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5f9b7f
modular_min_linear_v1_1439011603_305
Let $a = 5447$. Let $b$ be the number of positive integers $k$ such that $1 \leq k \leq 199410$ and $289$ divides $k$. Let $m = 10454$. Consider the set of all positive integers $x$ such that $1 \leq x \leq m$ and $$ 5447x \equiv b \pmod{10454}. $$ Let $r$ be the smallest such $x$. Compute $r$.
8,794
graphs = [ Graph( let={ "a": Const(5447), "b": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(199410)), Divides(divisor=Const(289), dividend=Var("k"))), domain='positive_integers')), "m": Const(10454), "r...
ALG
NT
EXTREMUM
sympy
C2
[ "C2" ]
9685eb
modular_min_linear_v1
null
5
0
[ "C2" ]
1
0.425
2026-02-08T15:24:21.576215Z
{ "verified": true, "answer": 8794, "timestamp": "2026-02-08T15:24:22.001126Z" }
7571bf
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 150, "completion_tokens": 2530 }, "timestamp": "2026-02-16T05:24:24.361Z", "answer": 8794 }, {...
1
[ { "lemma": "C2", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
1bc817
nt_count_coprime_v1_784195855_5137
Let $k = 19$ and $n$ be a positive integer such that $1 \leq n \leq 43681$. Determine the number of such integers $n$ for which $\gcd(n, k) = \phi(1)$, where $\phi$ denotes Euler's totient function.
41,382
graphs = [ Graph( let={ "upper": Const(43681), "k": Const(19), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), EulerPhi(n=Const(1)))))), }, goal=Ref("...
NT
null
COUNT
sympy
ONE_PHI_1
[ "ONE_PHI_1" ]
f6b5a5
nt_count_coprime_v1
null
4
0
[ "ONE_PHI_1" ]
1
3.681
2026-02-08T07:41:51.658492Z
{ "verified": true, "answer": 41382, "timestamp": "2026-02-08T07:41:55.339242Z" }
84181a
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 163, "completion_tokens": 466 }, "timestamp": "2026-02-20T04:48:19.214Z", "answer": 41382 } ]
2
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "ONE_PHI_1", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V3", "status": "n...
{ "lo": -10, "mid": -6.47, "hi": -2.95 }
c8b2ee
nt_min_crt_v1_865884756_6583
Let $m = 7$ and $k = 8$. Find the smallest positive integer $n$ such that $1 \leq n \leq 56$, $n \equiv 3 \pmod{7}$, and $n \equiv 5 \pmod{8}$. Let $F_j$ denote the Fibonacci sequence defined by $F_1 = 1$, $F_2 = 1$, and $F_j = F_{j-1} + F_{j-2}$ for $j \geq 3$. Determine the smallest positive index $j$ such that $F_j$...
16
graphs = [ Graph( let={ "m": Const(7), "k": Const(8), "a": Const(3), "b": Const(5), "upper": Const(56), "result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value...
NT
null
EXTREMUM
sympy
MIN_PRIME_FACTOR
[ "V1" ]
dae96f
nt_min_crt_v1
null
4
0
[ "MIN_PRIME_FACTOR", "V1" ]
2
0.114
2026-02-08T19:18:14.455556Z
{ "verified": true, "answer": 16, "timestamp": "2026-02-08T19:18:14.569440Z" }
228d34
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": 2011 }, "timestamp": "2026-02-18T21:50:20.270Z", "answer": 16 }, { ...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K5", "status": "same_pattern_wrong" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "V1", "status": "ok" ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
06c074
nt_sum_divisors_mod_v1_784195855_3653
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 32400$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11579$.
1,170
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(32400)))), expr=Sum(Var("x"), Var("y")))), "M": Const(11579)...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_sum_divisors_mod_v1
null
4
0
[ "B3" ]
1
0.001
2026-02-08T06:34:02.958164Z
{ "verified": true, "answer": 1170, "timestamp": "2026-02-08T06:34:02.959267Z" }
e189b4
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 140, "completion_tokens": 299 }, "timestamp": "2026-02-15T17:35:37.893Z", "answer": 3600 }, { "id": 11,...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.01, "mid": -4.68, "hi": -2.15 }
b8b223_n
alg_sum_powers_v1_1218484723_3425
A game assigns points using cubes: on turn $k$, a player gains $k^3$ points, for $k = 1$ to $186$. The total score is reduced modulo $m$, where $m$ is the number of distinct point totals $t$ between $9$ and $4540$ that can be formed as $t = 2a + 7b$ with $1 \le a \le 1045$ and $1 \le b \le 350$. What is $48400$ minus t...
46,943
ALG
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
alg_sum_powers_v1
null
5
null
[ "LIN_FORM" ]
1
0.009
2026-02-25T05:07:55.128434Z
null
2c5d38
b8b223
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 226, "completion_tokens": 6976 }, "timestamp": "2026-03-30T20:03:34.208Z", "answer": 46943 }, { "...
1
[ { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": 1.5, "mid": 4.69, "hi": 7.23 }
7e7324
antilemma_k2_v1_1742523217_127
Compute $$ \sum_{k=1}^{212} \phi(k) \left\lfloor \frac{212}{k} \right\rfloor, $$ where $\phi$ denotes Euler's totient function.
22,578
graphs = [ Graph( let={ "_n": Const(212), "x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(212), Var("k"))))), }, goal=Ref("x"), ) ]
NT
COMB
COMPUTE
sympy
K2
[ "K2" ]
6897ab
antilemma_k2_v1
null
4
0
[ "K2" ]
1
0.001
2026-02-08T02:53:17.837965Z
{ "verified": true, "answer": 22578, "timestamp": "2026-02-08T02:53:17.838497Z" }
069bee
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 162, "completion_tokens": 500 }, "timestamp": "2026-02-09T13:56:22.737Z", "answer": 22578 }, { "i...
1
[ { "lemma": "K15", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -0.58, "mid": 1.54, "hi": 3.31 }
f02f0c
nt_count_gcd_equals_v1_124444284_1108
Let $ A $ be the number of integers $ t $ such that $ 19 \leq t \leq 141 $ and there exist positive integers $ a $ and $ b $ with $ 1 \leq a \leq 9 $, $ 1 \leq b \leq 34 $, and $ t = 7a + 2b + 10 $. Let $ B $ be the number of integers $ t $ such that $ 12 \leq t \leq 152 $ and there exist positive integers $ a $ and $ ...
295
graphs = [ Graph( let={ "upper": Const(34596), "k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
nt_count_gcd_equals_v1
null
6
0
[ "LIN_FORM" ]
1
2.72
2026-02-08T03:41:06.668465Z
{ "verified": true, "answer": 295, "timestamp": "2026-02-08T03:41:09.388805Z" }
e4cbec
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 313, "completion_tokens": 5798 }, "timestamp": "2026-02-10T02:54:04.068Z", "answer": 295 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V3", "status": "no" } ]
{ "lo": -3.46, "mid": 1.03, "hi": 5.49 }
55f7ea
comb_catalan_compute_v1_1918700295_489
Let $T$ be the set of all integers $t$ such that $22 \leq t \leq 61$ and there exist integers $a \in \{1,2\}$, $b \in \{1,2,3,4,5\}$ satisfying $t = 15a + 6b + 1$. Let $n$ be the number of elements in $T$. Compute the $n$-th Catalan number.
16,796
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1...
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_catalan_compute_v1
null
4
0
[ "LIN_FORM" ]
1
0.001
2026-02-08T03:17:26.358802Z
{ "verified": true, "answer": 16796, "timestamp": "2026-02-08T03:17:26.360277Z" }
b92d54
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 209, "completion_tokens": 848 }, "timestamp": "2026-02-10T13:44:49.150Z", "answer": 16796 }, { "i...
1
[ { "lemma": "COUNT_CARTESIAN", "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", ...
{ "lo": -4.92, "mid": -2.9, "hi": -0.7 }
d0440c
modular_inverse_v1_124444284_8804
Let $x$ be a positive integer such that $1 \leq x \leq 336$ and $$ 33x \equiv 1 \pmod{337}. $$ Determine the value of $x$.
143
graphs = [ Graph( let={ "a": Const(33), "m": Const(337), "upper": Const(336), "result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("m")), Const...
NT
null
EXTREMUM
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
modular_inverse_v1
null
4
0
[ "MAX_PRIME_BELOW" ]
1
0.074
2026-02-08T11:55:05.123272Z
{ "verified": true, "answer": 143, "timestamp": "2026-02-08T11:55:05.197335Z" }
2532f5
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 106, "completion_tokens": 464 }, "timestamp": "2026-02-16T03:26:53.427Z", "answer": 53 }, { "id": 11, ...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V8", "status": "no" } ...
{ "lo": -6.96, "mid": -4.56, "hi": -1.46 }
46b51f
nt_num_divisors_compute_v1_1978505735_1911
Let $n$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 160$. Compute the number of positive divisors of $n$.
27
graphs = [ Graph( let={ "_n": Const(160), "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_num_divisors_compute_v1
null
4
0
[ "B1" ]
1
0.003
2026-02-08T16:31:23.955186Z
{ "verified": true, "answer": 27, "timestamp": "2026-02-08T16:31:23.958013Z" }
32687a
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 91, "completion_tokens": 526 }, "timestamp": "2026-02-17T05:03:07.656Z", "answer": 27 }, { ...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
2310c8
nt_sum_divisors_compute_v1_124444284_876
Let $p = 11$ and $t = (10! + 1) \mod p$. Let $n_1$ be the number of integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 181$, $1 \leq b \leq 63$, $7 \leq t \leq 913$, and $t = 4a + 3b$. Define $u = \sum_{d \mid n_1} \phi(d) - n_1$, where $\phi$ is Euler's totient function. Let $n = 3459...
21,195
graphs = [ Graph( let={ "p": Const(11), "t": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Const(1)), modulus=Ref("p")), "n1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Va...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/EULER_TOTIENT_SUM", "WILSON" ]
78be44
nt_sum_divisors_compute_v1
null
7
2
[ "EULER_TOTIENT_SUM", "LIN_FORM", "WILSON" ]
3
0.006
2026-02-08T03:33:25.680706Z
{ "verified": true, "answer": 21195, "timestamp": "2026-02-08T03:33:25.686965Z" }
b5a7a4
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 308, "completion_tokens": 3046 }, "timestamp": "2026-02-09T07:00:44.810Z", "answer": 21195 }, { ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "EULER_TOTIENT_SUM", "status": "ok_later" }, { "lemma": "K15", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_SUM", ...
{ "lo": -6.49, "mid": 0.51, "hi": 7.52 }
35d113
geo_count_lattice_rect_v1_655260480_1984
Let $a = 196$ and $b = 62$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Find the remainder when $39983$ times this number is divided by 76398.
24,003
graphs = [ Graph( let={ "a": Const(196), "b": Const(62), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), "_c": Const(39983), "Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(76398)), }, goal=Ref("Q"), )...
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
2
0
null
null
0.003
2026-02-08T16:30:06.628483Z
{ "verified": true, "answer": 24003, "timestamp": "2026-02-08T16:30:06.631749Z" }
8dec19
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 169, "completion_tokens": 1520 }, "timestamp": "2026-02-24T21:10:39.569Z", "answer": 24003 }, { ...
1
[]
{ "lo": -2.4, "mid": 1.57, "hi": 5.75 }
d62122
diophantine_fbi2_count_v1_865884756_925
Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1156$. Let $T$ be the set of all integers $d$ such that $5 \leq d \leq m$, $d$ divides $1260$, and $4 \leq \frac{1260}{d} \leq 67$. Compute the remainder when $36825$ multiplied by the number of elements in $T$ is divid...
23,995
graphs = [ Graph( let={ "_n": Const(67), "k": Const(1260), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPosit...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
diophantine_fbi2_count_v1
null
5
0
[ "B3" ]
1
0.036
2026-02-08T15:41:21.908177Z
{ "verified": true, "answer": 23995, "timestamp": "2026-02-08T15:41:21.944581Z" }
21307b
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 156, "completion_tokens": 1623 }, "timestamp": "2026-02-16T10:56:35.336Z", "answer": 23995 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "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 }
c5e89a
antilemma_k3_v1_717093673_628
Let $n = 45978$. Define $x$ to be the sum $$ \sum_{d \mid n} \phi(d), $$ where the sum is over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot x$ is divided by 56752.
