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c7c25e
nt_count_coprime_and_v1_2051736721_4283
Let $k_1 = 8$. Let $p$ be a prime number such that $2 \leq p \leq 5$, and define $m$ to be the largest such prime. Define $$ k_2 = \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor, $$ where $\phi$ denotes Euler's totient function. Let $n_1$ be a positive integer such that $1 \leq n_1 \leq 46147$, $\gcd(n_...
18,315
graphs = [ Graph( let={ "_n": Const(2), "upper": Const(46147), "k1": Const(8), "k2": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))), expr=Mu...
NT
null
COUNT
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW/K2" ]
7eb1ee
nt_count_coprime_and_v1
null
5
0
[ "K2", "MAX_PRIME_BELOW" ]
2
4.577
2026-02-08T17:52:09.487534Z
{ "verified": true, "answer": 18315, "timestamp": "2026-02-08T17:52:14.064308Z" }
9b3ad8
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 223, "completion_tokens": 1768 }, "timestamp": "2026-02-18T10:00:15.167Z", "answer": 18315 }, ...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K2", "status": "ok_later" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "V3", "stat...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
a3fbfa
comb_bell_compute_v1_124444284_2139
Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 519750$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $P$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Let $s$ be the minimum value of $x +...
4,140
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=519750)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1...
NT
COMB
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/B3" ]
3f0fb0
comb_bell_compute_v1
null
7
0
[ "B3", "COPRIME_PAIRS" ]
2
0.003
2026-02-08T04:20:45.614022Z
{ "verified": true, "answer": 4140, "timestamp": "2026-02-08T04:20:45.617080Z" }
c17185
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 249, "completion_tokens": 1623 }, "timestamp": "2026-02-10T16:32:44.239Z", "answer": 4140 }, { "...
1
[ { "lemma": "B3", "status": "ok_later" }, { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K13", "status": "no" }, ...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
12b2cc
nt_min_coprime_above_v1_1125832087_760
Let $\_n = 2$. Define $\text{start}$ to be the smallest integer $d \geq \_n$ that divides $1052651$. Let $\text{upper}$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 5$ and $1 \leq j \leq 223$. Let $\text{result}$ be the smallest integer $n$ such that $\text{start} < n \leq \text{upper}$ and $\gcd(n,...
5,975
graphs = [ Graph( let={ "_n": Const(2), "start": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1052651))))), "upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const...
NT
null
EXTREMUM
sympy
B3
[ "B3", "MIN_PRIME_FACTOR", "COUNT_CARTESIAN" ]
fd9d9a
nt_min_coprime_above_v1
negation_mod
6
0
[ "B3", "COUNT_CARTESIAN", "MIN_PRIME_FACTOR" ]
3
0.026
2026-02-08T03:15:34.444588Z
{ "verified": true, "answer": 5975, "timestamp": "2026-02-08T03:15:34.470107Z" }
e19805
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 322, "completion_tokens": 1623 }, "timestamp": "2026-02-10T13:11:53.783Z", "answer": 6981 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "MAX_...
{ "lo": 1.96, "mid": 5.23, "hi": 8.52 }
f52bb2
alg_linear_system_2x2_v1_1218484723_638
Let $\det = 6 \cdot (-10) - 8 \cdot 5$, $M = 142977 \cdot (-10) - 184186 \cdot 5$, and $R = 6 \cdot 184186 - \left|\{ v : 20 \le v \le 1280,\ \text{there exist integers } a, b \text{ with } 1 \le a, b \le 8 \text{ such that } 20 \cdot a^2 = v \}\right| \cdot 142977$. Let $S = \frac{M}{\det} + \frac{R}{\det}$ and $Q = |...
23,894
graphs = [ Graph( let={ "_n": Const(8), "num_x": Sub(Mul(Const(142977), Const(-10)), Mul(Const(184186), Const(5))), "num_y": Sub(Mul(Const(6), Const(184186)), Mul(CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(20)), Leq(Var("v"), Const(1280)...
ALG
null
COMPUTE
sympy
QF_PSD_DISTINCT
[ "QF_PSD_DISTINCT" ]
a8f9cb
alg_linear_system_2x2_v1
null
4
0
[ "QF_PSD_DISTINCT" ]
1
0.004
2026-02-25T02:22:54.948693Z
{ "verified": true, "answer": 23894, "timestamp": "2026-02-25T02:22:54.952949Z" }
8638fd
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 269, "completion_tokens": 1064 }, "timestamp": "2026-03-28T23:32:56.292Z", "answer": 23894 }, { "...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_DISTINCT", "status": "ok" } ]
{ "lo": -4.31, "mid": -1.92, "hi": 0.62 }
273052
nt_min_coprime_above_v1_48377204_2006
Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 33285$ and $$ n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}. $$ Let $T$ be the set of all integers $n_1$ such that $n_1 > |S|$, $n_1 \leq 3409$, and $\gcd(n_1, 374) = 1$. Compute the minimum element of $T$.
3,027
graphs = [ Graph( let={ "start": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(33285)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))), "upper": Const(3409), ...
NT
null
EXTREMUM
sympy
L3C
[ "L3C" ]
73f8b0
nt_min_coprime_above_v1
null
5
0
[ "L3C" ]
1
0.061
2026-02-08T16:33:01.256294Z
{ "verified": true, "answer": 3027, "timestamp": "2026-02-08T16:33:01.316897Z" }
7bdcc4
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 158, "completion_tokens": 1280 }, "timestamp": "2026-02-17T06:24:05.406Z", "answer": 3027 }, {...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "L3C", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V3", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
edca53
diophantine_fbi2_min_v1_1520064083_311
Let $d$ be an integer such that $5 \le d \le 24$, $d$ divides $14$, and $\frac{14}{d} \ge 2$. Determine the value of the smallest such $d$.
7
graphs = [ Graph( let={ "k": Const(14), "a": Const(4), "b": Const(1), "upper": Const(24), "result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref...
NT
null
EXTREMUM
sympy
OMEGA_ONE
[ "OMEGA_ONE", "LIN_FORM", "WILSON" ]
a6aa9b
diophantine_fbi2_min_v1
null
3
0
[ "LIN_FORM", "OMEGA_ONE", "WILSON" ]
3
0.052
2026-02-08T03:14:37.507153Z
{ "verified": true, "answer": 7, "timestamp": "2026-02-08T03:14:37.559248Z" }
ebc60c
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 159, "completion_tokens": 425 }, "timestamp": "2026-02-10T13:37:08.681Z", "answer": 7 }, { "id": ...
1
[ { "lemma": "K17", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "OMEGA_ONE", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V1", "status": "no" },...
{ "lo": -9.14, "mid": -6.05, "hi": -3.74 }
3cf431
algebra_poly_eval_v1_865884756_3350
Let $n = 8$ and $m = 24$. Let $S$ be the set of all integers $t$ such that $15 \leq t \leq 42$ and $t = 6a + 9b$ for some integers $a$ with $1 \leq a \leq 4$ and $b$ with $1 \leq b \leq 2$. Let $k$ be the number of elements in $S$. Compute the value of $8 \cdot 24^2 + k \cdot 24 - 7$, take its absolute value, find the ...
4,140
graphs = [ Graph( let={ "_n": Const(8), "n": Const(24), "result": Sum(Mul(Ref("_n"), Pow(Ref("n"), Const(2))), Mul(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'), rig...
COMB
null
COMPUTE
sympy
K13
[ "LIN_FORM" ]
7b2633
algebra_poly_eval_v1
null
5
0
[ "K13", "LIN_FORM" ]
2
0.011
2026-02-08T17:19:10.999592Z
{ "verified": true, "answer": 4140, "timestamp": "2026-02-08T17:19:11.010171Z" }
e7604c
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 193, "completion_tokens": 760 }, "timestamp": "2026-02-17T23:32:43.258Z", "answer": 4140 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V8", "sta...
{ "lo": -8, "mid": -4.75, "hi": -2.28 }
8664e8
geo_count_lattice_rect_v1_784195855_3393
Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 30$ and $0 \leq y \leq 95$. Multiply this number by $79143$, and find the remainder when the result is divided by $76723$.
