14:37.740446Z" }
dd057a
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 370, "completion_tokens": 1946 }, "timestamp": "2026-02-24T09:11:08.497Z", "answer": 13956 }, { "...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok_later" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", ...
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
6278d2
antilemma_product_of_sums_v1_798873815_68
Let $S$ be the set of all integers $t$ such that $9 \leq t \leq 38$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 12$, and $t = 7a + 2b$. Let $S_1 = \sum_{k=1}^{|S|} k$. Let $T$ be the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 5$ and $1 \leq j \leq 7$...
31,500
graphs = [ Graph( let={ "S1": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/SUM_ARITHMETIC", "PRODUCT_OF_SUMS", "ONE_PHI_2" ]
0630f6
antilemma_product_of_sums_v1
null
5
0
[ "LIN_FORM", "ONE_PHI_2", "PRODUCT_OF_SUMS", "SUM_ARITHMETIC" ]
4
0.003
2026-02-08T02:25:37.850182Z
{ "verified": true, "answer": 31500, "timestamp": "2026-02-08T02:25:37.852793Z" }
0c103b
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 295, "completion_tokens": 2824 }, "timestamp": "2026-02-08T18:57:44.931Z", "answer": 31500 }, { "...
1
[ { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "ONE_PHI_2", "status": "ok" }, { "le...
{ "lo": -1.91, "mid": 1.73, "hi": 4.74 }
76b7e1
antilemma_cartesian_v1_1520064083_7676
Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 42$ and $1 \leq b \leq 42$. Compute the value of $$ 3^{|x|} \bmod 99991 + 16110. $$
94,701
graphs = [ Graph( let={ "x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(42)), right=IntegerRange(start=Const(1), end=Const(42)))), "Q": Sum(ModExp(base=Const(3), exp=Abs(arg=Ref(name='x')), mod=Const(99991)), Const(16110)), }, goal=R...
COMB
GEOM
COMPUTE
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
antilemma_cartesian_v1
null
2
0
[ "COUNT_CARTESIAN" ]
1
0.001
2026-02-08T09:14:26.843306Z
{ "verified": true, "answer": 94701, "timestamp": "2026-02-08T09:14:26.844029Z" }
d1e21b
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 177, "completion_tokens": 32768 }, "timestamp": "2026-02-24T10:52:14.366Z", "answer": null }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "statu...
{ "lo": 3.25, "mid": 5.68, "hi": 8.81 }
85fdab
alg_linear_system_2x2_v1_1218484723_5938
Let $F_n$ denote the $n$-th Fibonacci number. Let $S$ be the number of positive integers $n$ with $1 \le n \le 58080$ such that $10 \mid F_n$. Define $$C = \left|\{(a_1, b_1) : 1 \le a_1 \le 40,\ 1 \le b_1 \le 40,\ 34a_1 b_1 + 17a_1^{2} + 17b_1^{2} = 40817\}\right|,$$ and $$D = \left|\{v : C \le v \le S,\ \text{there ...
95,325
graphs = [ Graph( let={ "_e": Const(40), "_d": Const(5), "_c": Const(2), "_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(58080)), Divides(divisor=Const(10), dividend=Fibonacci(arg=Var(name='n')))))),...
NT
null
COMPUTE
sympy
COUNT_FIB_DIVISIBLE
[ "COUNT_FIB_DIVISIBLE/QF_PSD_DISTINCT/QF_PSD_MIN", "QF_PSD_COUNT/QF_PSD_DISTINCT/QF_PSD_MIN", "MAX_PRIME_BELOW/QF_PSD_MIN" ]
e86ed3
alg_linear_system_2x2_v1
null
8
0
[ "COUNT_FIB_DIVISIBLE", "MAX_PRIME_BELOW", "QF_PSD_COUNT", "QF_PSD_DISTINCT", "QF_PSD_MIN" ]
5
0.221
2026-02-25T07:32:17.257932Z
{ "verified": true, "answer": 95325, "timestamp": "2026-02-25T07:32:17.478807Z" }
bd4e45
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 552, "completion_tokens": 4490 }, "timestamp": "2026-03-29T23:32:23.241Z", "answer": 95325 }, { "...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "K16", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": ...
{ "lo": -3.33, "mid": 1.03, "hi": 5.26 }
616514
antilemma_k2_v1_151522320_1658
Let $n = 314$ and let $$ x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor, $$ where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $64813 \cdot x$ is divided by $65227$. Compute $Q$.
6,908
graphs = [ Graph( let={ "_n": Const(314), "x": Summation(var="k", start=Const(1), end=Const(314), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))), "_c": Const(64813), "Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(65227)), }, ...
NT
COMB
COMPUTE
sympy
K13
[ "K2" ]
6897ab
antilemma_k2_v1
null
6
0
[ "K13", "K2" ]
2
0.011
2026-02-08T04:10:19.075586Z
{ "verified": true, "answer": 6908, "timestamp": "2026-02-08T04:10:19.086532Z" }
55a36e
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 194, "completion_tokens": 1768 }, "timestamp": "2026-02-10T15:38:17.165Z", "answer": 6908 }, { "...
1
[ { "lemma": "K15", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -3.49, "mid": 1.84, "hi": 7.55 }