51,850
graphs = [ Graph( let={ "_n": Const(45978), "x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), "Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(56752)), }, goal=Ref("Q"), ) ]
NT
COMB
COMPUTE
sympy
K3
[ "K3" ]
54c41e
antilemma_k3_v1
null
3
0
[ "K3" ]
1
0.001
2026-02-08T15:34:34.026106Z
{ "verified": true, "answer": 51850, "timestamp": "2026-02-08T15:34:34.026644Z" }
65f095
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 120, "completion_tokens": 2101 }, "timestamp": "2026-02-16T08:28:54.972Z", "answer": 51850 }, ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
2e7bb1
sequence_fibonacci_compute_v1_784195855_9296
Let $n$ be the number of integers $t$ with $20 \leq t \leq 84$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 7$, and $t = 14a + 6b$. Compute the $n$-th Fibonacci number.
10,946
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
3
0
[ "LIN_FORM" ]
1
0.002
2026-02-08T16:40:50.196640Z
{ "verified": true, "answer": 10946, "timestamp": "2026-02-08T16:40:50.198218Z" }
3a5a5a
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": 1500 }, "timestamp": "2026-02-17T09:27:40.924Z", "answer": 10946 }, ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
6d889e
nt_count_gcd_equals_v1_1439011603_2501
Let $p_0$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 216$ and $\gcd(p, q) = 1$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 20250000$. Let $k$ be the smallest divisor of $194477$ that is at least $p_0$. Com...
20
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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),...
NT
null
COUNT
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MIN_PRIME_FACTOR", "B3" ]
f8b22e
nt_count_gcd_equals_v1
null
6
0
[ "B3", "COPRIME_PAIRS", "MIN_PRIME_FACTOR" ]
3
0.848
2026-02-08T16:50:17.261959Z
{ "verified": true, "answer": 20, "timestamp": "2026-02-08T16:50:18.110057Z" }
4c62bf
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 173, "completion_tokens": 2543 }, "timestamp": "2026-02-17T13:31:20.918Z", "answer": 20 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
23f4b2
comb_bell_compute_v1_677425708_3201
Let $n$ be the number of integers $t$ with $8 \leq t \leq 18$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 2a + 3b + 3$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Let $Q$ be the remainder when ...
62,722
graphs = [ Graph( let={ "_n": Const(73945), "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=Va...
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_bell_compute_v1
null
5
0
[ "LIN_FORM" ]
1
0.001
2026-02-08T05:32:16.568430Z
{ "verified": true, "answer": 62722, "timestamp": "2026-02-08T05:32:16.569579Z" }
fa28b5
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 250, "completion_tokens": 2495 }, "timestamp": "2026-02-24T04:05:30.858Z", "answer": 62722 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -0.06, "mid": 2.89, "hi": 5.27 }
7999ec
algebra_quadratic_discriminant_v1_1742523217_3037
Let $a = 2$, $b = -20$, and let $c$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 625$. Define $\Delta = b^2 - 4ac$. Compute $44121 \cdot \Delta$.
0
graphs = [ Graph( let={ "_n": Const(44121), "a": Const(2), "b": Const(-20), "c": 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
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
algebra_quadratic_discriminant_v1
null
4
0
[ "B3" ]
1
0.001
2026-02-08T05:30:27.882982Z
{ "verified": true, "answer": 0, "timestamp": "2026-02-08T05:30:27.884234Z" }
3646ff
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": 554 }, "timestamp": "2026-02-12T11:44:09.386Z", "answer": 0 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.01, "mid": -4.68, "hi": -2.15 }
ca6ac2
geo_count_lattice_triangle_v1_153355830_1996
Let $$A = \left|180\cdot 144 + 43\left(0 - \sum_{k=1}^{17} \varphi(k)\left\lfloor\frac{17}{k}\right\rfloor\right)\right|,$$ where $\varphi$ is Euler's totient function. Let $U$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 8100$, and let $m$ be the minimum value of $x+y$ over all $(x,y)$...
9,666
graphs = [ Graph( let={ "_c": Const(17), "_m": Const(2), "_n": Const(153), "area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=144)), Mul(Const(value=43), Sub(left=Const(value=0), right=Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=Cons...
NT
null
COUNT
sympy
COUNT_FIB_DIVISIBLE
[ "COUNT_FIB_DIVISIBLE", "B3", "K2" ]
b81c9e
geo_count_lattice_triangle_v1
null
8
0
[ "B3", "COUNT_FIB_DIVISIBLE", "K2" ]
3
0.014
2026-02-08T06:50:46.725864Z
{ "verified": true, "answer": 9666, "timestamp": "2026-02-08T06:50:46.740106Z" }
d6b190
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 313, "completion_tokens": 1953 }, "timestamp": "2026-02-13T05:17:05.056Z", "answer": 9666 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "L3c", "status": "no" }, { ...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
59ce85
comb_count_surjections_v1_784195855_5679
Let $n_1 = 0$ and $n_2 = 0$. Define $u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$ and $w = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n = 7u$ and $k = 3w$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty subsets.
1,806
graphs = [ Graph( let={ "n2": Const(0), "w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))), "n1": Const(0), "u": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V...
COMB
null
COUNT
sympy
BINOMIAL_ALTERNATING
[ "BINOMIAL_ALTERNATING" ]
c21569
comb_count_surjections_v1
null
4
2
[ "BINOMIAL_ALTERNATING" ]
1
0.001
2026-02-08T08:02:15.237025Z
{ "verified": true, "answer": 1806, "timestamp": "2026-02-08T08:02:15.238099Z" }
257f7f
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 245, "completion_tokens": 774 }, "timestamp": "2026-02-24T08:43:51.811Z", "answer": 1806 }, { "id...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "...
{ "lo": -4.92, "mid": -2.91, "hi": -0.68 }
ee3a3d
comb_binomial_compute_v1_677425708_3143
Let $n = 15$ and let $k = \sum_{i=1}^{3} i$. Compute $\binom{n}{k}$.
5,005
graphs = [ Graph( let={ "_n": Const(3), "n": Const(15), "k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), "result": Binom(n=Ref("n"), k=Ref("k")), }, goal=Ref("result"), ) ]
ALG
COMB
COMPUTE
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
comb_binomial_compute_v1
null
2
0
[ "SUM_ARITHMETIC" ]
1
0.002
2026-02-08T05:30:25.722456Z
{ "verified": true, "answer": 5005, "timestamp": "2026-02-08T05:30:25.724163Z" }
99b5bd
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 143, "completion_tokens": 487 }, "timestamp": "2026-02-24T03:49:13.900Z", "answer": 5005 }, { "id...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" } ]
{ "lo": -9.23, "mid": -6.18, "hi": -4.06 }
d16b1d
comb_binomial_compute_v1_971394319_547
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 $pq = 2286900$. Compute $\binom{n}{9}$.
11,440
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=2286900)), 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_binomial_compute_v1
null
6
0
[ "COPRIME_PAIRS" ]
1
0.001
2026-02-08T13:10:03.924333Z
{ "verified": true, "answer": 11440, "timestamp": "2026-02-08T13:10:03.925665Z" }
248dcd
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 103, "completion_tokens": 1392 }, "timestamp": "2026-02-15T10:46:21.652Z", "answer": 11440 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no"...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
22ad01
comb_count_surjections_v1_1520064083_9656
Let $n = 6$. Consider all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 6$ and $1 \leq j \leq 6$ such that $i + j = 6$. Let $k$ be the number of such pairs. Define $R = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder when $89093 \cdot R$ is divided by $7001...
44,500
graphs = [ Graph( let={ "n": Const(6), "k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6...
COMB
null
COUNT
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS" ]
75ab0f
comb_count_surjections_v1
null
4
0
[ "COUNT_SUM_EQUALS" ]
1
0.011
2026-02-08T10:57:14.227513Z
{ "verified": true, "answer": 44500, "timestamp": "2026-02-08T10:57:14.238196Z" }
7b1889
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 226, "completion_tokens": 1565 }, "timestamp": "2026-02-24T12:30:24.482Z", "answer": 44500 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
9c0345
nt_min_phi_inverse_v1_168721529_896
Find the smallest positive integer $n \leq 50$ such that $\phi(n) = 12$.
13
graphs = [ Graph( let={ "upper": Const(50), "k": Const(12), "result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))), }, goal=Ref("result"), ) ]
NT
null
EXTREMUM
sympy
MOBIUS_COPRIME
[ "LTE_SUM/MAX_PRIME_BELOW/MAX_VAL" ]
b866a6
nt_min_phi_inverse_v1
null
4
0
[ "LTE_SUM", "MAX_PRIME_BELOW", "MAX_VAL", "MOBIUS_COPRIME" ]
4
0.119
2026-02-08T13:20:36.402346Z
{ "verified": true, "answer": 13, "timestamp": "2026-02-08T13:20:36.520924Z" }
dba975
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 137, "completion_tokens": 1281 }, "timestamp": "2026-02-09T10:28:37.701Z", "answer": 13 }, { "id"...
1
[ { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_SUM", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "MAX_VAL", "status": "ok_later" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V3", "status": "no" ...
{ "lo": -1.93, "mid": 2.14, "hi": 6.33 }
5d543a
nt_count_with_divisor_count_v1_124444284_5106
Let $t$ be an integer such that $36 \leq t \leq 699$. Let $N$ be the number of values of $t$ for which there exist positive integers $a \leq 27$ and $b \leq 14$ such that $t = 15a + 21b$. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = N$. Determine the value of $441...
88,242
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=27)), Geq(left=...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM/B1" ]
b32639
nt_count_with_divisor_count_v1
null
6
0
[ "B1", "LIN_FORM" ]
2
1.823
2026-02-08T06:23:44.350723Z
{ "verified": true, "answer": 88242, "timestamp": "2026-02-08T06:23:46.173353Z" }
d77e11
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 186, "completion_tokens": 5447 }, "timestamp": "2026-02-12T23:42:53.587Z", "answer": 88242 }, ...
1
[ { "lemma": "B1", "status": "ok_later" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V3", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemm...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
f52c79
modular_inverse_v1_971394319_1159
Let $a$ be the sum of all positive integers $n$ at most $270$ that are divisible by $135$. Let $m = 929$. Let $u$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 215296$. Let $r$ be the smallest positive integer $x$ such that $1 \leq x \leq u$ and $a \cdot x \equiv 1 \pmod{m...
17,867
graphs = [ Graph( let={ "_m": Const(135), "_n": Const(64149), "a": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(270)), Eq(Mod(value=Var("n"), modulus=Ref("_m")), Const(0))))), "m": Const(929), ...
NT
null
EXTREMUM
sympy
SUM_DIVISIBLE
[ "SUM_DIVISIBLE", "B3" ]
26d1a5
modular_inverse_v1
null
6
0
[ "B3", "SUM_DIVISIBLE" ]
2
0.04
2026-02-08T13:31:01.692966Z
{ "verified": true, "answer": 17867, "timestamp": "2026-02-08T13:31:01.732591Z" }
421417
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 170, "completion_tokens": 1443 }, "timestamp": "2026-02-15T16:37:44.150Z", "answer": 17867 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" ...
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
9e99a7
lin_form_endings_v1_677425708_2810
Let $a = 9$ and $b = 21$. Let $k = 4$ and let $L$ be the least common multiple of $a$ and $b$. Define $s = kL + a + b$. Compute the remainder when $15209 \cdot s$ is divided by $62333$.
50,294
graphs = [ Graph( let={ "a_coeff": Const(9), "b_coeff": Const(21), "k_val": Const(4), "lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")), "_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")), "_scale...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
2
null
[ "LIN_FORM" ]
1
0.001
2026-02-08T05:16:51.157987Z
{ "verified": true, "answer": 50294, "timestamp": "2026-02-08T05:16:51.158809Z" }
6b12b1
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": 657 }, "timestamp": "2026-02-12T06:31:09.255Z", "answer": 50294 }, {...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
f032df
nt_sum_totient_over_divisors_v1_784195855_8103
Let $m = 70$ and $n_0 = 2$. Define $S$ as the set of all positive integers $n$ such that \begin{itemize} \item $1 \leq n \leq \sum_{k=1}^{70} \phi(k) \left\lfloor \frac{70}{k} \right\rfloor$, and \item the sum of the decimal digits of $n$ leaves a remainder of 1 when divided by 2. \end{itemize} Let $N$ be the number of...
1,243
graphs = [ Graph( let={ "_m": Const(70), "_n": Const(2), "n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(70), Var("k"))))...