66,681
graphs = [ Graph( let={ "a": Const(30), "b": Const(95), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), "Q": Mod(value=Mul(Const(79143), Ref("result")), modulus=Const(76723)), }, goal=Ref("Q"), ) ]
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
4
0
null
null
0
2026-02-08T06:24:31.377575Z
{ "verified": true, "answer": 66681, "timestamp": "2026-02-08T06:24:31.377953Z" }
7a95e0
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 170, "completion_tokens": 2564 }, "timestamp": "2026-02-24T06:10:44.173Z", "answer": 66681 }, { "...
1
[]
{ "lo": -2.46, "mid": 0.47, "hi": 3.59 }
171182
nt_sum_divisors_mod_v1_1978505735_6492
Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 129600$. Let $\sigma$ be the sum of the positive divisors of $n$. Let $M = 11159$. Compute the remainder when $50917 \cdot \sigma$ is divided by $53068$.
52,614
graphs = [ Graph( let={ "_n": Const(53068), "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(129600)))), expr=Sum(Var("x"), Var("y"))...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_sum_divisors_mod_v1
null
4
0
[ "B3" ]
1
0.004
2026-02-08T19:36:31.222090Z
{ "verified": true, "answer": 52614, "timestamp": "2026-02-08T19:36:31.225652Z" }
174a8a
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 127, "completion_tokens": 2244 }, "timestamp": "2026-02-18T23:01:04.849Z", "answer": 52614 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
a3952d
nt_sum_gcd_range_mod_v1_865884756_2790
Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 640000$. Let $S = \sum_{n=1}^{N} \gcd(n, 108)$. Compute the remainder when $S$ is divided by 11657.
9,536
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(640000)))), expr=Sum(Var("x"), Var("y")))), "k": Const(108),...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_sum_gcd_range_mod_v1
null
4
0
[ "B3" ]
1
0.347
2026-02-08T16:56:13.506813Z
{ "verified": true, "answer": 9536, "timestamp": "2026-02-08T16:56:13.853342Z" }
2a518f
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": 2189 }, "timestamp": "2026-02-17T16:10:32.151Z", "answer": 9536 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
037087
nt_sum_totient_over_divisors_v1_168721529_636
Let $n = 64160$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function.
64,160
graphs = [ Graph( let={ "n": Const(64160), "result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))), }, goal=Ref("result"), ) ]
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MOBIUS_SQUAREFREE", "LTE_DIFF/MOBIUS_SQUAREFREE", "LIN_FORM/MOBIUS_SQUAREFREE", "WILSON" ]
b1680b
nt_sum_totient_over_divisors_v1
null
3
0
[ "COPRIME_PAIRS", "LIN_FORM", "LTE_DIFF", "MOBIUS_SQUAREFREE", "WILSON" ]
5
0.063
2026-02-08T13:10:13.377538Z
{ "verified": true, "answer": 64160, "timestamp": "2026-02-08T13:10:13.440604Z" }
92a0e0
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 153, "completion_tokens": 491 }, "timestamp": "2026-02-09T07:15:27.747Z", "answer": 64160 }, { "i...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "ok" ...
{ "lo": -6.97, "mid": -4.58, "hi": -1.65 }
0aa07a
comb_count_surjections_v1_124444284_1886
Let $n = 5$ and $k = 5$. Define $S(n,k)$ to be the Stirling number of the second kind. Compute the value of $42^2 - k! \cdot S(n,k)$.
1,644
graphs = [ Graph( let={ "n": Const(5), "k": Const(5), "result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))), "_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(42)), right=IntegerRange(start=Const(1), ...
COMB
null
COUNT
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
009729
comb_count_surjections_v1
negation_mod
3
0
[ "COUNT_CARTESIAN" ]
1
0.003
2026-02-08T04:11:55.089876Z
{ "verified": true, "answer": 1644, "timestamp": "2026-02-08T04:11:55.093032Z" }
e28ed2
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": 232 }, "timestamp": "2026-02-23T23:41:49.703Z", "answer": 1644 }, { "id...
2
[ { "lemma": "COUNT_CARTESIAN", "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": "V8_SU...
{ "lo": -10, "mid": -7.79, "hi": -5.57 }
d1b9e3
sequence_lucas_compute_v1_458359167_1323
Let $c = 2$ and $m = 2$. Define $N$ to be the largest prime number $n$ such that $n \ge m$ and $n$ is at most the number of positive integers $k$ with $1 \le k \le 156$ for which the sum of the digits of $k$ is divisible by $c$. Let $p$ be the number of prime numbers less than or equal to $N$ and at least 2. Compute th...
24,476
graphs = [ Graph( let={ "_c": Const(2), "_m": Const(2), "_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(156)), Eq(M...
NT
null
COMPUTE
sympy
L3B
[ "L3B/MAX_PRIME_BELOW/COUNT_PRIMES" ]
5bb2ab
sequence_lucas_compute_v1
null
6
0
[ "COUNT_PRIMES", "L3B", "MAX_PRIME_BELOW" ]
3
0.002
2026-02-08T04:33:03.864294Z
{ "verified": true, "answer": 24476, "timestamp": "2026-02-08T04:33:03.866755Z" }
1dd1e9
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 222, "completion_tokens": 3027 }, "timestamp": "2026-02-10T17:01:12.873Z", "answer": 24476 }, { ...
1
[ { "lemma": "COUNT_PRIMES", "status": "ok_later" }, { "lemma": "K13", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "L3B", "status": "ok" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok_later" ...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
47b530
antilemma_k2_v1_458359167_1436
Let $S = \sum_{k=1}^{337} \phi(k) \left\lfloor \frac{337}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Compute $S$.
56,953
graphs = [ Graph( let={ "x": Summation(var="k", start=Const(1), end=Const(337), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(337), Var("k"))))), }, goal=Ref("x"), ) ]
NT
COMB
COMPUTE
sympy
VIETA_SUM
[ "K2" ]
6897ab
antilemma_k2_v1
null
5
0
[ "K2", "VIETA_SUM" ]
2
0.005
2026-02-08T04:36:46.698919Z
{ "verified": true, "answer": 56953, "timestamp": "2026-02-08T04:36:46.704113Z" }
052d52
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 161, "completion_tokens": 903 }, "timestamp": "2026-02-10T17:20:42.366Z", "answer": 56953 }, { "...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
ef7cd8
lin_form_endings_v1_1978505735_4625
Let $a = 105$, $b = 45$, and $k = 59$. Let $d = \gcd(a, b)$, and let $m = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor$. Define $x$ to be the remainder when $16142 \cdot m$ is divided by $59374$. Find the value of $x$.
2,394
graphs = [ Graph( let={ "a_coeff": Const(105), "b_coeff": Const(45), "k_val": Const(59), "step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")), "_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))), "_scale_k": Const(1...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
5
null
[ "LIN_FORM" ]
1
0.001
2026-02-08T18:24:38.738535Z
{ "verified": true, "answer": 2394, "timestamp": "2026-02-08T18:24:38.739745Z" }
c18ad0
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 130, "completion_tokens": 950 }, "timestamp": "2026-02-18T16:54:58.029Z", "answer": 2394 }, { ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
a1ab11
geo_count_lattice_rect_v1_1520064083_10244
Let $a = 66$ and $b = 21$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Compute $\text{result}$.
1,474
graphs = [ Graph( let={ "a": Const(66), "b": Const(21), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), }, goal=Ref("result"), ) ]
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
3
0
null
null
0.001
2026-02-08T11:18:37.041179Z
{ "verified": true, "answer": 1474, "timestamp": "2026-02-08T11:18:37.041776Z" }
859793
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 165, "completion_tokens": 288 }, "timestamp": "2026-02-24T13:23:43.364Z", "answer": 1474 }, { "id...
1
[]
{ "lo": -9.23, "mid": -6.18, "hi": -4.06 }
d5f6a0
comb_catalan_compute_v1_124444284_8218
Let $T$ be the set of all integers $t$ with $7 \leq t \leq 30$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 10$, and $t = 5a + 2b$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2$ equals the number of elements in $T$. ...
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=...
COMB
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM/COMB1" ]
268a62
comb_catalan_compute_v1
null
6
0
[ "COMB1", "LIN_FORM" ]
2
0.002
2026-02-08T09:36:30.141218Z
{ "verified": true, "answer": 16796, "timestamp": "2026-02-08T09:36:30.143188Z" }
ac0a81
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 241, "completion_tokens": 1415 }, "timestamp": "2026-02-24T11:33:38.642Z", "answer": 16796 }, { "...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V8", "status": "...
{ "lo": -5.97, "mid": -3.97, "hi": -1.93 }
af1cec
modular_count_residue_v1_717093673_2050
Let $m = \sum_{k=1}^{5} k$. Let $r = 13$ and $U = 49729$. Compute the number of positive integers $n$ such that $1 \leq n \leq U$ and $n \equiv r \pmod{m}$. Let this count be $C$. Find the value of $44121 \cdot C \bmod{89660}$.
25,655
graphs = [ Graph( let={ "_n": Const(89660), "upper": Const(49729), "m": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")), "r": Const(13), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Le...
NT
null
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
modular_count_residue_v1
null
3
0
[ "SUM_ARITHMETIC" ]
1
2.52
2026-02-08T16:28:19.503763Z
{ "verified": true, "answer": 25655, "timestamp": "2026-02-08T16:28:22.023746Z" }
24ead0
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 132, "completion_tokens": 1457 }, "timestamp": "2026-02-17T05:37:43.466Z", "answer": 25655 }, ...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V5", "status": "no"...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
4d31e8
alg_qf_psd_sum_v1_1218484723_6441
Let $M = \min\{ 41a_1^2 + 16b_1^2 + 32a_1b_1 : a_1, b_1 \in \{1, 2, \dots, 8\} \}$. Find the remainder when $$\sum_{a=1}^{M} \sum_{b=1}^{89} \left(17a^2 - 28ab + 13b^2\right)$$ is divided by $99741$.
6,396
graphs = [ Graph( let={ "_n": Const(2), "result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]),...
ALG
null
COMPUTE
sympy
QF_PSD_MIN
[ "QF_PSD_MIN" ]
c66ce3
alg_qf_psd_sum_v1
null
5
0
[ "QF_PSD_MIN" ]
1
0.021
2026-02-25T08:00:13.063668Z
{ "verified": true, "answer": 6396, "timestamp": "2026-02-25T08:00:13.084354Z" }
182543
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 220, "completion_tokens": 2626 }, "timestamp": "2026-03-30T01:43:25.755Z", "answer": 6396 }, { "i...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_MIN", "status": "ok" } ]
{ "lo": -3.33, "mid": 1.03, "hi": 5.26 }
98ecb3
nt_count_divisible_and_v1_1248542787_153
Let $t$ be an integer. Define $S$ as the set of all integers $t$ such that $7 \leq t \leq 22$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 6$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Let $d_1$ be the largest integer $k$ such that $11^k$ divides $|S|^{285311670611} - \phi(1)^{285311670611}$. Let $d_2 = 1...
45,436
graphs = [ Graph( let={ "_n": Const(11), "upper": Const(94968), "d1": MaxKDivides(target=Sub(Pow(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))...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM/LTE_DIFF", "ONE_PHI_1" ]
da7f9f
nt_count_divisible_and_v1
null
7
0
[ "LIN_FORM", "LTE_DIFF", "ONE_PHI_1" ]
3
3.576
2026-02-08T02:58:25.170319Z
{ "verified": true, "answer": 45436, "timestamp": "2026-02-08T02:58:28.745991Z" }
ee6647
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 320, "completion_tokens": 7979 }, "timestamp": "2026-02-09T13:39:43.105Z", "answer": 45436 }, { ...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "ok_later" }, { "lemma": "MOD_ADD", "status": "no"...
{ "lo": -6.49, "mid": 0.51, "hi": 7.52 }
243588
sequence_fibonacci_compute_v1_124444284_385
Let $d$ be a positive divisor of 20677. Define $S$ to be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 18$. Let $m$ be the smallest integer $d$ such that $d \geq |S|$. Compute the remainder when $44121 \cdot F_m$ is divided by 95464, wh...
50,281
graphs = [ Graph( let={ "_m": Const(44121), "_n": Const(95464), "n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(l...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MIN_PRIME_FACTOR" ]
52cee2
sequence_fibonacci_compute_v1
null
6
0
[ "COPRIME_PAIRS", "MIN_PRIME_FACTOR" ]
2
0.003
2026-02-08T03:14:43.235565Z
{ "verified": true, "answer": 50281, "timestamp": "2026-02-08T03:14:43.239041Z" }
559418
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 237, "completion_tokens": 6886 }, "timestamp": "2026-02-09T16:52:26.425Z", "answer": 49831 }, { ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok_later" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V5", ...
{ "lo": 1.71, "mid": 5.04, "hi": 8.38 }
33ee3a
nt_max_prime_below_v1_168721529_208
Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $n \geq |S|$ and $n \leq 77841$. Determine the value of the largest element in $T$.
77,839
graphs = [ Graph( let={ "upper": Const(77841), "result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V...
NT
null
EXTREMUM
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
nt_max_prime_below_v1
null
4
0
[ "COPRIME_PAIRS" ]
1
4.399
2026-02-08T12:54:16.792697Z
{ "verified": true, "answer": 77839, "timestamp": "2026-02-08T12:54:21.191474Z" }
4981e1
CC BY 4.0
[ { "id": 4, "model": "NousResearch/Hermes-4-405B", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 149, "completion_tokens": 4575 }, "timestamp": "2026-02-09T14:30:04.657Z", "answer": 77839 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -6.97, "mid": -4.58, "hi": -1.65 }
b8ce0f
nt_count_primes_v1_2051736721_5214
Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 400$. Let $c$ be the number of positive integers $n_1$ with $1 \le n_1 \le s$ such that $15$ divides the $n_1$-th Fibonacci number. Determine the value of the number of prime numbers $n$ such that $c \le n \le 1...
1,900
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(400)))), expr=Sum(Var("x"), Var("y")))), "upper": Const(163...
NT
null
COUNT
sympy
B3
[ "B3/COUNT_FIB_DIVISIBLE" ]
9b7a57
nt_count_primes_v1
null
6
0
[ "B3", "COUNT_FIB_DIVISIBLE" ]
2
0.358
2026-02-08T18:25:30.104562Z
{ "verified": true, "answer": 1900, "timestamp": "2026-02-08T18:25:30.462789Z" }
41bad4
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 149, "completion_tokens": 2461 }, "timestamp": "2026-02-18T16:47:11.613Z", "answer": 1900 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok_later" }, { "lemma": "K15", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status"...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
2622c0
alg_poly3_sum_v1_1218484723_6850
Find the remainder when $$ \sum_{a=1}^{327} \sum_{b=1}^{327} \left( 39a^2b + \sum_{k=1}^{5} k a b^2 - 63a^3 - 26b^3 \right) $$ is divided by $75322$.
15,874
graphs = [ Graph( let={ "_n": Const(5), "result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(327)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(327)))), expr=Sum(Mul(Const(...
ALG
null
COMPUTE
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
alg_poly3_sum_v1
null
4
0
[ "SUM_ARITHMETIC" ]
1
0.229
2026-02-25T08:18:46.564856Z
{ "verified": true, "answer": 15874, "timestamp": "2026-02-25T08:18:46.793979Z" }
058db6
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 183, "completion_tokens": 11407 }, "timestamp": "2026-03-30T02:50:28.882Z", "answer": 15874 }, { ...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" } ]
{ "lo": 1.53, "mid": 4.7, "hi": 7.23 }
f06aef
algebra_vieta_sum_v1_601307018_7153
Let $M$ be the sum of all positive integers $x$ satisfying $x^2 - 9x + d = 0$, where $d$ is the largest positive divisor of $342$ such that $d^2 \leq 342$. Find the remainder when $44121 \cdot M$ is divided by $99191€.
325
graphs = [ Graph( let={ "_n": Const(44121), "result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-9), Var("x")), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Cons...