NT
null
COMPUTE
sympy
K2
[ "K2/L3B" ]
e3cab0
nt_sum_totient_over_divisors_v1
null
7
0
[ "K2", "L3B" ]
2
0.003
2026-02-08T10:49:29.952894Z
{ "verified": true, "answer": 1243, "timestamp": "2026-02-08T10:49:29.955866Z" }
150df6
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 174, "completion_tokens": 2992 }, "timestamp": "2026-02-16T16:07:44.205Z", "answer": 1243 }, {...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "L3B", "status": "ok_later" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
a6f95e
alg_qf_psd_min_v1_601307018_7491
Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 35$ and $1 \le b \le 35$ such that $$25b^{2} + 34a^{2} + 22ab \le 18225.$$ Let $Q$ be the minimum value of $$1100996\,a_1^{2} + 677536\,b_1^{2} - 1693840\,a_1b_1$$ over all ordered pairs $(a_1, b_1)$ of positive integers with $1 \le ...
84,692
graphs = [ Graph( let={ "_c": Const(10), "_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(35)), Leq(Sum(Mul(Const(25), Pow(Var("b"), Const(2))), ...
ALG
null
COMPUTE
sympy
B3_DIFF
[ "B3_DIFF/QF_PSD_MIN/QF_PSD_DISTINCT", "QF_PSD_COUNT_LEQ/QF_PSD_MIN" ]
b619ce
alg_qf_psd_min_v1
null
8
0
[ "B3_DIFF", "QF_PSD_COUNT_LEQ", "QF_PSD_DISTINCT", "QF_PSD_MIN" ]
4
1.219
2026-03-10T08:01:38.589265Z
{ "verified": true, "answer": 84692, "timestamp": "2026-03-10T08:01:39.808256Z" }
18a5cd
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 473, "completion_tokens": 11751 }, "timestamp": "2026-04-19T06:52:27.513Z", "answer": 84692 }, { ...
1
[ { "lemma": "B3_DIFF", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT_LEQ", "status": "ok" }, { "lemma": "QF_PSD_DISTINCT", "status": "ok_later" }, { "lemma": "QF_PSD_MIN", "status": "ok_later" } ]
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
547c82
alg_qf_psd_count_v1_1218484723_6304
Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 295$ and $$1 \le b \le \left|\bigl\{(a1, b1) : 1 \le a1 \le 40,\, 1 \le b1 \le 40,\\ 10a1^{2} - 18a1b1 + \left|\bigl\{(a2, b2) : 1 \le a2 \le 25,\, 1 \le b2 \le 25,\, 16b2^{2} = 64\bigr\}\right| b1^{2} \\\le \left|\bigl\{t : \text{th...
10
graphs = [ Graph( let={ "_m": Const(2), "_n": Const(40), "result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(295)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSe...
ALG
null
COUNT
sympy
LIN_FORM
[ "QF_PSD_COUNT/QF_PSD_COUNT_LEQ", "LIN_FORM/QF_PSD_COUNT_LEQ" ]
ba3525
alg_qf_psd_count_v1
null
7
0
[ "LIN_FORM", "QF_PSD_COUNT", "QF_PSD_COUNT_LEQ" ]
3
2.477
2026-02-25T07:52:16.258781Z
{ "verified": true, "answer": 10, "timestamp": "2026-02-25T07:52:18.736086Z" }
1162c9
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 387, "completion_tokens": 32768 }, "timestamp": "2026-03-30T01:09:49.794Z", "answer": null }, { ...
1
[ { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT", "status": "ok" }, { "lemma": "QF_PSD_COUNT_LEQ", "status": "ok_later" } ]
{ "lo": 3.81, "mid": 6.33, "hi": 9.49 }
a573fd
geo_visible_lattice_v1_458359167_4077
Let $n = 55$. Define $S$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Let $r$ be the number of elements in $S$. Compute the Bell number $B_m$, where $m$ is the remainder when $|r|$ is divided by $11$.
21,147
graphs = [ Graph( let={ "n": Const(55), "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
4
0
null
null
0.245
2026-02-08T11:30:03.955909Z
{ "verified": true, "answer": 21147, "timestamp": "2026-02-08T11:30:04.200608Z" }
6393ae
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 202, "completion_tokens": 4331 }, "timestamp": "2026-02-24T14:11:01.814Z", "answer": 21147 }, { "...
1
[]
{ "lo": -3.84, "mid": -1.67, "hi": 1.32 }
1fa4c2
nt_count_divisors_in_range_v1_48377204_3176
Let $ n = 83160 $. Let $ a = 36 $ and let $ b $ be the sum of Euler's totient function $ \phi(d) $ over all positive divisors $ d $ of 2972. Determine the number of positive divisors $ d_1 $ of $ n $ such that $ a \leq d_1 \leq b $.
84
graphs = [ Graph( let={ "n": Const(83160), "a": Const(36), "b": SumOverDivisors(n=Const(value=2972), var='d', expr=EulerPhi(n=Var(name='d'))), "result": CountOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Divides(divisor=Var("d1"), dividend=Ref("n")), G...
NT
null
COUNT
sympy
K3
[ "K3" ]
54c41e
nt_count_divisors_in_range_v1
null
4
0
[ "K3" ]
1
0.034
2026-02-08T17:13:26.357014Z
{ "verified": true, "answer": 84, "timestamp": "2026-02-08T17:13:26.390868Z" }
606171
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 121, "completion_tokens": 2549 }, "timestamp": "2026-02-17T21:44:43.865Z", "answer": 84 }, { ...
1
[ { "lemma": "K3", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
742d2d
modular_min_modexp_v1_1915831931_2021
Let $m$ be the largest prime number less than or equal to the number of integers $t$ with $21 \le t \le 1179$ for which there exist positive integers $a \le 107$ and $b \le 18$ such that $t = 9a + 12b$. Let $u$ be the number of positive integers $k \le 23976$ that are divisible by $444$. Determine the smallest positive...
26,220
graphs = [ Graph( let={ "_n": Const(2), "a": Const(11), "b": Const(185), "m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condit...
NT
null
EXTREMUM
sympy
LIN_FORM
[ "LIN_FORM/MAX_PRIME_BELOW", "C2" ]
c04a9a
modular_min_modexp_v1
null
6
0
[ "C2", "LIN_FORM", "MAX_PRIME_BELOW" ]
3
0.079
2026-02-08T16:35:24.116019Z
{ "verified": true, "answer": 26220, "timestamp": "2026-02-08T16:35:24.194786Z" }
ad12fd
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 197, "completion_tokens": 5329 }, "timestamp": "2026-02-17T07:00:04.667Z", "answer": 26220 }, ...
1
[ { "lemma": "C2", "status": "ok" }, { "lemma": "K13", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
cbcec6
nt_count_digit_sum_v1_153355830_746
Let $S$ be the sum of the integers from $1$ to $7$. Let $N$ be the number of positive integers $n \leq 161604$ such that the sum of the decimal digits of $n$ equals $S$. Let $Q$ be the remainder when $45272 \cdot N$ is divided by $94965$. Compute $Q$.
2,066
graphs = [ Graph( let={ "_n": Const(7), "upper": Const(161604), "target_sum": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("uppe...
NT
null
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
nt_count_digit_sum_v1
null
3
0
[ "SUM_ARITHMETIC" ]
1
6.174
2026-02-08T04:09:26.000171Z
{ "verified": true, "answer": 2066, "timestamp": "2026-02-08T04:09:32.174163Z" }
7c3da5
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 191, "completion_tokens": 7539 }, "timestamp": "2026-02-10T15:31:59.656Z", "answer": 2066 }, { "...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" } ]
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
a08e95
diophantine_fbi2_count_v1_124444284_5139
Let $d_{\text{min}}$ be the smallest divisor of $1225$ that is at least $2$. Compute the number of positive divisors $d$ of $120$ such that $d_{\text{min}} \leq d \leq 68$, and $4 \leq \frac{120}{d} \leq 67$.
9
graphs = [ Graph( let={ "k": Const(120), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1225)))))), Leq(Var("d"), Const(68)), D...
NT
null
COUNT
sympy
COUNT_COPRIME_GRID
[ "MIN_PRIME_FACTOR" ]
bc3776
diophantine_fbi2_count_v1
null
5
0
[ "COUNT_COPRIME_GRID", "MIN_PRIME_FACTOR" ]
2
0.404
2026-02-08T06:24:57.426096Z
{ "verified": true, "answer": 9, "timestamp": "2026-02-08T06:24:57.830152Z" }
f682bd
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": 803 }, "timestamp": "2026-02-12T23:40:56.009Z", "answer": 9 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -5.92, "mid": -3.14, "hi": 0.26 }
f26939
comb_count_derangements_v1_601307018_2017
Let $D_n$ denote the number of derangements of $n$ elements. For each integer $a$ with $0 \le a \le 2808$, define $M = a^2 - 603 \bmod 2809$ and $R = M^2 - 603 \bmod 2809$. Let $S$ be the number of such $a$ for which $R = a$ and $M \ne a$. Let $n = \sum_{k=0}^{S} 2^k$. Compute $D_n$.
1,854
graphs = [ Graph( let={ "_m": Const(2), "_n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(2808)), Eq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p1"), Var("a"))))), "n": Summation(var="k", start=Const(0), end=Ref("_n")...
COMB
null
COUNT
sympy
HALFPLANE_COUNT
[ "POLY_ORBIT_HENSEL/SUM_GEOM" ]
8a1734
comb_count_derangements_v1
null
8
0
[ "HALFPLANE_COUNT", "POLY_ORBIT_HENSEL", "SUM_GEOM" ]
3
0.236
2026-03-10T02:45:08.379759Z
{ "verified": true, "answer": 1854, "timestamp": "2026-03-10T02:45:08.615756Z" }
fb18dd
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 228, "completion_tokens": 6884 }, "timestamp": "2026-04-18T16:01:21.932Z", "answer": 1854 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "POLY_ORBIT_HENSEL", "status": "ok" }, { "lemma": "SUM_GEOM", "status": "ok_later" }, { "lemma": "V7", ...
{ "lo": 1.36, "mid": 4.42, "hi": 6.81 }
936af3
nt_count_coprime_v1_717093673_1235
Let $k$ be the largest prime number less than or equal to $26$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq 50400$ and $\gcd(n_1, k) = 1$.
48,209
graphs = [ Graph( let={ "_n": Const(26), "upper": Const(50400), "k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditi...
NT
null
COUNT
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
nt_count_coprime_v1
null
4
0
[ "MAX_PRIME_BELOW" ]
1
4.147
2026-02-08T15:58:19.135207Z
{ "verified": true, "answer": 48209, "timestamp": "2026-02-08T15:58:23.281977Z" }
a8dda8
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 103, "completion_tokens": 571 }, "timestamp": "2026-02-16T17:16:32.108Z", "answer": 48209 }, {...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
c7f003
comb_count_derangements_v1_153355830_1543
Let $n = 7$. Let $r$ be the number of derangements of $n$ elements. Let $d$ be the smallest divisor of 17303 that is at least 2. Compute the Bell number $B_{|r| \bmod d}$.
203
graphs = [ Graph( let={ "_n": Const(2), "n": Const(7), "result": Subfactorial(arg=Ref(name='n')), "Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"...
NT
COMB
COUNT
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
58d7e9
comb_count_derangements_v1
bell_mod
5
0
[ "MIN_PRIME_FACTOR" ]
1
0.002
2026-02-08T06:29:19.801198Z
{ "verified": true, "answer": 203, "timestamp": "2026-02-08T06:29:19.802727Z" }
36f72c
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 104, "completion_tokens": 1165 }, "timestamp": "2026-02-13T00:49:29.334Z", "answer": 203 }, { ...
1
[ { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "V3", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -3.51, "mid": 1.33, "hi": 6.56 }
7d7c5a
nt_count_gcd_equals_v1_151522320_2391
Let $k=13$ and $d=13$. Let $N$ be the number of integers $n$ such that $1\le n\le 6561$ and $\gcd(n,k)=d$. Let $$Q\equiv 83121\cdot N\pmod{61490},$$ with $0\le Q<61490$. Compute $Q$.