NT
null
COMPUTE
sympy
POLY_ORBIT_HENSEL
[ "B3_CLOSEST" ]
25e610
algebra_vieta_sum_v1
null
4
0
[ "B3_CLOSEST", "POLY_ORBIT_HENSEL" ]
2
0.393
2026-03-10T07:46:16.995883Z
{ "verified": true, "answer": 325, "timestamp": "2026-03-10T07:46:17.388510Z" }
4a9ccc
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 183, "completion_tokens": 802 }, "timestamp": "2026-04-19T06:06:14.662Z", "answer": 325 }, { "id...
1
[ { "lemma": "B3_CLOSEST", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V8", "status": "no" } ]
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
604965
nt_count_coprime_v1_124444284_3530
Let $r$ be the sum of all real numbers $x$ such that $x^2 - 17x - 4898 = 0$. Let $N$ be the number of positive integers $n$ less than or equal to $34969$ for which $\gcd(n, r) = 1$. Compute $N$.
32,912
graphs = [ Graph( let={ "upper": Const(34969), "k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-17), Var("x")), Const(-4898)), Const(0)))), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"),...
NT
null
COUNT
sympy
VIETA_SUM
[ "VIETA_SUM" ]
b33a7a
nt_count_coprime_v1
null
4
0
[ "VIETA_SUM" ]
1
5.504
2026-02-08T05:26:20.599617Z
{ "verified": true, "answer": 32912, "timestamp": "2026-02-08T05:26:26.103173Z" }
2d2b06
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": 582 }, "timestamp": "2026-02-12T08:36:24.664Z", "answer": 32912 }, {...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" }, { "lemma": "VIETA_SUM", "stat...
{ "lo": -5.55, "mid": -3.01, "hi": 0.32 }
275798
modular_min_linear_v1_1248542787_299
Let $\phi(n)$ denote Euler's totient function. Find the smallest nonnegative integer $x$ such that $20673x \equiv 14703 \pmod{38018}$ and $x \leq 38018$. Let this value be $r$. Determine the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $|r| + 2$.
31,644
graphs = [ Graph( let={ "a": Const(20673), "b": Const(14703), "m": Const(38018), "result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=Const(1))), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("...
NT
null
EXTREMUM
sympy
ONE_PHI_1
[ "ONE_PHI_1" ]
f6b5a5
modular_min_linear_v1
null
6
0
[ "ONE_PHI_1" ]
1
2.225
2026-02-08T03:03:03.936921Z
{ "verified": true, "answer": 31644, "timestamp": "2026-02-08T03:03:06.162196Z" }
0cf6c0
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 195, "completion_tokens": 6316 }, "timestamp": "2026-02-09T14:57:16.373Z", "answer": 31644 }, { ...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "ONE_PHI_1", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" ...
{ "lo": -6.49, "mid": 0.51, "hi": 7.52 }
ba2d13
nt_count_with_divisor_count_v1_2051736721_2748
Let $n$ be a positive integer such that $1 \leq n \leq 27225$ and the number of positive divisors of $n$ is exactly 5. Let $A$ be the number of such integers $n$. Let $B$ be the smallest divisor of 35 that is at least 2. Compute $B - A$.
0
graphs = [ Graph( let={ "upper": Const(27225), "div_count": Const(5), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))), "_c": MinOverSet(s...
NT
null
COUNT
sympy
MAX_PRIME_BELOW
[ "MIN_PRIME_FACTOR" ]
fd27b3
nt_count_with_divisor_count_v1
negation_mod
3
0
[ "MAX_PRIME_BELOW", "MIN_PRIME_FACTOR" ]
2
3.786
2026-02-08T16:53:12.047214Z
{ "verified": true, "answer": 0, "timestamp": "2026-02-08T16:53:15.832859Z" }
64575f
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": 672 }, "timestamp": "2026-02-17T14:47:10.594Z", "answer": 0 }, { ...
1
[ { "lemma": "K18", "status": "no" }, { "lemma": "K5", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
07ea97
modular_modexp_compute_v1_1742523217_3939
Let $e$ be the number of integers $n$ with $1 \leq n \leq 1057$ such that the sum of the decimal digits of $n$ is odd. Compute the remainder when $41^e$ is divided by $17424$.
17,321
graphs = [ Graph( let={ "_n": Const(2), "a": Const(41), "e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1057)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))), "m": Const(17424), ...
NT
null
COMPUTE
sympy
L3B
[ "L3B" ]
cc148f
modular_modexp_compute_v1
null
5
0
[ "L3B" ]
1
0.001
2026-02-08T06:09:23.104389Z
{ "verified": true, "answer": 17321, "timestamp": "2026-02-08T06:09:23.105361Z" }
db7972
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 102, "completion_tokens": 3896 }, "timestamp": "2026-02-12T20:09:32.464Z", "answer": 17321 }, ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "L3B", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V5", "status": "n...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
b4a087_l
geo_count_lattice_rect_v1_784195855_7193
Let $a = 349$ and $b = 105$. Define $R$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $r$ be the remainder when $|R|$ is divided by $11$. Compute the Bell number $B_r$, which counts the number of partitions of a set of $r$ elements. Find the value of $B_r$.
1
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
4
0
null
null
0.002
2026-02-08T09:08:25.147989Z
{ "verified": false, "answer": 4140, "timestamp": "2026-02-08T09:08:25.149540Z" }
10ea69
b4a087
legacy_text
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 206, "completion_tokens": 1630 }, "timestamp": "2026-02-24T10:34:52.718Z", "answer": 4140 }, { "i...
1
[]
{ "lo": -3.84, "mid": -1.67, "hi": 1.32 }
1da02c
alg_poly_preperiod_count_v1_601307018_576
Let $N = (a^2 + a - 12) \bmod 31$, $M = (N^2 + N - 12) \bmod 31$, $R = (M^2 + M - 12) \bmod 31$, and $S = (R^2 + R - 12) \bmod 31$. Find the number of non-negative integers $a$ with $0 \leq a \leq 12523$ such that $S = N$, $M \neq N$, and $R \neq N$.
4,848
graphs = [ Graph( let={ "p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-12)), modulus=Const(31)), "p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-12)), modulus=Const(31)), "p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-12)), ...
ALG
null
COUNT
sympy
POLY_ORBIT_COUNT
[ "POLY_ORBIT_COUNT" ]
4ad965
alg_poly_preperiod_count_v1
null
6
null
[ "POLY_ORBIT_COUNT" ]
1
0.042
2026-03-10T01:06:33.526138Z
{ "verified": true, "answer": 4848, "timestamp": "2026-03-10T01:06:33.568187Z" }
b0b05e
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 232, "completion_tokens": 9022 }, "timestamp": "2026-03-28T23:26:42.791Z", "answer": 4848 }, { "i...
1
[ { "lemma": "POLY_ORBIT_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": 1.27, "mid": 3.84, "hi": 5.91 }
64e7a6
antilemma_k3_v1_2051736721_2999
Let $n = 36998$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function.
36,998
graphs = [ Graph( let={ "_n": Const(36998), "x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), }, goal=Ref("x"), ) ]
NT
COMB
COMPUTE
sympy
K3
[ "K3" ]
54c41e
antilemma_k3_v1
null
3
0
[ "K3" ]
1
0.001
2026-02-08T17:03:49.145362Z
{ "verified": true, "answer": 36998, "timestamp": "2026-02-08T17:03:49.146248Z" }
2f9907
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 100, "completion_tokens": 1401 }, "timestamp": "2026-02-16T08:57:47.839Z", "answer": 10720 }, { "id": 11...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -8.26, "mid": -5.01, "hi": -1.76 }
e2bed7
sequence_lucas_compute_v1_655260480_4849
Let $m = 18$. Define $s = \sum_{d \mid m} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $n$ be the largest positive divisor of 342 that is less than or equal to $s$. Let $L_n$ denote the $n$th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remaind...
45,417
graphs = [ Graph( let={ "_m": Const(18), "_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))), "n": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), Ref("_n")), Divides(divisor=Var("d1"), dividen...
NT
null
COMPUTE
sympy
K3
[ "K3/MAX_DIVISOR" ]
43ff77
sequence_lucas_compute_v1
null
4
0
[ "K3", "MAX_DIVISOR" ]
2
0.002
2026-02-08T18:09:01.442610Z
{ "verified": true, "answer": 45417, "timestamp": "2026-02-08T18:09:01.444939Z" }
a52776
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 179, "completion_tokens": 2029 }, "timestamp": "2026-02-18T14:57:31.297Z", "answer": 45417 }, ...
1
[ { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": "ok_later" }, { "lemma": "V3", "status": "no" }, { "lemma": "V...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
b8b7bb
nt_sum_divisors_mod_v1_153355830_1142
Let $n$ be the number of integers $t$ such that $7 \leq t \leq 372$ and $t = 3a + 4b$ for some positive integers $a \leq 120$ and $b \leq 3$. Let $M = 10861$. Compute the remainder when the sum of all positive divisors of $n$ is divided by $M$.
1,170
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=120)), Geq(left=Var(name='b'), right=Const(value...
NT
null
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
nt_sum_divisors_mod_v1
null
5
0
[ "LIN_FORM" ]
1
0.002
2026-02-08T04:25:02.117796Z
{ "verified": true, "answer": 1170, "timestamp": "2026-02-08T04:25:02.119740Z" }
6ef18a
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 130, "completion_tokens": 1314 }, "timestamp": "2026-02-12T20:26:00.767Z", "answer": 1170 }, {...
1
[ { "lemma": "K14", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
09b956
nt_euler_phi_compute_v1_124444284_713
Let $m_0=67081$. Let $A$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq=24$, $\gcd(p,q)=1$, and $p<q$. Let $n_0$ be the number of elements in $A$. Let $B$ be the set of all integers $d$ such that $d\ge n_0$ and $d$ divides $20677$, and let $n_1$ be the smallest element o...
55,944
graphs = [ Graph( let={ "_m": Const(67081), "_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(nam...
NT
null
COMPUTE
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MIN_PRIME_FACTOR/EULER_TOTIENT_SUM", "WILSON" ]
9caf8d
nt_euler_phi_compute_v1
null
7
2
[ "COPRIME_PAIRS", "EULER_TOTIENT_SUM", "MIN_PRIME_FACTOR", "WILSON" ]
4
0.004
2026-02-08T03:27:56.114481Z
{ "verified": true, "answer": 55944, "timestamp": "2026-02-08T03:27:56.118503Z" }
1b0558
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 323, "completion_tokens": 1676 }, "timestamp": "2026-02-09T20:58:20.613Z", "answer": 55944 }, { "...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "EULER_TOTIENT_SUM", "status": "ok_later" }, { "lemma": "K13", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok_later" }, { "lemma": "MOD_ADD", ...
{ "lo": -6.51, "mid": -0.31, "hi": 5.43 }
f9392e_n
alg_qf_psd_count_v1_1419126231_1899
A game designer assigns scores based on two player stats, $a$ and $b$, each ranging from 1 to 109. A combo is valid if the score expression $10a^2 - 10ab + 5b^2$ equals exactly 31450. How many valid stat combinations $(a, b)$ exist?
10
ALG
null
COUNT
sympy
K2
[ "K2/V8" ]
c69745
alg_qf_psd_count_v1
null
3
null
[ "K2", "V8" ]
2
0.318
2026-02-25T11:27:42.698547Z
null
c3a712
f9392e
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 1, "correct": { "strict": false, "boxed": false, "relaxed": true }, "usage": { "prompt_tokens": 179, "completion_tokens": 23801 }, "timestamp": "2026-03-31T05:13:41.287Z", "answer": 9 }, { "i...
1
[ { "lemma": "K2", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V8", "status": "ok_later" } ]
{ "lo": 1.5, "mid": 4.69, "hi": 7.23 }
85f636
geo_count_lattice_triangle_v1_601307018_8316
Let $R$ be the number of positive integers $v$ with $10 \leq v \leq \min\{ x + y : x,y > 0,\ xy = 1918225,\ x \leq y \}$ such that there exist integers $a,b$ with $1 \leq a,b \leq 11$ satisfying $25a^2 - 24ab + 9b^2 = v$. Let $S = |111 \cdot 128 + 49 \cdot (-64)|$. Let $$T = \gcd(R, 64) + \gcd(|49 - 111|, |128 - 64|) +...
14,319
graphs = [ Graph( let={ "_c": Const(2), "_m": Const(20), "_n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(10)), Leq(Var("v"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a...
GEOM
NT
COUNT
sympy
B3
[ "B3/QF_PSD_DISTINCT/QF_PSD_MIN" ]
b70603
geo_count_lattice_triangle_v1
null
7
0
[ "B3", "QF_PSD_DISTINCT", "QF_PSD_MIN" ]
3
0.022
2026-03-10T08:48:42.525261Z
{ "verified": true, "answer": 14319, "timestamp": "2026-03-10T08:48:42.547737Z" }
41928d
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 337, "completion_tokens": 19191 }, "timestamp": "2026-04-19T08:50:09.980Z", "answer": 14319 }, { ...
1
[ { "lemma": "B3", "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 }
c9fe6b
comb_count_derangements_v1_1915831931_1960
Let $n$ be the largest prime number satisfying $2 \leq n \leq 7$. Compute the number of derangements of $n$ elements.
1,854
graphs = [ Graph( let={ "_n": Const(2), "n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(7)), IsPrime(Var("n1"))))), "result": Subfactorial(arg=Ref(name='n')), }, goal=Ref("result"), ) ]
NT
COMB
COUNT
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
dc3ad3
comb_count_derangements_v1
null
2
0
[ "MAX_PRIME_BELOW" ]
1
0.002
2026-02-08T16:33:10.025474Z
{ "verified": true, "answer": 1854, "timestamp": "2026-02-08T16:33:10.027680Z" }
099a7c
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 79, "completion_tokens": 1000 }, "timestamp": "2026-02-17T06:48:57.391Z", "answer": 1854 }, { ...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K13", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V3", "status": ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
05fef2
geo_count_lattice_rect_v1_717093673_3631
Let $a = 43$ and $b = 65$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Find the value of this number.
2,904
graphs = [ Graph( let={ "a": Const(43), "b": Const(65), "result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')), }, goal=Ref("result"), ) ]
GEOM
null
COUNT
sympy
[]
geo_count_lattice_rect_v1
null
3
0
null
null
0.001
2026-02-08T17:43:56.640227Z
{ "verified": true, "answer": 2904, "timestamp": "2026-02-08T17:43:56.641486Z" }
60098f
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 95, "completion_tokens": 469 }, "timestamp": "2026-02-24T22:58:25.578Z", "answer": 2904 }, { ...
1
[]
{ "lo": -8.52, "mid": -5.43, "hi": -3.2 }
a9d57e
alg_poly4_min_v1_1218484723_729
Find the minimum value of $15552a^3b + 27648ab^3 + 2916a^4 + 18432b^4 + 31104a^2b^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 169$ and $1 \leq b \leq B$, where $B = \max\{ xy : x > 0, y > 0, x + y = N \}$ and $N$ is the number of ordered pairs $(a_1, b_1)$ with $1 \leq a_1, b_1 \leq 30$ ...
95,652
graphs = [ Graph( let={ "_n": Const(169), "result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), MaxOverSet(set=MapOverSet(set=SolutionsSet(...
ALG
null
COMPUTE
sympy
POLY4_COUNT
[ "POLY4_COUNT/B1" ]
9db650
alg_poly4_min_v1
null
6
0
[ "B1", "POLY4_COUNT" ]
2
0.117
2026-02-25T02:28:01.184319Z
{ "verified": true, "answer": 95652, "timestamp": "2026-02-25T02:28:01.301497Z" }
d66d4a
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": 3943 }, "timestamp": "2026-03-10T01:14:14.275Z", "answer": 95652 }, { "...
1
[ { "lemma": "B1", "status": "ok_later" }, { "lemma": "POLY4_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -2.78, "mid": -0.24, "hi": 2.7 }
3f863f
diophantine_fbi2_count_v1_153355830_753
Let $k = 420$. Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 84$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 13$, and $t = 5a + 3b$.\\ Let $D$ be the number of positive divisors $d$ of $k$ such that $6 \leq d \leq |T|$, $\frac{k}{d} \geq 3$, and $\frac{k}{d} \leq...