18,294
graphs = [ Graph( let={ "upper": Const(6561), "k": Const(13), "d": Const(13), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))), "Q...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM/C3/MAX_PRIME_BELOW", "MIN_PRIME_FACTOR" ]
81a593
nt_count_gcd_equals_v1
null
4
0
[ "C3", "LIN_FORM", "MAX_PRIME_BELOW", "MIN_PRIME_FACTOR" ]
4
2.646
2026-02-08T04:47:27.302422Z
{ "verified": true, "answer": 18294, "timestamp": "2026-02-08T04:47:29.948129Z" }
372dd9
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 196, "completion_tokens": 697 }, "timestamp": "2026-02-11T21:56:02.276Z", "answer": 18294 }, { "...
1
[ { "lemma": "C3", "status": "ok_later" }, { "lemma": "K5", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_MUL", "statu...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
797c48
comb_catalan_compute_v1_1915831931_2779
Let $m = 10$. Let $k$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 9$, $1 \leq j \leq 10$, and $i + j = m$. Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = k$. Compute the $n$th Catalan number.
16,796
graphs = [ Graph( let={ "_m": Const(10), "_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(9)), right=IntegerRange(start=Const(1), end=Con...
COMB
null
COMPUTE
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS/COMB1" ]
5b2e59
comb_catalan_compute_v1
null
6
0
[ "COMB1", "COUNT_SUM_EQUALS" ]
2
0.091
2026-02-08T17:08:21.826938Z
{ "verified": true, "answer": 16796, "timestamp": "2026-02-08T17:08:21.917657Z" }
8ffb68
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 155, "completion_tokens": 1854 }, "timestamp": "2026-02-17T20:19:34.576Z", "answer": 16796 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "st...
{ "lo": -5.64, "mid": -3.17, "hi": -0.81 }
930a1a
nt_sum_divisors_compute_v1_153355830_574
Compute the sum of all positive divisors of 47524.
83,937
graphs = [ Graph( let={ "n": Const(47524), "result": SumDivisors(n=Ref("n")), }, goal=Ref("result"), ) ]
NT
null
COMPUTE
sympy
MOBIUS_COPRIME
[ "MOBIUS_COPRIME", "WILSON" ]
9e4f5c
nt_sum_divisors_compute_v1
null
3
0
[ "MOBIUS_COPRIME", "WILSON" ]
2
0.002
2026-02-08T03:10:21.206864Z
{ "verified": true, "answer": 83937, "timestamp": "2026-02-08T03:10:21.208996Z" }
692d4c
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 123, "completion_tokens": 971 }, "timestamp": "2026-02-10T15:14:48.001Z", "answer": 83937 }, { "...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MOBIUS_COPRIME", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V8", "status": "no" }, ...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
63ac46_n
comb_factorial_compute_v1_1218484723_2342
A lab is cataloging experimental setups, each described by two positive integers $(a,b)$ with $1 \le a \le 30$ and $1 \le b \le 30$. For each setup, a complexity score is computed as $$108ab^{2} + M\,a^{2}b + C\,b^{3} + 64a^{E},$$ where $$M = \min\{x + y : x, y > 0,\ xy = 5184\},$$ $$C = \left|\{(a_1,b_1) : 1 \le a_1 \...
40,320
COMB
null
COMPUTE
sympy
QF_PSD_COUNT
[ "QF_PSD_COUNT/POLY3_COUNT", "K2/POLY3_COUNT", "B3/POLY3_COUNT" ]
ddf00d
comb_factorial_compute_v1
null
7
null
[ "B3", "K2", "POLY3_COUNT", "QF_PSD_COUNT" ]
4
0.032
2026-02-25T04:09:44.150614Z
null
a68e8b
63ac46
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 374, "completion_tokens": 2306 }, "timestamp": "2026-03-30T18:18:35.805Z", "answer": 40320 }, { "...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "POLY3_COUNT", "status": "ok_lat...
{ "lo": -5.37, "mid": 0.23, "hi": 5.22 }
6ee2cc
antilemma_k2_v1_349078426_1524
Let $x = \sum_{k=1}^{58} \phi(k) \left\lfloor \frac{58}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the remainder when $\sum_{d \mid 256} \phi(d) - x$ is divided by $73507$.
72,052
graphs = [ Graph( let={ "_n": Const(58), "x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(58), Var("k"))))), "Q": Mod(value=Sub(SumOverDivisors(n=Const(value=256), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("x")), mo...
NT
COMB
COMPUTE
sympy
K13
[ "K3", "K2" ]
dd2711
antilemma_k2_v1
negation_mod
5
0
[ "K13", "K2", "K3" ]
3
0.004
2026-02-08T13:41:53.340136Z
{ "verified": true, "answer": 72052, "timestamp": "2026-02-08T13:41:53.344069Z" }
94a9f9
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 117, "completion_tokens": 1210 }, "timestamp": "2026-02-15T19:59:50.989Z", "answer": 72052 }, ...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "K3", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "V...
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
f7dd50
alg_poly3_min_v1_1218484723_3028
Let $C = \min\{ 18a_1b_1^2 + 36a_1^2b_1 + 9b_1^3 : a_1, b_1 \in \mathbb{Z}^+,\, 1 \leq a_1, b_1 \leq 26 \}$. Find the remainder when $$\min\{ -81a^2b - 27ab^2 - 9b^3 : a, b \in \mathbb{Z}^+,\, 1 \leq a \leq 63,\, 1 \leq b \leq C \}$$ is divided by $61683$.
43,926
graphs = [ Graph( let={ "_n": Const(36), "result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(63)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=Solu...
ALG
null
COMPUTE
sympy
POLY3_MIN
[ "POLY3_MIN" ]
e2e279
alg_poly3_min_v1
null
6
0
[ "POLY3_MIN" ]
1
0.014
2026-02-25T04:47:08.727624Z
{ "verified": true, "answer": 43926, "timestamp": "2026-02-25T04:47:08.741230Z" }
e894b1
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 261, "completion_tokens": 2950 }, "timestamp": "2026-03-29T07:57:13.543Z", "answer": 43926 }, { "...
1
[ { "lemma": "POLY3_MIN", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -2.45, "mid": 1.37, "hi": 5.29 }
3d01ff
nt_count_digit_sum_v1_717093673_3387
Let $n = 92146$. Let $s$ be the largest integer $k$ such that $3^k \leq 9234553868882$. Let $c$ be the number of positive integers $m$ with $1 \leq m \leq 357604$ such that the sum of the decimal digits of $m$ equals $s$. Compute the remainder when $44121 \times c$ is divided by $n$.
70,635
graphs = [ Graph( let={ "_n": Const(92146), "upper": Const(357604), "target_sum": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(3), Var("k")), Const(9234553868882)))), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(...
NT
null
COUNT
sympy
MAX_VAL
[ "MAX_VAL" ]
1da621
nt_count_digit_sum_v1
null
5
0
[ "MAX_VAL" ]
1
16.887
2026-02-08T17:33:47.534466Z
{ "verified": true, "answer": 70635, "timestamp": "2026-02-08T17:34:04.421566Z" }
c9fec9
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 138, "completion_tokens": 6326 }, "timestamp": "2026-02-18T04:01:00.953Z", "answer": 70635 }, ...
1
[ { "lemma": "K16", "status": "same_pattern_wrong" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MAX_VAL", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V7", "st...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
4080fd
lte_diff_endings_v1_1742523217_1141
Let $a = 35$, $b = 8$, $p = 3$, and $n = 1134$. Compute the largest integer $k$ such that $p^k$ divides $a^n - b^n$. Multiply this $k$ by $6370$, and compute the remainder when the result is divided by $68246$.
44,590
graphs = [ Graph( let={ "a_val": Const(35), "b_val": Const(8), "p_val": Const(3), "n_val": Const(1134), "a_pow": Pow(Ref("a_val"), Ref("n_val")), "b_pow": Pow(Ref("b_val"), Ref("n_val")), "pow_diff": Sub(Ref("a_pow"), Ref("b...
NT
null
COMPUTE
sympy
LTE_DIFF
[ "LTE_DIFF" ]
cf8260
lte_diff_endings_v1
null
7
null
[ "LTE_DIFF" ]
1
0.001
2026-02-08T03:28:28.509837Z
{ "verified": true, "answer": 44590, "timestamp": "2026-02-08T03:28:28.510554Z" }
1dd7fc
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 185, "completion_tokens": 636 }, "timestamp": "2026-02-10T04:01:15.268Z", "answer": 44590 }, { "i...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_DIFF", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status": "no...
{ "lo": -6.51, "mid": -0.31, "hi": 5.43 }
0520be
v7_endings_v1_548369836_191
Compute the number of integers $k$ such that $0 \leq k \leq 3440$ and the largest integer $e$ for which $5^e$ divides $\binom{3440}{k}$ is exactly 3.
1,004
graphs = [ Graph( let={ "x": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(3440)), Eq(MaxKDivides(target=Binom(n=Const(3440), k=Var("k")), base=Const(5)), Const(3))))), }, goal=Ref("x"), ) ]
NT
null
COMPUTE
sympy
V7
[ "V7" ]
0672d4
v7_endings_v1
null
7
null
[ "V7" ]
1
0.003
2026-02-08T02:48:20.029271Z
{ "verified": true, "answer": 1004, "timestamp": "2026-02-08T02:48:20.031781Z" }
de8f93
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 166, "completion_tokens": 7468 }, "timestamp": "2026-02-08T20:11:59.369Z", "answer": 1004 }, { "i...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V7", "status": "ok" }, { "lemma": "V8", "status": "no" ...
{ "lo": 1.3, "mid": 4.19, "hi": 6.61 }
fd1c29
alg_poly_orbit_hensel_v1_601307018_3768
For each non-negative integer $a$, define $N = (a^3 + a^2 - 4a + 4) \bmod 289$ and $M = (N^3 + N^2 - 4N + 4) \bmod 289$. Find the number of integers $a$ with $0 \le a \le 146811$ such that $M = a$ and $N \ne a$.
1,016
graphs = [ Graph( let={ "p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Pow(Var("a"), Const(2)), Mul(Const(-4), Var("a")), Const(4)), modulus=Const(289)), "p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Pow(Ref("p1"), Const(2)), Mul(Const(-4), Ref("p1")), Const(4)), modulus=Const(289)), ...
ALG
null
COUNT
sympy
POLY_ORBIT_COUNT
[ "POLY_ORBIT_COUNT" ]
4ad965
alg_poly_orbit_hensel_v1
null
6
null
[ "POLY_ORBIT_COUNT" ]
1
0.014
2026-03-10T04:20:57.733318Z
{ "verified": true, "answer": 1016, "timestamp": "2026-03-10T04:20:57.747639Z" }
d5490c
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 204, "completion_tokens": 9987 }, "timestamp": "2026-03-29T10:01:08.156Z", "answer": 2 }, { "i...
1
[ { "lemma": "POLY_ORBIT_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": 1.19, "mid": 4.27, "hi": 6.7 }
b1cbc8
comb_count_derangements_v1_1520064083_845
Let $d$ be the smallest integer greater than or equal to $2$ that divides $77$. Compute the number of derangements of $d$ elements.
1,854
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(77))))), "result": Subfactorial(arg=Ref(name='n')), }, goal=Ref("result"), ) ]
NT
COMB
COUNT
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
comb_count_derangements_v1
null
3
0
[ "MIN_PRIME_FACTOR" ]
1
0.001
2026-02-08T03:37:47.218927Z
{ "verified": true, "answer": 1854, "timestamp": "2026-02-08T03:37:47.219687Z" }
b67005
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 143, "completion_tokens": 691 }, "timestamp": "2026-02-10T15:07:34.533Z", "answer": 1854 }, { "id...
1
[ { "lemma": "K16", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V3", "status": "no" }...
{ "lo": -7.01, "mid": -4.68, "hi": -2.15 }
231ae6
sequence_count_fib_divisible_v1_458359167_2622
Let $m = \sum_{d \mid 198} \phi(d)$. Find the number of positive integers $n \leq m$ such that $11$ divides the $n$-th Fibonacci number.
19
graphs = [ Graph( let={ "upper": SumOverDivisors(n=Const(value=198), var='d', expr=EulerPhi(n=Var(name='d'))), "d": Const(11), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"...
NT
null
COUNT
sympy
MAX_DIVISOR
[ "K3" ]
54c41e
sequence_count_fib_divisible_v1
null
4
0
[ "K3", "MAX_DIVISOR" ]
2
0.036
2026-02-08T06:23:01.247530Z
{ "verified": true, "answer": 19, "timestamp": "2026-02-08T06:23:01.283609Z" }
1a2476
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": 1564 }, "timestamp": "2026-02-13T03:13:29.025Z", "answer": 19 }, { ...