47,159
graphs = [ Graph( let={ "_n": Const(3), "k": Const(420), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(nam...
NT
null
COUNT
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC", "LIN_FORM" ]
7209d0
diophantine_fbi2_count_v1
null
4
0
[ "LIN_FORM", "SUM_ARITHMETIC" ]
2
0.015
2026-02-08T04:09:49.937382Z
{ "verified": true, "answer": 47159, "timestamp": "2026-02-08T04:09:49.952441Z" }
9c2e38
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 281, "completion_tokens": 4891 }, "timestamp": "2026-02-10T15:32:20.254Z", "answer": 47159 }, { ...
1
[ { "lemma": "K5", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "le...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
dc7f18
comb_catalan_compute_v1_548369836_291
Let $n$ be the number of integers $t$ with $5 \leq t \leq 17$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Compute the $n$-th Catalan number, defined by $$C_n = \frac{1}{n+1} \binom{2n}{n}.$$
58,786
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=4)), 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
0.003
2026-02-08T02:51:28.086840Z
{ "verified": true, "answer": 58786, "timestamp": "2026-02-08T02:51:28.089627Z" }
ef4ffa
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": 1439 }, "timestamp": "2026-02-08T20:17:39.620Z", "answer": 58786 }, { "...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "s...
{ "lo": -1.87, "mid": 0.05, "hi": 1.73 }
893c66
nt_count_divisible_and_v1_2051736721_2619
Let $d_1$ be the number of integers $t$ such that $5 \le t \le 12$ and there exist positive integers $a \le 3$, $b \le 2$ satisfying $t = 2a + 3b$. Let $d_2 = 9$. Determine the number of positive integers $n$ such that $1 \le n \le 22662$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$.
1,259
graphs = [ Graph( let={ "upper": Const(22662), "d1": 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(lef...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
nt_count_divisible_and_v1
null
3
0
[ "LIN_FORM" ]
1
6.965
2026-02-08T16:49:01.674958Z
{ "verified": true, "answer": 1259, "timestamp": "2026-02-08T16:49:08.639612Z" }
5cca6f
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 158, "completion_tokens": 816 }, "timestamp": "2026-02-17T12:04:40.987Z", "answer": 1259 }, { ...
1
[ { "lemma": "K15", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" }...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
4f9be9
comb_count_partitions_v1_717093673_884
Let $N = 94987$. Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $d_0$ be the smallest positive divisor of $N$ that is at least the number of elements in $A$. Compute the number of integer partitions of $d_0$.
63,261
graphs = [ Graph( let={ "_n": Const(94987), "n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=...
NT
COMB
COUNT
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS/MIN_PRIME_FACTOR" ]
52cee2
comb_count_partitions_v1
null
5
0
[ "COPRIME_PAIRS", "MIN_PRIME_FACTOR" ]
2
0.002
2026-02-08T15:44:41.360856Z
{ "verified": true, "answer": 63261, "timestamp": "2026-02-08T15:44:41.362659Z" }
9fc46d
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 142, "completion_tokens": 1250 }, "timestamp": "2026-02-16T12:11:06.651Z", "answer": 63261 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
96af86
antilemma_v1_legendre_1520064083_2622
Compute the largest integer $x$ such that $7^x$ divides $54376!$.
9,060
graphs = [ Graph( let={ "x": MaxKDivides(target=Factorial(Const(54376)), base=Const(7)), }, goal=Ref("x"), ) ]
NT
null
COMPUTE
sympy
V1
[ "V1" ]
dae96f
antilemma_v1_legendre
null
5
0
[ "V1" ]
1
0
2026-02-08T04:53:28.766874Z
{ "verified": true, "answer": 9060, "timestamp": "2026-02-08T04:53:28.767221Z" }
6692dc
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 116, "completion_tokens": 590 }, "timestamp": "2026-02-18T14:34:11.643Z", "answer": 9060 } ]
2
[ { "lemma": "C2", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "K5", "status": "same_pattern_wrong" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no"...
{ "lo": -10, "mid": -6.47, "hi": -2.95 }
d8d16b
diophantine_fbi2_min_v1_971394319_2006
Let $k = 14$. Define $T$ as the set of all integers $t$ such that $9 \leq t \leq 44$ and there exist integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 4$, and $t = 4a + 5b$. Let $\text{upper}$ be the number of elements in $T$. Find the smallest integer $d$ such that $6 \leq d \leq \text{upper}$, $d$ divides $...
7
graphs = [ Graph( let={ "_n": Const(2), "k": Const(14), "upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=...
NT
null
EXTREMUM
sympy
MIN_PRIME_FACTOR
[ "LIN_FORM", "L3B" ]
f85b0e
diophantine_fbi2_min_v1
null
4
0
[ "L3B", "LIN_FORM", "MIN_PRIME_FACTOR" ]
3
0.126
2026-02-08T14:05:00.879075Z
{ "verified": true, "answer": 7, "timestamp": "2026-02-08T14:05:01.005503Z" }
207d8c
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 185, "completion_tokens": 2239 }, "timestamp": "2026-02-15T23:41:46.355Z", "answer": 7 }, { ...
1
[ { "lemma": "K18", "status": "no" }, { "lemma": "L3B", "status": "ok" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "le...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
c91a34
comb_count_permutations_fixed_v1_809748730_1678
Let $n$ be the smallest integer $d \geq 2$ that divides 77. Compute $\binom{n}{0} \cdot !n$, where $!n$ denotes the number of derangements of $n$ 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))))), "k": Const(0), "result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(le...
NT
COMB
COUNT
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
comb_count_permutations_fixed_v1
null
3
0
[ "MIN_PRIME_FACTOR" ]
1
0.002
2026-02-08T12:37:33.504552Z
{ "verified": true, "answer": 1854, "timestamp": "2026-02-08T12:37:33.506060Z" }
5c9de5
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 96, "completion_tokens": 1314 }, "timestamp": "2026-02-15T02:56:36.232Z", "answer": 1854 }, { ...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "V1", "status": "no" ...
{ "lo": -6.96, "mid": -4.56, "hi": -1.46 }
e36e78
nt_count_with_divisor_count_v1_124444284_4202
Let $ n = 84391 $ and $ u = 30976 $. Let $ d_0 $ be the smallest divisor of $ 1001 $ that is at least $ 2 $. Define $ c $ to be the number of positive integers $ n $ such that $ 1 \leq n \leq u $ and the number of positive divisors of $ n $ is equal to $ d_0 $. Compute the remainder when $ 44121 \times c $ is divided b...
47,972
graphs = [ Graph( let={ "_n": Const(84391), "upper": Const(30976), "div_count": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1001))))), "result": CountOverSet(set=SolutionsSet(var=Var...
NT
null
COUNT
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
bc3776
nt_count_with_divisor_count_v1
null
3
0
[ "MIN_PRIME_FACTOR" ]
1
2.223
2026-02-08T05:51:06.049926Z
{ "verified": true, "answer": 47972, "timestamp": "2026-02-08T05:51:08.273239Z" }
c3e721
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 149, "completion_tokens": 1049 }, "timestamp": "2026-02-12T15:28:07.923Z", "answer": 47972 }, ...
1
[ { "lemma": "K16", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V8", "status": "...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
65b6e6
modular_min_linear_v1_1470522791_320
Let $ m = 69069 $, $ a = 22961 $, and $ b = 30329 $. Let $ x $ be the smallest positive integer solution to the congruence $ ax \equiv b \pmod{m} $. Compute the value of \[ 353702 \cdot (|x| \bmod 97) + 329703 \cdot (x^2 + 1 \bmod 101) + 215534 \cdot \left(|x| + 1 \bmod d_0\right), \] where $ d_0 $ is the smallest divi...
52,229
graphs = [ Graph( let={ "_n": Const(2), "a": Const(22961), "b": Const(30329), "m": Const(69069), "result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")...