1
[ { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -5.55, "mid": -3.01, "hi": 0.32 }
1fa2dd
geo_count_lattice_triangle_v1_1526740231_397
Let $A$ be the area of the triangle with vertices at $(0,0)$, $(111,13)$, and $(21,120)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle. Compute the remainder when $44121 \cdot \frac{A + 2 - B}{2}$ is divided by $61067$.
9,458
graphs = [ Graph( let={ "_n": Const(21), "area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=120)), Mul(Const(value=21), Sub(left=Const(value=0), right=Const(value=13))))), "boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=13))), GCD(a=Abs(arg=Su...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
geo_count_lattice_triangle_v1
null
6
0
[ "LIN_FORM" ]
1
0.005
2026-02-08T11:30:39.038884Z
{ "verified": true, "answer": 9458, "timestamp": "2026-02-08T11:30:39.043764Z" }
983ef9
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 125, "completion_tokens": 2392 }, "timestamp": "2026-02-14T15:10:43.984Z", "answer": 9458 }, {...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" ...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
49137a
sequence_count_fib_divisible_v1_48377204_923
Let $u = 945$ and $d = 8$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $F_n$ is divisible by $d$, where $F_n$ denotes the $n$th Fibonacci number. Let $r$ be this count. Find the smallest positive integer $k$ such that $F_k$ is divisible by $r + 2$.
108
graphs = [ Graph( let={ "upper": Const(945), "d": Const(8), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))), "Q": Fibo...
NT
null
COUNT
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
sequence_count_fib_divisible_v1
null
6
0
[ "MIN_PRIME_FACTOR" ]
1
2.034
2026-02-08T15:45:35.244567Z
{ "verified": true, "answer": 108, "timestamp": "2026-02-08T15:45:37.278830Z" }
0ef0e0
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 137, "completion_tokens": 2157 }, "timestamp": "2026-02-16T13:24:16.568Z", "answer": 108 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "VAL_SUM_EQ", "status": "no" ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
ca646f
comb_binomial_compute_v1_2051736721_1487
Let $n = 15$ and let $k = \sum_{k1=1}^{3} k1$. Compute $\binom{n}{k}$.
5,005
graphs = [ Graph( let={ "n": Const(15), "k": Summation(var="k1", start=Const(1), end=Const(3), expr=Var("k1")), "result": Binom(n=Ref("n"), k=Ref("k")), }, goal=Ref("result"), ) ]
ALG
COMB
COMPUTE
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
comb_binomial_compute_v1
null
2
0
[ "SUM_ARITHMETIC" ]
1
0.002
2026-02-08T16:04:05.344885Z
{ "verified": true, "answer": 5005, "timestamp": "2026-02-08T16:04:05.346468Z" }
4909e3
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 145, "completion_tokens": 420 }, "timestamp": "2026-02-24T19:47:50.966Z", "answer": 5005 }, { "i...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" } ]
{ "lo": -5.65, "mid": -3.17, "hi": -0.81 }
76ab0b
nt_sum_divisors_mod_v1_1978505735_5137
Let $x$ and $y$ be positive integers such that $xy = 396900$. Let $n$ be the minimum possible value of $x + y$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11491$.
4,368
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(396900)))), expr=Sum(Var("x"), Var("y")))), "M": Const(11491...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_sum_divisors_mod_v1
null
5
0
[ "B3" ]
1
0.002
2026-02-08T18:47:55.318738Z
{ "verified": true, "answer": 4368, "timestamp": "2026-02-08T18:47:55.320439Z" }
c4326b
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 111, "completion_tokens": 1404 }, "timestamp": "2026-02-18T19:48:15.109Z", "answer": 4368 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
c2b163
nt_sum_divisors_mod_v1_1874849503_1015
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Define $\text{result}$ as the remainder when $\sigma$ is divided by $11161$. Let $Q$ be the remaind...
5,343
graphs = [ Graph( let={ "n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(176400)))), expr=Sum(Var("x"), Var("y")))), "M": Const(11161...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_sum_divisors_mod_v1
null
6
0
[ "B3" ]
1
0.004
2026-02-08T13:30:28.641867Z
{ "verified": true, "answer": 5343, "timestamp": "2026-02-08T13:30:28.645881Z" }
a7c5c8
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 233, "completion_tokens": 1791 }, "timestamp": "2026-02-09T23:57:48.371Z", "answer": 5343 }, { "i...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -5.49, "mid": 0.03, "hi": 6.12 }
22949f
antilemma_sum_factor_cartesian_v1_1520064083_3001
Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $c = |P|$. Let $\phi_c = \phi(c)$. Let $S$ be the set of all ordered pairs $(i, j)$ of integers with $1 \le i \le 12$ and $1 \le j \le 20$. Compute $$ \sum_{(i,j) \in S} i \cd...
16,380
graphs = [ Graph( let={ "x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(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(n...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/ONE_PHI_2/SUM_FACTOR_CARTESIAN", "SUM_FACTOR_CARTESIAN" ]
0bec54
antilemma_sum_factor_cartesian_v1
null
6
0
[ "COPRIME_PAIRS", "ONE_PHI_2", "SUM_FACTOR_CARTESIAN" ]
3
0.001
2026-02-08T05:24:21.740668Z
{ "verified": true, "answer": 16380, "timestamp": "2026-02-08T05:24:21.741829Z" }
4f2d5c
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 246, "completion_tokens": 660 }, "timestamp": "2026-02-18T16:20:19.019Z", "answer": 98280 } ]
0
[ { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": ...
{ "lo": -6.48, "mid": 1.54, "hi": 9.56 }
f736b3
nt_count_with_divisor_count_v1_349078426_1592
Let $n = 6$. Consider all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the set of all values of $xy$ for such pairs. Let $d_{\text{max}}$ be the maximum value in $P$. Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 75025$ and the number of positive divisors of $k...
82
graphs = [ Graph( let={ "_n": Const(6), "upper": Const(75025), "div_count": 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...
NT
null
COUNT
sympy
B1
[ "B1" ]
5b950e
nt_count_with_divisor_count_v1
null
6
0
[ "B1" ]
1
8.379
2026-02-08T13:44:02.655601Z
{ "verified": true, "answer": 82, "timestamp": "2026-02-08T13:44:11.034200Z" }
c52d8b
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": 2126 }, "timestamp": "2026-02-15T20:04:41.805Z", "answer": 82 }, { ...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
7a6700
comb_sum_binomial_row_v1_458359167_2077
Let $n$ be an integer. Consider the set of all prime numbers $n$ such that $2 \leq n \leq 13$. Let $p$ be the largest prime in this set. Compute $2^p$.
8,192
graphs = [ Graph( let={ "_n": Const(13), "n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "result": Pow(Const(2), Ref("n")), }, goal=Ref("result"), ) ]
NT
null
SUM
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
comb_sum_binomial_row_v1
null
2
0
[ "MAX_PRIME_BELOW" ]
1
0.002
2026-02-08T05:07:09.710872Z
{ "verified": true, "answer": 8192, "timestamp": "2026-02-08T05:07:09.713190Z" }
ccd25d
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 160, "completion_tokens": 302 }, "timestamp": "2026-02-11T22:54:49.344Z", "answer": 8192 }, { "id...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -9.14, "mid": -6.05, "hi": -3.74 }
b62f39
nt_max_prime_below_v1_784195855_6725
Let $N$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 29$, $1 \leq j \leq 166$, and $\gcd(i,j) = 1$. Let $p$ be the largest prime number $n$ such that $2 \leq n \leq 11821$. Let $q$ be the largest prime number at most $N$, and let $r$ be the largest prime number at most $400$. Com...
14,696
graphs = [ Graph( let={ "_m": Const(2), "_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=...
NT
null
EXTREMUM
sympy
COUNT_COPRIME_GRID
[ "COUNT_COPRIME_GRID/MAX_PRIME_BELOW" ]
d6c842
nt_max_prime_below_v1
two_moduli
7
0
[ "COUNT_COPRIME_GRID", "MAX_PRIME_BELOW" ]
2
0.279
2026-02-08T08:49:10.763883Z
{ "verified": true, "answer": 14696, "timestamp": "2026-02-08T08:49:11.043340Z" }
6e88a1
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 184, "completion_tokens": 3548 }, "timestamp": "2026-02-13T21:58:56.198Z", "answer": 14696 }, ...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "MOD_ADD", ...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
ccf230
geo_count_lattice_triangle_v1_1918700295_32
Let $A$ be twice the area of a triangle with vertices at $(0,0)$, $(105,200)$, and $(16,0)$, given by \[ A = \left| 105 \cdot 200 + 16 \cdot (0 - J) \right|, \] where $J$ is the number of positive integers $j$ such that $1 \le j \le 200$ and $j^2 \le 40000$. Let $B$ be the sum of the greatest common divisors of the ab...
8,850
graphs = [ Graph( let={ "_n": Const(200), "area_2x": Abs(arg=Sum(Mul(Const(value=105), Const(value=200)), Mul(Const(value=16), Sub(left=Const(value=0), right=CountOverSet(set=SolutionsSet(var=Var(name='j'), condition=And(Geq(left=Var(name='j'), right=Const(value=1)), Leq(left=Var(nam...
ALG
NT
COUNT
sympy
C3
[ "C3" ]
8a214c
geo_count_lattice_triangle_v1
null
7
0
[ "C3" ]
1
0.007
2026-02-08T02:57:31.122871Z
{ "verified": true, "answer": 8850, "timestamp": "2026-02-08T02:57:31.130195Z" }
d0149a
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 308, "completion_tokens": 2167 }, "timestamp": "2026-02-23T20:41:39.269Z", "answer": 8850 }, { "i...
1
[ { "lemma": "C3", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -2.06, "mid": 0.33, "hi": 2.31 }
67fb61
comb_factorial_compute_v1_1978505735_6095
Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 3104$ and $\binom{3104}{j}$ is odd. Compute $n!$.
40,320
graphs = [ Graph( let={ "_n": Const(3104), "n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(3104)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), "res...
ALG
COMB
COMPUTE
sympy
V8
[ "V8" ]
86348e
comb_factorial_compute_v1
null
6
0
[ "V8" ]
1
0.001
2026-02-08T19:24:49.774024Z
{ "verified": true, "answer": 40320, "timestamp": "2026-02-08T19:24:49.775483Z" }
80dfec
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 91, "completion_tokens": 2356 }, "timestamp": "2026-02-18T22:23:40.817Z", "answer": 40320 }, {...
1
[ { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8", "status": "ok" } ]
{ "lo": -3.12, "mid": 1.47, "hi": 6.57 }
3af47f
alg_qf_psd_orbit_v1_1218484723_628
Let $T$ be the number of integer pairs $(a_3, b_3)$ with $1 \le a_3, b_3 \le 40$ such that $2b_3^4 + 8a_3^3b_3 + 12a_3^2b_3^2 + 2a_3^4 + 8a_3b_3^3 = 13530402$. Let $U$ be the number of integer pairs $(a_2, b_2)$ with $1 \le a_2 \le 30$, $1 \le b_2 \le T$, and $34a_2^2 - 2a_2b_2 + 5b_2^2 = 10985$. Let $S$ be the set of ...
5
graphs = [ Graph( let={ "_c": Const(3), "_m": Const(2), "_n": Const(40), "result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(46)), Geq(Var("b"), Const(1)), Leq(V...
ALG
null
COUNT
sympy
SUM_GEOM
[ "POLY4_COUNT/QF_PSD_COUNT/SUM_SQUARES_IDENTITY" ]
d75633
alg_qf_psd_orbit_v1
null
8
0
[ "POLY4_COUNT", "QF_PSD_COUNT", "SUM_GEOM", "SUM_SQUARES_IDENTITY" ]
4
1.771
2026-02-25T02:22:38.941942Z
{ "verified": true, "answer": 5, "timestamp": "2026-02-25T02:22:40.712953Z" }
3d37b5
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 482, "completion_tokens": 9972 }, "timestamp": "2026-04-18T18:19:04.497Z", "answer": 5 }, { "id"...
1
[ { "lemma": "POLY4_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT", "status": "ok_later" }, { "lemma": "SUM_SQUARES_IDENTITY", "status": "ok_later" } ]
{ "lo": 1.68, "mid": 4.46, "hi": 6.83 }
9e0c9a
nt_count_intersection_v1_1915831931_773
Let $N = 20000$ and $a = 7$. Let $b = \sum_{k=1}^{4} k$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$.