NT
null
EXTREMUM
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR" ]
b5b91a
modular_min_linear_v1
crt_mix_3
6
0
[ "MIN_PRIME_FACTOR" ]
1
3.067
2026-02-08T12:56:39.153611Z
{ "verified": true, "answer": 52229, "timestamp": "2026-02-08T12:56:42.220158Z" }
176b2b
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 218, "completion_tokens": 3736 }, "timestamp": "2026-02-15T07:34:24.384Z", "answer": 52229 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MIN_PRIME_FACTOR", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V1", "status": "no" } ]
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
c3bb21
nt_count_divisors_in_range_v1_548369836_335
Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 28$ and $1 \leq j \leq 30$. Let $\mathcal{D}$ be the set of all positive divisors $d$ of $n$ satisfying $1 \leq d \leq 216$. Let $r$ be the number of elements in $\mathcal{D}$. Compute $\sum_{k=1}^{r} \phi(k)$, where $\phi$ denotes Euler's totient...
270
graphs = [ Graph( let={ "n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), end=Const(30)))), "a": Const(1), "b": Const(216), "result": CountOverSet(set=SolutionsSet(var=Var("d"), conditio...
NT
null
COUNT
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
nt_count_divisors_in_range_v1
null
5
0
[ "COUNT_CARTESIAN" ]
1
0.005
2026-02-08T02:52:09.807468Z
{ "verified": true, "answer": 270, "timestamp": "2026-02-08T02:52:09.812563Z" }
c53f54
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 230, "completion_tokens": 2242 }, "timestamp": "2026-02-23T17:55:30.007Z", "answer": 270 }, { "id...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "K16", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": 0.15, "mid": 1.94, "hi": 3.63 }
b9e62e
antilemma_sum_equals_v1_458359167_580
Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 83$ and $1 \leq i, j \leq 82$. Compute the remainder when $44121 \cdot x$ is divided by $70612$.
16,710
graphs = [ Graph( let={ "_n": Const(83), "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(82)), right=IntegerRange(start=Const(1), end=Con...
COMB
GEOM
COMPUTE
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS" ]
75ab0f
antilemma_sum_equals_v1
null
3
0
[ "COUNT_SUM_EQUALS" ]
1
0.004
2026-02-08T03:25:56.026166Z
{ "verified": true, "answer": 16710, "timestamp": "2026-02-08T03:25:56.029702Z" }
e77e80
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 172, "completion_tokens": 736 }, "timestamp": "2026-02-10T14:21:24.458Z", "answer": 16710 }, { "i...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "n...
{ "lo": -2.46, "mid": 0.47, "hi": 3.59 }
99c0ef
nt_num_divisors_compute_v1_1439011603_1190
Let $n = 29241$. Compute the number of positive divisors of $n$.
15
graphs = [ Graph( let={ "n": Const(29241), "result": NumDivisors(n=Ref("n")), }, goal=Ref("result"), ) ]
NT
null
COMPUTE
sympy
COUNT_COPRIME_GRID
[ "LIN_FORM/B1" ]
b32639
nt_num_divisors_compute_v1
null
2
0
[ "B1", "COUNT_COPRIME_GRID", "LIN_FORM" ]
3
0.062
2026-02-08T15:58:01.943770Z
{ "verified": true, "answer": 15, "timestamp": "2026-02-08T15:58:02.005275Z" }
281a57
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 65, "completion_tokens": 491 }, "timestamp": "2026-02-16T16:51:06.221Z", "answer": 15 }, { ...
1
[ { "lemma": "B1", "status": "ok_later" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "K16", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_VAL", "status": "n...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
d7f0a2
antilemma_cartesian_v1_124444284_2905
Let $x$ be the number of ordered pairs $(i,j)$ where $i$ is an integer from $1$ to $16$ and $j$ is an integer from $1$ to $24$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|x| + 2$.
291
graphs = [ Graph( let={ "x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(24)))), "Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))), }, goal=Ref("Q"), )...
COMB
GEOM
COMPUTE
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
antilemma_cartesian_v1
null
2
0
[ "COUNT_CARTESIAN" ]
1
0.005
2026-02-08T05:04:10.953750Z
{ "verified": true, "answer": 291, "timestamp": "2026-02-08T05:04:10.959005Z" }
979d4a
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 183, "completion_tokens": 4920 }, "timestamp": "2026-02-24T02:35:48.696Z", "answer": 291 }, { "id...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": 1.97, "mid": 4.36, "hi": 6.69 }
56660a_n
comb_count_surjections_v1_1218484723_6832
A software system assigns 6 distinct tasks to a set of identical servers, such that no server is idle and each task goes to exactly one server. Initially, a parameter $k$ is computed through a series of inclusion-exclusion-like sums: starting with $R = 4$, compute $c$ as the alternating sum of binomial coefficients $\s...
720
COMB
null
COUNT
sympy
BINOMIAL_ALTERNATING
[ "BINOMIAL_ALTERNATING", "ZERO_BINOM_0" ]
38a409
comb_count_surjections_v1
null
4
null
[ "BINOMIAL_ALTERNATING", "ZERO_BINOM_0" ]
2
0.002
2026-02-25T08:18:23.112123Z
null
874ab7
56660a
narrative
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": 904 }, "timestamp": "2026-03-31T01:48:31.490Z", "answer": 720 }, { "id"...
2
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "V8_S...
{ "lo": -10, "mid": -5.89, "hi": -1.79 }
702eff
alg_sum_ap_v1_1218484723_6490
Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $$ 13a^2 - 2ab + 2b^2 \le 10125. $$ Let $T$ be the set of integers $t$ for which there exist integers $a, b$ with $1 \le a \le 1989$, $1 \le b \le 958$, $t = 2a + 3b$, and $5 \le t \le 6852$. Define $$ R = \sum_{k=0}...
14,232
graphs = [ Graph( let={ "_m": Const(2), "_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Sum(Mul(Const(-2), Var("a"), Var("b")), Mul(Co...
ALG
null
COMPUTE
sympy
QF_PSD_COUNT_LEQ
[ "QF_PSD_COUNT_LEQ/LIN_FORM" ]
5171b8
alg_sum_ap_v1
null
5
0
[ "LIN_FORM", "QF_PSD_COUNT_LEQ" ]
2
0.016
2026-02-25T08:03:15.375390Z
{ "verified": true, "answer": 14232, "timestamp": "2026-02-25T08:03:15.391496Z" }
0c253b
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 272, "completion_tokens": 28190 }, "timestamp": "2026-03-30T01:58:18.459Z", "answer": 14232 }, { ...
1
[ { "lemma": "LIN_FORM", "status": "ok_later" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT_LEQ", "status": "ok" } ]
{ "lo": 3.81, "mid": 6.33, "hi": 9.49 }
bfbb9e
algebra_quadratic_discriminant_v1_2051736721_3754
Let $a = -1$, $b = 20$, and $c = -100$. Define $\Delta = b^2 - 4ac$. Let $n = 124$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the maximum value of $xy$ over all such pairs. Compute $\Delta^2 + \Delta + P$.
3,844
graphs = [ Graph( let={ "_n": Const(124), "a": Const(-1), "b": Const(20), "c": Const(-100), "result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))), "_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[...
NT
null
COMPUTE
sympy
B1
[ "B1" ]
bf138c
algebra_quadratic_discriminant_v1
quadratic_mod
4
0
[ "B1" ]
1
0.003
2026-02-08T17:31:00.009974Z
{ "verified": true, "answer": 3844, "timestamp": "2026-02-08T17:31:00.013139Z" }
75a6bc
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 152, "completion_tokens": 250 }, "timestamp": "2026-02-16T09:46:46.793Z", "answer": 3844 }, { "id": 11, ...
2
[ { "lemma": "B1", "status": "ok" }, { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" } ]
{ "lo": -10, "mid": -7.27, "hi": -4.54 }
ecf284
nt_sum_over_divisible_v1_153355830_1385
Let $T$ be the set of all integers $t$ such that $26 \leq t \leq 143$ and $t = 4a + 7b + 15$ for some positive integers $a \leq 18$ and $b \leq 8$. Let $d$ be the largest positive divisor of $10300$ that does not exceed the number of elements in $T$. Compute the sum of all positive integers $n \leq 68644$ that are divi...
29,627
graphs = [ Graph( let={ "_n": Const(10300), "upper": Const(68644), "divisor": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(va...