1,143
graphs = [ Graph( let={ "_n": Const(4), "N": Const(20000), "a": Const(7), "b": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n...
NT
null
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
nt_count_intersection_v1
null
4
0
[ "SUM_ARITHMETIC" ]
1
0.997
2026-02-08T15:40:23.983186Z
{ "verified": true, "answer": 1143, "timestamp": "2026-02-08T15:40:24.980160Z" }
42e6b3
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": 856 }, "timestamp": "2026-02-16T11:25:37.481Z", "answer": 1143 }, { ...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
9ce41f
nt_count_coprime_v1_1978505735_3094
Let $N$ be the number of positive integers $n$ with $1 \leq n \leq 1199$ such that $\gcd(n, 6) = 1$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Determine the number of positive integers $n_1$ with $1 \leq n_1 \leq 34596$ such that $\gcd(n_1, k) = 1$.
13,838
graphs = [ Graph( let={ "_n": Const(1199), "upper": Const(34596), "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")), CountOverSet...
NT
null
COUNT
sympy
C4
[ "C4/B3" ]
046ad7
nt_count_coprime_v1
null
6
0
[ "B3", "C4" ]
2
4.251
2026-02-08T17:20:45.636117Z
{ "verified": true, "answer": 13838, "timestamp": "2026-02-08T17:20:49.887005Z" }
057b4f
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 157, "completion_tokens": 1418 }, "timestamp": "2026-02-18T00:39:11.889Z", "answer": 13838 }, ...
1
[ { "lemma": "B3", "status": "ok_later" }, { "lemma": "C4", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
76b592
comb_sum_binomial_row_v1_1915831931_765
Let $m = 5$. Define $S$ as the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 5$ and $1 \leq j \leq 2$. Let $T$ be the set obtained by applying the transformation $\phi(k) \left\lfloor \frac{m}{k} \right\rfloor$ to each pair $(k, j)$ in $S$, where $\phi$ denotes Euler's totient function...
32,768
graphs = [ Graph( let={ "_m": Const(5), "n": Div(Mul(Const(6), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Con...
NT
null
SUM
sympy
SUM_INDEPENDENT
[ "SUM_INDEPENDENT", "K2" ]
d64c9f
comb_sum_binomial_row_v1
null
4
0
[ "K2", "SUM_INDEPENDENT" ]
2
0.003
2026-02-08T15:39:50.889655Z
{ "verified": true, "answer": 32768, "timestamp": "2026-02-08T15:39:50.892591Z" }
f813da
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 176, "completion_tokens": 1170 }, "timestamp": "2026-02-16T11:27:40.622Z", "answer": 32768 }, ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "SUM_INDEPENDENT", "status": "...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
6a4e64
geo_count_lattice_rect_v1_601307018_1710
Find the number of lattice points $(x, y)$ with $0 \le x \le 85$ and $0 \le y \le 22$.
1,978
graphs = [ Graph( let={ "a": Const(85), "b": Const(22), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), }, goal=Ref("result"), ) ]
GEOM
GEOM
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
2
0
null
null
0.001
2026-03-10T02:27:49.911871Z
{ "verified": true, "answer": 1978, "timestamp": "2026-03-10T02:27:49.912542Z" }
0c5630
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 143, "completion_tokens": 123 }, "timestamp": "2026-03-29T03:09:42.058Z", "answer": 1978 }, { "id...
2
[]
{ "lo": -10, "mid": -6.41, "hi": -2.82 }
972a14
diophantine_fbi2_count_v1_124444284_9309
Let $k = 60$. Determine the number of positive integers $d$ such that $6 \leq d \leq 60$, $d$ divides $k$, and the quotient $\frac{k}{d}$ satisfies $5 \leq \frac{k}{d} \leq 59$.
3
graphs = [ Graph( let={ "k": Const(60), "a": Const(5), "b": Const(4), "upper": Const(55), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(60)), Divides(divisor=Var("d"), dividend=Ref(...
NT
null
COUNT
sympy
V8
[ "B3" ]
0cd20d
diophantine_fbi2_count_v1
null
2
0
[ "B3", "V8" ]
2
0.056
2026-02-08T12:22:43.478370Z
{ "verified": true, "answer": 3, "timestamp": "2026-02-08T12:22:43.534159Z" }
62f653
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 107, "completion_tokens": 667 }, "timestamp": "2026-02-15T00:43:30.635Z", "answer": 3 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
a07f55
algebra_quadratic_discriminant_v1_1218484723_6461
Let $R = -1^{\left|\{ (a_1, b_1) : 1 \le a_1 \le 15,\ 1 \le b_1 \le 15,\ a_1 \le b_1,\ 2b_1^{2} + 2a_1^{2} - 4a_1 b_1 = \left|\{ (a_2, b_2) : 1 \le a_2 \le 30,\ 1 \le b_2 \le \left|\{ (a_3, b_3) : 1 \le a_3 \le 40,\ 1 \le b_3 \le 40,\\ 17a_3^{4} + 102a_3^{2} b_3^{2} + 17b_3^{4} + 68a_3^{3} b_3 + 68a_3 b_3^{3} = 1569985...
64,787
graphs = [ Graph( let={ "_m": Const(2), "_n": Const(4), "a": Const(3), "b": Const(-1), "c": Const(11), "result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Co...
ALG
null
COMPUTE
sympy
POLY4_COUNT
[ "POLY4_COUNT/QF_PSD_COUNT_LEQ/QF_PSD_ORBIT" ]
e02fc0
algebra_quadratic_discriminant_v1
null
7
0
[ "POLY4_COUNT", "QF_PSD_COUNT_LEQ", "QF_PSD_ORBIT" ]
3
0.018
2026-02-25T08:01:26.053001Z
{ "verified": true, "answer": 64787, "timestamp": "2026-02-25T08:01:26.070685Z" }
30db7f
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 402, "completion_tokens": 8277 }, "timestamp": "2026-03-30T01:50:33.095Z", "answer": 64787 }, { "...
1
[ { "lemma": "POLY4_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT_LEQ", "status": "ok_later" }, { "lemma": "QF_PSD_ORBIT", "status": "ok_later" } ]
{ "lo": 1.53, "mid": 4.7, "hi": 7.23 }
edc58c
geo_count_lattice_triangle_v1_1218484723_5041
Let $M = \left|256128 + 200 \cdot (0 - 256)\right|$, $R = \gcd(256, 256) + \gcd(|200 - 256|, |128 - 256|) + \gcd(|0 - 200|, |0 - 128|)$, and $S = \frac{M + 2 - R}{2}$. Compute $70000 - S$.
60,919
graphs = [ Graph( let={ "_n": Const(128), "area_2x": Abs(arg=Sum(Mul(Const(value=256), Ref(name='_n')), Mul(Const(value=200), Sub(left=Const(value=0), right=Const(value=256))))), "boundary": Sum(GCD(a=Abs(arg=Const(value=256)), b=Abs(arg=Const(value=256))), GCD(a=Abs(arg=...
GEOM
NT
COUNT
sympy
VIETA_SUM
[ "VIETA_SUM" ]
b33a7a
geo_count_lattice_triangle_v1
null
4
0
[ "VIETA_SUM" ]
1
0.005
2026-02-25T06:39:57.281539Z
{ "verified": true, "answer": 60919, "timestamp": "2026-02-25T06:39:57.286734Z" }
77a518
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 207, "completion_tokens": 751 }, "timestamp": "2026-03-29T19:10:21.874Z", "answer": -32329 }, { ...
1
[ { "lemma": "VIETA_SUM", "status": "ok" } ]
{ "lo": 3.81, "mid": 6.33, "hi": 9.49 }
ceb419
diophantine_fbi2_count_v1_397696148_965
Let $n = 15$. For each integer $k$ from 1 to $n$, define $$ a_k = \varphi(k) \left\lfloor \frac{1}{k} \sum_{k=1}^{5} \varphi(k) \left\lfloor \frac{5}{k} \right\rfloor \right\rfloor, $$ where $\varphi$ denotes Euler's totient function. Let $k = \sum_{k=1}^{15} a_k$. Now consider the set of all positive integers $d$ suc...
11
graphs = [ Graph( let={ "_n": Const(15), "k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))), Var("k"))))), "result...
NT
null
COUNT
sympy
V1
[ "K2/K2" ]
ddede2
diophantine_fbi2_count_v1
null
5
0
[ "K2", "V1" ]
2
0.131
2026-02-08T11:58:21.830939Z
{ "verified": true, "answer": 11, "timestamp": "2026-02-08T11:58:21.961607Z" }
a76503
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 203, "completion_tokens": 2135 }, "timestamp": "2026-02-14T23:43:46.545Z", "answer": 11 }, { ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" ...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
5bb0de
nt_lcm_compute_v1_349078426_1832
Let $S$ be the set of all integers $t$ such that $21 \leq t \leq 6681$ and $t = 9a + 12b$ for some positive integers $a \leq 221$ and $b \leq 391$. Let $N = |S|$. Let $a_{\text{max}}$ be the largest prime number at most $N$. Let $T$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1020100$, ...
3,970
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=221)), Geq(left=Var(name='b'), right=Const(valu...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/MAX_PRIME_BELOW", "B3" ]
2a7052
nt_lcm_compute_v1
null
6
0
[ "B3", "LIN_FORM", "MAX_PRIME_BELOW" ]
3
0.004
2026-02-08T13:57:02.653001Z
{ "verified": true, "answer": 3970, "timestamp": "2026-02-08T13:57:02.656648Z" }
6a045c
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 221, "completion_tokens": 6423 }, "timestamp": "2026-02-15T22:41:39.261Z", "answer": 3970 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "sta...
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
9876f6
geo_count_lattice_rect_v1_1520064083_6735
Compute the number of lattice points $(x,y)$ such that $0 \le x \le 300$ and $0 \le y \le 132$.
40,033
graphs = [ Graph( let={ "a": Const(300), "b": Const(132), "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
0.002
2026-02-08T08:17:31.439128Z
{ "verified": true, "answer": 40033, "timestamp": "2026-02-08T08:17:31.440797Z" }
47ad53
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 143, "completion_tokens": 120 }, "timestamp": "2026-02-24T09:14:58.096Z", "answer": 40033 }, { "i...
2
[]
{ "lo": -10, "mid": -7.79, "hi": -5.57 }
59e960
comb_bell_compute_v1_809748730_176
Let $m = 74529$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq T$ and $\binom{s}{j} \equiv 1 \pmod{2}$, where $T$ is the number of integers $t...
11,485
graphs = [ Graph( let={ "_m": Const(74529), "_n": Const(2), "n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name=...
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/V8", "B3/V8" ]
3f10a4
comb_bell_compute_v1
null
7
0
[ "B3", "LIN_FORM", "V8" ]
3
0.004
2026-02-08T11:21:29.653889Z
{ "verified": true, "answer": 11485, "timestamp": "2026-02-08T11:21:29.657676Z" }
2ce720
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 309, "completion_tokens": 6253 }, "timestamp": "2026-02-24T13:33:00.663Z", "answer": 11485 }, { "...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_F...
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
8403f7
comb_factorial_compute_v1_124444284_411
Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 10241$ such that $\binom{10241}{j}$ is odd. Compute $n!$.
40,320
graphs = [ Graph( let={ "_n": Const(10241), "n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(10241)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), "r...
ALG
COMB
COMPUTE
sympy
V8
[ "V8" ]
86348e
comb_factorial_compute_v1
null
7
0
[ "V8" ]
1
0.003
2026-02-08T03:15:56.420222Z
{ "verified": true, "answer": 40320, "timestamp": "2026-02-08T03:15:56.423077Z" }
76da6c
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 157, "completion_tokens": 1576 }, "timestamp": "2026-02-09T17:19:44.575Z", "answer": 40320 }, { "...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8", "status": "ok" } ]
{ "lo": -2.46, "mid": 0.47, "hi": 3.59 }
ac813d
antilemma_sum_equals_v1_1918700295_4060
Let $n$ be the number of ordered pairs $(i, j)$ where $i$ and $j$ are integers with $1 \leq i \leq 3$ and $1 \leq j \leq 3$. Determine the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = n$. Compute this value.
6
graphs = [ Graph( let={ "_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))), "x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(...
COMB
GEOM
COMPUTE
sympy
LIN_FORM
[ "COUNT_CARTESIAN/COUNT_SUM_EQUALS", "COUNT_SUM_EQUALS" ]
8bee9e
antilemma_sum_equals_v1
null
3
0
[ "COUNT_CARTESIAN", "COUNT_SUM_EQUALS", "LIN_FORM" ]
3
0.047
2026-02-08T09:06:20.434483Z
{ "verified": true, "answer": 6, "timestamp": "2026-02-08T09:06:20.481815Z" }
ef5d72
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": 709 }, "timestamp": "2026-02-24T10:34:30.185Z", "answer": 6 }, { "id": ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no...
{ "lo": -4.92, "mid": -2.91, "hi": -0.68 }
b53d90
nt_count_divisible_and_v1_397696148_194
Let $n = 198$ and $U = 194460$. Determine the number of positive integers $m$ such that $1 \leq m \leq U$, $m$ is divisible by $12$, and $m$ is divisible by $15$. Let this count be $C$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $M$ be the maximum value of $xy$ over...
29,519
graphs = [ Graph( let={ "_n": Const(198), "upper": Const(194460), "d1": Const(12), "d2": Const(15), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), mod...
NT
null
COUNT
sympy
B1
[ "B1" ]
bf138c
nt_count_divisible_and_v1
quadratic_mod
4
0
[ "B1" ]
1
7.807
2026-02-08T11:21:40.905103Z
{ "verified": true, "answer": 29519, "timestamp": "2026-02-08T11:21:48.712208Z" }
26669a
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 183, "completion_tokens": 1291 }, "timestamp": "2026-02-14T12:22:37.317Z", "answer": 29519 }, ...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
f323df
nt_count_divisible_and_v1_1470522791_56
Let $d_1$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 36$. Let $d_2 = 18$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 66060$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute $38416 - N$.
36,581
graphs = [ Graph( let={ "upper": Const(66060), "d1": 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(36)))), expr=Sum(Var("x"), Var("y"))...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
nt_count_divisible_and_v1
null
4
0
[ "B3" ]
1
5.91
2026-02-08T12:48:30.772144Z
{ "verified": true, "answer": 36581, "timestamp": "2026-02-08T12:48:36.682110Z" }
881984
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 148, "completion_tokens": 709 }, "timestamp": "2026-02-15T05:08:05.029Z", "answer": 36581 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
f48906
modular_min_linear_v1_677425708_1696
Let $a = 14198$. Let $S$ be the set of all positive integers $x_1$ and $x_2$ such that $x_1$ and $x_2$ are both odd and $x_1 + x_2 = 494$. Let $n_{\text{max}}$ be the number of elements in $S$. Define $b$ to be the largest prime number $n$ such that $2 \leq n \leq n_{\text{max}}$. Let $m = 26583$. Let $x$ be a positive...
6,704
graphs = [ Graph( let={ "a": Const(14198), "b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(na...
NT
null
EXTREMUM
sympy
COMB1
[ "COMB1/MAX_PRIME_BELOW" ]
6a06f8
modular_min_linear_v1
null
7
0
[ "COMB1", "MAX_PRIME_BELOW" ]
2
5.022
2026-02-08T04:22:42.632659Z
{ "verified": true, "answer": 6704, "timestamp": "2026-02-08T04:22:47.655131Z" }
853db4
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 258, "completion_tokens": 3370 }, "timestamp": "2026-02-11T23:49:42.103Z", "answer": 6704 }, {...
1
[ { "lemma": "COMB1", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "MOD_FACTORIAL", "stat...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
201070
modular_sum_quadratic_residues_v1_1742523217_4433
Let $m = 2$. Define $n$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 60$, $\gcd(p, q) = 1$, and $p < q$. Let $p_{\text{min}}$ be the smallest divisor of $302764416173$ that is at least $m$. Compute the value of $\frac{p_{\text{min}}(p_{\text{min}} - 1)}{...
9,653
graphs = [ Graph( let={ "_m": Const(2), "_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=60)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q...
NT
null
SUM
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MIN_PRIME_FACTOR" ]
52cee2
modular_sum_quadratic_residues_v1
null
5
0
[ "COPRIME_PAIRS", "MIN_PRIME_FACTOR" ]
2
0.003
2026-02-08T07:17:30.770336Z
{ "verified": true, "answer": 9653, "timestamp": "2026-02-08T07:17:30.772887Z" }
5e6994
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 155, "completion_tokens": 2854 }, "timestamp": "2026-02-13T09:19:53.475Z", "answer": 9653 }, {...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K13", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok_later" }, { "lemma": "MOD_MUL", "statu...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
293f9b
antilemma_k2_v1_124444284_4513
Let $d = 2$. Let $S$ be the set of all real solutions $x$ to the equation $x^2 - 303x - 2488 = 0$, and let $n$ be the sum of all elements in $S$. For each positive integer $k$ from $1$ to $n$, define $$ a_k = \varphi(k) \left\lfloor \frac{1}{k} \sum_{d \mid m} \varphi(d) \right\rfloor, $$ where $m$ is the sum of all re...
12,522
graphs = [ Graph( let={ "_d": Const(2), "_c": Const(18396), "_m": Const(44121), "_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_d")), Mul(Const(-303), Var("x")), Const(-2488)), Const(0)))), "x": Summation(var="k...
NT
COMB
COMPUTE
sympy
VIETA_SUM
[ "VIETA_SUM/K3/K2", "VIETA_SUM/K2", "K2" ]
578119
antilemma_k2_v1
null
7
0
[ "K2", "K3", "VIETA_SUM" ]
3
0.002
2026-02-08T06:03:42.158622Z
{ "verified": true, "answer": 12522, "timestamp": "2026-02-08T06:03:42.160844Z" }
ec5f87
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 244, "completion_tokens": 2303 }, "timestamp": "2026-02-12T19:04:34.843Z", "answer": 12522 }, ...
1
[ { "lemma": "K15", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "K3", "status": "ok_later" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
e8f356
comb_sum_binomial_row_v1_458359167_2241
Let $n = 13$. Define $p_0$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $p_0^{13}$.
8,192
graphs = [ Graph( let={ "n": Const(13), "result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq(left=GCD(a=Var(name='p'), b=Var...
NT
null
SUM
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
comb_sum_binomial_row_v1
null
4
0
[ "COPRIME_PAIRS" ]
1
0.001
2026-02-08T05:13:36.011835Z
{ "verified": true, "answer": 8192, "timestamp": "2026-02-08T05:13:36.012866Z" }
feadbe
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": 1141 }, "timestamp": "2026-02-12T05:54:28.330Z", "answer": 8192 }, {...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "MOD_ADD", "status": "...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
8e41f2
comb_count_surjections_v1_48377204_256
Let $n$ be the number of ordered pairs $(i, j)$ where $i \in \{1, 2\}$ and $j \in \{1, 2, 3\}$. Let $k$ be the number of ordered pairs $(i, j)$ with $i \in \{1, 2, 3\}$, $j \in \{1, 2, 3, 4\}$, and $i + j = 4$. Define $S = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute the re...
2,430
graphs = [ Graph( let={ "_m": Const(4), "_n": Const(70030), "n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))), "k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("...
COMB
null
COUNT
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS", "COUNT_CARTESIAN" ]
e4fc6a
comb_count_surjections_v1
null
3
0
[ "COUNT_CARTESIAN", "COUNT_SUM_EQUALS" ]
2
0.01
2026-02-08T15:19:15.147337Z
{ "verified": true, "answer": 2430, "timestamp": "2026-02-08T15:19:15.157749Z" }
c64251
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 266, "completion_tokens": 982 }, "timestamp": "2026-02-24T20:23:30.264Z", "answer": 2430 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "n...
{ "lo": -2.43, "mid": 1.2, "hi": 4.84 }
85fab6
antilemma_sum_equals_v1_1125832087_558
Determine the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 64$, $1 \leq j \leq 65$, and $i + j = 65$.
64
graphs = [ Graph( let={ "_n": Const(65), "x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(64)), right=IntegerRange(start=Const(1), end=Con...
COMB
GEOM
COMPUTE
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS" ]
75ab0f
antilemma_sum_equals_v1
null
2
0
[ "COUNT_SUM_EQUALS" ]
1
0.005
2026-02-08T03:09:07.458296Z
{ "verified": true, "answer": 64, "timestamp": "2026-02-08T03:09:07.463519Z" }
8dd584
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": 241 }, "timestamp": "2026-02-10T13:13:31.232Z", "answer": 64 }, { "id":...
2
[ { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", ...
{ "lo": -10, "mid": -7.79, "hi": -5.57 }
69181f
comb_factorial_compute_v1_2051736721_4899
Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 36928$ and $\binom{36928}{j}$ is odd. Compute $n!$.
40,320
graphs = [ Graph( let={ "_n": Const(36928), "n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(36928), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), "r...
ALG
COMB
COMPUTE
sympy
V8
[ "V8" ]
86348e
comb_factorial_compute_v1
null
6
0
[ "V8" ]
1
0.002
2026-02-08T18:15:14.761719Z
{ "verified": true, "answer": 40320, "timestamp": "2026-02-08T18:15:14.763255Z" }
4c9b59
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 91, "completion_tokens": 1808 }, "timestamp": "2026-02-18T15:23:27.058Z", "answer": 40320 }, {...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V8", "status": "ok"...
{ "lo": -3.12, "mid": 1.47, "hi": 6.57 }
0b24cf
nt_count_coprime_v1_655260480_441
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9$. Define $\sigma$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $P$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = \sigma$. Define $k$ to be the maximum value of $x_1 ...
31,974
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(9)))), expr=Sum(Var("x"), Var("y")))), "upper": Const(47961...
NT
null
COUNT
sympy
B3
[ "B3/B1" ]
7f76f7
nt_count_coprime_v1
null
4
0
[ "B1", "B3" ]
2
4.653
2026-02-08T15:23:26.474350Z
{ "verified": true, "answer": 31974, "timestamp": "2026-02-08T15:23:31.126928Z" }
b7cb8b
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 203, "completion_tokens": 742 }, "timestamp": "2026-02-16T05:23:07.251Z", "answer": 31974 }, {...
1
[ { "lemma": "B1", "status": "ok_later" }, { "lemma": "B3", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
195aa2
nt_min_phi_inverse_v1_2051736721_1725
Let $c = 4$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = c$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $n_{\text{max}}$ be the maximum value in $P$. Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 120$ and there exist integers $a$ ...
31,602
graphs = [ Graph( let={ "_c": Const(4), "_m": Const(50952), "_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("_c")))), exp...
NT
null
EXTREMUM
sympy
B1
[ "B1/SUM_ARITHMETIC", "LIN_FORM" ]
d43315
nt_min_phi_inverse_v1
null
7
0
[ "B1", "LIN_FORM", "SUM_ARITHMETIC" ]
3
0.012
2026-02-08T16:10:50.613265Z
{ "verified": true, "answer": 31602, "timestamp": "2026-02-08T16:10:50.625705Z" }
75d173
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 290, "completion_tokens": 1840 }, "timestamp": "2026-02-16T22:37:34.653Z", "answer": 31602 }, ...
1
[ { "lemma": "B1", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_VAL", "...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
650161
geo_count_lattice_rect_v1_1978505735_7859
Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 30$ and $0 \leq y \leq 48$. A lattice point is a point with integer coordinates.
1,519
graphs = [ Graph( let={ "a": Const(30), "b": Const(48), "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
0.002
2026-02-08T20:31:45.277650Z
{ "verified": true, "answer": 1519, "timestamp": "2026-02-08T20:31:45.279778Z" }
e62e7f
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 91, "completion_tokens": 377 }, "timestamp": "2026-02-25T02:03:49.634Z", "answer": 1519 }, { ...
2
[]
{ "lo": -10, "mid": -7.4, "hi": -4.8 }
2eabba
nt_min_phi_inverse_v1_865884756_2636
Let $m = 2$ and let $n$ be the largest integer $k$ such that $2^k \leq 50313417$. Let $s$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = n$. Find the smallest positive integer $n'$ such that $1 \leq n' \leq s$ and $\phi(n') = 1$, where $\phi$ denotes Euler's totient...
1
graphs = [ Graph( let={ "_m": Const(2), "_n": MaxOverSet(set=SolutionsSet(var=Var("k1"), condition=Leq(Pow(Ref("_m"), Var("k1")), Const(50313417)))), "upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg...
NT
null
EXTREMUM
sympy
ONE_PHI_1
[ "MAX_VAL/B3" ]
b7a7b3
nt_min_phi_inverse_v1
null
6
0
[ "B3", "MAX_VAL", "ONE_PHI_1" ]
3
0.057
2026-02-08T16:51:45.095206Z
{ "verified": true, "answer": 1, "timestamp": "2026-02-08T16:51:45.151811Z" }
570af2
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 151, "completion_tokens": 703 }, "timestamp": "2026-02-17T12:54:13.056Z", "answer": 1 }, { ...
1
[ { "lemma": "B3", "status": "ok_later" }, { "lemma": "K15", "status": "no" }, { "lemma": "K16", "status": "same_pattern_wrong" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_VAL", "status": "ok" }, { "lemma": "V8", "status": "no" }...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
369058
antilemma_count_primes_v1_798873815_220
Let $n = 1373$. Define $x$ to be the number of prime numbers $p$ such that $2 \leq p \leq n$. Compute the value of $$ x + 2^{x \bmod 15} \bmod 99477.$$ Give the result as an integer between $0$ and $99476$, inclusive.
1,244
graphs = [ Graph( let={ "_n": Const(1373), "x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))), "Q": Sum(Ref("x"), Mod(value=Pow(Const(2), Mod(value=Ref("x"), modulus=Const(15))), modulus=C...
NT
null
COMPUTE
sympy
COUNT_PRIMES
[ "COUNT_PRIMES" ]
07c874
antilemma_count_primes_v1
null
4
0
[ "COUNT_PRIMES" ]
1
0.001
2026-02-08T02:31:30.413431Z
{ "verified": true, "answer": 1244, "timestamp": "2026-02-08T02:31:30.413935Z" }
f8711a
CC BY 4.0
[ { "id": 4, "model": "NousResearch/Hermes-4-405B", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 136, "completion_tokens": 335 }, "timestamp": "2026-02-08T21:10:39.665Z", "answer": 1244 }, {...
1
[ { "lemma": "COUNT_PRIMES", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -1.78, "mid": 2.35, "hi": 6.69 }
6a2da9
nt_count_divisible_and_v1_1520064083_4035
Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 22240656 $. Let $ u $ be the minimum value of $ x + y $ over all such pairs. Let $ d_1 = \sum_{k=1}^{3} k $ and $ d_2 = 9 $. Determine the number of positive integers $ n \leq u $ such that $ n $ is divisible by both $ d_1 $ and ...
7,075
graphs = [ Graph( let={ "_m": Const(3), "_n": Const(84991), "upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(22240656...
NT
null
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC", "B3" ]
dee757
nt_count_divisible_and_v1
null
6
0
[ "B3", "SUM_ARITHMETIC" ]
2
2.548
2026-02-08T06:02:45.181662Z
{ "verified": true, "answer": 7075, "timestamp": "2026-02-08T06:02:47.729879Z" }
26cedd
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": 1993 }, "timestamp": "2026-02-12T19:10:32.007Z", "answer": 7075 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" ...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
ca28a3
nt_num_divisors_compute_v1_784195855_2610
Let $n$ be the number of positive integers less than or equal to 52 whose digit sum is odd. Compute the number of positive divisors of $n$.
4
graphs = [ Graph( let={ "_n": Const(52), "n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))), "result": NumDivisors(n=Ref("n")), }, ...
NT
null
COMPUTE
sympy
L3B
[ "L3B" ]
cc148f
nt_num_divisors_compute_v1
null
3
0
[ "L3B" ]
1
0.002
2026-02-08T05:54:21.798179Z
{ "verified": true, "answer": 4, "timestamp": "2026-02-08T05:54:21.799988Z" }
1b73f5
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 80, "completion_tokens": 681 }, "timestamp": "2026-02-12T16:11:13.326Z", "answer": 4 }, { ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "L3B", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_SUB", "status":...
{ "lo": -5.92, "mid": -3.14, "hi": 0.26 }
4a99b7
nt_max_prime_below_v1_124444284_2609
Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of prime numbers $n$ such that $N \leq n \leq 22801$. Compute the largest element of $S$.
22,787
graphs = [ Graph( let={ "upper": Const(22801), "result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V...
NT
null
EXTREMUM
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
nt_max_prime_below_v1
null
5
0
[ "COPRIME_PAIRS" ]
1
0.524
2026-02-08T04:50:29.064731Z
{ "verified": true, "answer": 22787, "timestamp": "2026-02-08T04:50:29.589224Z" }
e7a214
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": 5961 }, "timestamp": "2026-02-11T22:17:22.091Z", "answer": 22787 }, { ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "V5", "status": "no" ...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
a5a037
comb_count_surjections_v1_458359167_961
Let $n$ be the number of integers $t$ with $10 \le t \le 24$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 3$, $1 \le b \le 2$, and $t = 4a + 6b$. Let $k = 2$. Let $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when $59035 \c...
31,752
graphs = [ Graph( let={ "_n": Const(88498), "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=Va...
COMB
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_count_surjections_v1
null
5
0
[ "LIN_FORM" ]
1
0.001
2026-02-08T04:12:15.416650Z
{ "verified": true, "answer": 31752, "timestamp": "2026-02-08T04:12:15.417909Z" }
3190cd
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 249, "completion_tokens": 1472 }, "timestamp": "2026-02-23T23:48:04.849Z", "answer": 31752 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" ...
{ "lo": -2.46, "mid": 0.47, "hi": 3.59 }
1acef8
nt_lcm_compute_v1_153355830_268
Let $ T $ be the set of all integers $ t $ such that $ 7 \le t \le 100 $ and there exist positive integers $ a $ and $ b $ with $ 1 \le a \le 14 $, $ 1 \le b \le 15 $, and $ t = 5a + 2b $. Let $ s = |T| $. Define $ P $ to be the set of all ordered pairs $ (x, y) $ of positive integers such that $ x + y = s $. Let $ a $...
53,077
graphs = [ Graph( let={ "_m": Const(64742), "_n": Const(44121), "a": 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")), CountOverSet(s...
NT
null
COMPUTE
sympy
L3B
[ "COUNT_COPRIME_GRID", "LIN_FORM/B1" ]
539abe
nt_lcm_compute_v1
null
6
0
[ "B1", "COUNT_COPRIME_GRID", "L3B", "LIN_FORM" ]
4
0.009
2026-02-08T03:00:05.457907Z
{ "verified": true, "answer": 53077, "timestamp": "2026-02-08T03:00:05.467162Z" }
1c7dba
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 344, "completion_tokens": 5717 }, "timestamp": "2026-02-10T12:31:13.053Z", "answer": 53077 }, { ...
1
[ { "lemma": "B1", "status": "ok_later" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma...
{ "lo": -3.45, "mid": 1.18, "hi": 5.72 }
0ab724
nt_count_divisible_and_v1_898971024_2486
Let $n = 3$. Let $u$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 980100$. Let $d_1 = 4$ and let $d_2 = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the number of positive integers $m$ such t...
165
graphs = [ Graph( let={ "_n": Const(3), "upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(980100)))), expr=Sum(Var("x"), Var("y"))...
NT
null
COUNT
sympy
B3
[ "B3", "K2" ]
f1ea07
nt_count_divisible_and_v1
null
7
0
[ "B3", "K2" ]
2
0.148
2026-02-08T16:47:03.923675Z
{ "verified": true, "answer": 165, "timestamp": "2026-02-08T16:47:04.071484Z" }
95bcd7
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 186, "completion_tokens": 1019 }, "timestamp": "2026-02-17T12:54:04.805Z", "answer": 165 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "V5", "statu...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
989e2a
nt_num_divisors_compute_v1_1742523217_4971
Let $n$ be the sum of the first $k$ positive integers, where $k$ is the number of positive integers $m$ at most 1848 for which 14 divides the $m$-th Fibonacci number. Let $d(n)$ denote the number of positive divisors of $n$. Compute the remainder when $91177 \cdot d(n)$ is divided by 51696.
11,344
graphs = [ Graph( let={ "_n": Const(51696), "n": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1848)), Divides(divisor=Const(14), dividend=Fibonacci(arg=Var(name='n')))))), expr=Var("k")),...
NT
null
COMPUTE
sympy
COUNT_FIB_DIVISIBLE
[ "COUNT_FIB_DIVISIBLE/SUM_ARITHMETIC" ]
a57ec2
nt_num_divisors_compute_v1
null
7
0
[ "COUNT_FIB_DIVISIBLE", "SUM_ARITHMETIC" ]
2
0.002
2026-02-08T10:41:39.000355Z
{ "verified": true, "answer": 11344, "timestamp": "2026-02-08T10:41:39.002000Z" }
203254
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": 2496 }, "timestamp": "2026-02-14T08:23:16.820Z", "answer": 11344 }, ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC"...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
0169c4
nt_sum_over_divisible_v1_48377204_884
Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 21316$ and $n$ is divisible by $62$. Let $r$ be the sum of all elements in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $u$ be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Let $P$...
17,028
graphs = [ Graph( let={ "_m": Const(36), "_n": Const(98947), "upper": Const(21316), "divisor": Const(62), "result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"),...
NT
COMB
SUM
sympy
B3
[ "B3/MAX_PRIME_BELOW" ]
2f1f5e
nt_sum_over_divisible_v1
bell_mod
6
0
[ "B3", "MAX_PRIME_BELOW" ]
2
2.66
2026-02-08T15:45:10.544755Z
{ "verified": true, "answer": 17028, "timestamp": "2026-02-08T15:45:13.205097Z" }
1f6c81
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": 1215 }, "timestamp": "2026-02-16T13:18:42.650Z", "answer": 17028 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
d14ed8
sequence_fibonacci_compute_v1_397696148_2681
Let $p$ and $q$ be positive integers such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Determine the number of such integers $p$. Let $n$ be the smallest divisor of 19343 that is greater than or equal to this count. Compute the $n$th Fibonacci number.
28,657
graphs = [ Graph( let={ "_m": Const(19343), "_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=GCD(a=Var(name='p'), b=Var(na...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MIN_PRIME_FACTOR" ]
52cee2
sequence_fibonacci_compute_v1
null
5
0
[ "COPRIME_PAIRS", "MIN_PRIME_FACTOR" ]
2
0.002
2026-02-08T13:29:03.382794Z
{ "verified": true, "answer": 28657, "timestamp": "2026-02-08T13:29:03.384686Z" }
db8219
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": 1461 }, "timestamp": "2026-02-15T16:41:55.698Z", "answer": 28657 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "st...
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
191767
modular_mod_compute_v1_1978505735_4713
Let $m = 2$ and $n = 57673$. Define $S$ as the set of all integers $n_1$ such that $1 \leq n_1 \leq 96$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{3}$. Let $a$ be the largest prime number less than or equal to the number of elements in $S$. Let $m' = 13924$ and define $r$ as the remainder when $a$ i...
49,587
graphs = [ Graph( let={ "_m": Const(2), "_n": Const(57673), "a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(96)),...
NT
null
COMPUTE
sympy
L3C
[ "L3C/MAX_PRIME_BELOW" ]
8ff24e
modular_mod_compute_v1
null
6
0
[ "L3C", "MAX_PRIME_BELOW" ]
2
0.002
2026-02-08T18:27:11.822055Z
{ "verified": true, "answer": 49587, "timestamp": "2026-02-08T18:27:11.824422Z" }
a1a962
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 214, "completion_tokens": 3483 }, "timestamp": "2026-02-18T17:40:11.447Z", "answer": 49587 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "L3C", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" }, { "lemma": "V7", "status": "no" },...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
1d336a
modular_count_residue_v1_1874849503_1130
Let $N = 68121$. Let $m$ be the smallest divisor of $2146981$ that is greater than or equal to $2$. Let $r = 9$. Consider the set of all positive integers $n$ such that $1 \leq n \leq N$ and $n \equiv r \pmod{m}$. Compute the number of elements in this set.
4,007
graphs = [ Graph( let={ "upper": Const(68121), "m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(2146981))))), "r": Const(9), "result": CountOverSet(set=SolutionsSet(var=Var("n"), con...
NT
null
COUNT
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
modular_count_residue_v1
null
3
0
[ "MIN_PRIME_FACTOR" ]
1
2.504
2026-02-08T13:38:36.068253Z
{ "verified": true, "answer": 4007, "timestamp": "2026-02-08T13:38:38.571862Z" }
854004
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 195, "completion_tokens": 1236 }, "timestamp": "2026-02-10T01:29:28.089Z", "answer": 4007 }, { "i...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -5.49, "mid": 0.03, "hi": 6.12 }