NT
null
SUM
sympy
LIN_FORM
[ "LIN_FORM/MAX_DIVISOR" ]
8c55ae
nt_sum_over_divisible_v1
null
5
0
[ "LIN_FORM", "MAX_DIVISOR" ]
2
4.639
2026-02-08T06:22:25.962968Z
{ "verified": true, "answer": 29627, "timestamp": "2026-02-08T06:22:30.602212Z" }
361815
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": 4490 }, "timestamp": "2026-02-12T23:09:29.590Z", "answer": 29627 }, ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_DIVISOR", "status": "ok_later" }, { "lemma": "MAX_VAL", "statu...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
f264a3
nt_count_divisors_in_range_v1_1742523217_2635
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Define $n$ to be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Let $S$ be the set of all positive divisors $d$ of $n$ such that $6 \leq d \leq 241$. Compute the remainder when $44121 \cdot |S|$ is divided by $51...
39,304
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(129600)))), expr=Sum(Var("x"), Var("y")))), "a": Const(6), ...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
nt_count_divisors_in_range_v1
null
6
0
[ "B3" ]
1
0.006
2026-02-08T04:53:35.813172Z
{ "verified": true, "answer": 39304, "timestamp": "2026-02-08T04:53:35.818929Z" }
84f358
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 219, "completion_tokens": 2459 }, "timestamp": "2026-02-11T22:20:22.317Z", "answer": 39304 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "MOD_MUL", "status...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
ab292d
nt_count_divisible_v1_397696148_188
Let $n = 15539$ and $U = 43681$. For each integer $k$, define $c_k = (-1)^k \binom{3}{k}$. Let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 6$. Let $s$ be the number of elements in $T$, and let $\sigma = \sum_{k=0}^{s} c_k$. Determine the number of integers $m$ such t...
1,876
graphs = [ Graph( let={ "_n": Const(15539), "upper": Const(43681), "divisor": Const(20), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), S...
COMB
null
COUNT
sympy
COMB1
[ "COMB1/BINOMIAL_ALTERNATING" ]
e72f96
nt_count_divisible_v1
null
5
0
[ "BINOMIAL_ALTERNATING", "COMB1" ]
2
5.567
2026-02-08T11:21:20.882398Z
{ "verified": true, "answer": 1876, "timestamp": "2026-02-08T11:21:26.448940Z" }
1d15d3
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 282, "completion_tokens": 8510 }, "timestamp": "2026-02-24T13:31:30.963Z", "answer": 1876 }, { "i...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok_later" }, { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8", "status": "no" ...
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
81fd94
nt_sum_totient_over_divisors_v1_1439011603_590
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1175056$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $$\sum_{d \mid n} \phi(d).$$
2,168
graphs = [ Graph( let={ "n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1175056)))), expr=Sum(Var("x"), Var("y")))), "result": SumOv...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
nt_sum_totient_over_divisors_v1
null
5
0
[ "B3" ]
1
0.002
2026-02-08T15:36:05.594989Z
{ "verified": true, "answer": 2168, "timestamp": "2026-02-08T15:36:05.597049Z" }
9a7217
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 115, "completion_tokens": 2620 }, "timestamp": "2026-02-16T10:11:26.267Z", "answer": 2168 }, {...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
b9f670
modular_min_modexp_v1_1520064083_963
Let $a = 2$, $b = 312$, and $m = 773$. Define $N$ to be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 4$ and $1 \leq j \leq 193$. Determine the smallest positive integer $x$ such that $1 \leq x \leq N$ and $$a^x \equiv b \pmod{m}.$$
611
graphs = [ Graph( let={ "a": Const(2), "b": Const(312), "m": Const(773), "upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(193)))), "result": MinOverSet(set=Solu...
NT
null
EXTREMUM
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN" ]
409d7d
modular_min_modexp_v1
null
7
0
[ "COUNT_CARTESIAN" ]
1
0.09
2026-02-08T03:41:34.275922Z
{ "verified": true, "answer": 611, "timestamp": "2026-02-08T03:41:34.365717Z" }
8c4495
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 210, "completion_tokens": 5456 }, "timestamp": "2026-02-10T15:34:48.844Z", "answer": 611 }, { "id...
1
[ { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8", "status": "n...
{ "lo": -3.53, "mid": 1.02, "hi": 5.49 }
1c94ef
comb_sum_binomial_row_v1_548369836_419
Let $m=3$. Consider all ordered pairs $(x_1,x_2)$ of positive integers such that $x_1$ and $x_2$ are both odd and $$x_1+x_2=4.$$ Let $n_0$ be the number of such ordered pairs. Let $n_2=0$ and $$s=\sum_{k=0}^{n_2}(-1)^k\binom{n_2}{k}.$$ Let $a=1$ and $b=ms$, and define $$n_1=a+b.$$ Let $$c=\sum_{k=\binom{8}{8}-1}^{n_1...
65,536
graphs = [ Graph( let={ "_m": Const(3), "_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Co...
COMB
null
SUM
sympy
COMB1
[ "COMB1/COUNT_CARTESIAN/BINOMIAL_ALTERNATING", "ZERO_BINOM_N" ]
c51063
comb_sum_binomial_row_v1
null
4
2
[ "BINOMIAL_ALTERNATING", "COMB1", "COUNT_CARTESIAN", "ZERO_BINOM_N" ]
4
0.003
2026-02-08T02:54:15.659920Z
{ "verified": true, "answer": 65536, "timestamp": "2026-02-08T02:54:15.663136Z" }
12cdee
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 337, "completion_tokens": 938 }, "timestamp": "2026-02-08T20:27:02.062Z", "answer": 65536 }, { "i...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok_later" }, { "lemma": "C2", "status": "no" }, { "lemma": "COMB1", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "ok_later" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "CO...
{ "lo": -5.97, "mid": -3.96, "hi": -1.98 }
1ce729
alg_qf_psd_count_leq_v1_1419126231_1018
Find the number of ordered triples $(a, b, c)$ of integers with $1 \le a, b, c \le 12$ such that $$ -588ac + 882c^2 + \left|\left\{ (a_1, b_1) \in \mathbb{Z}^2 : 1 \le a_1, b_1 \le 40,\ -2a_1b_1 + 41b_1^2 + 2a_1^2 \le 52688 \right\}\right| \cdot b^2 + 1862a^2 -1372bc + 2744ab \le 91091. $$
272
graphs = [ Graph( let={ "_n": Const(2), "result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(12)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(12)), Geq(Var("c"), Const(1)), Leq(Var("c"...
ALG
null
COUNT
sympy
QF_PSD_COUNT_LEQ
[ "QF_PSD_COUNT_LEQ" ]
009d0f
alg_qf_psd_count_leq_v1
null
5
0
[ "QF_PSD_COUNT_LEQ" ]
1
0.017
2026-02-25T10:31:39.012584Z
{ "verified": true, "answer": 272, "timestamp": "2026-02-25T10:31:39.029837Z" }
4d7d16
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 260, "completion_tokens": 32768 }, "timestamp": "2026-03-30T11:11:27.667Z", "answer": null }, { ...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT_LEQ", "status": "ok" } ]
{ "lo": 3.8, "mid": 6.33, "hi": 9.49 }
aa9277
nt_count_divisors_in_range_v1_124444284_4546
Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Let $A$ be the set of all positive divisors $d$ of $n$ such that $5 \leq d \leq 147$. Let $a$ be the number of elements in $A$. Let $B$ be the set of all in...
215
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")))), "a": Const(5), ...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM", "B3" ]
ad075d
nt_count_divisors_in_range_v1
negation_mod
6
0
[ "B3", "LIN_FORM" ]
2
0.007
2026-02-08T06:05:09.536075Z
{ "verified": true, "answer": 215, "timestamp": "2026-02-08T06:05:09.542626Z" }
20d717
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 235, "completion_tokens": 4332 }, "timestamp": "2026-02-12T19:09:56.425Z", "answer": 215 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V7", "status": "no" }, { ...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
4b25d7
comb_count_permutations_fixed_v1_865884756_309
Consider the Cartesian product of the integer intervals $\{1,2,3\}$ and $\{1,2,3\}$. Let $N$ be the number of ordered pairs in this product. Let $n_{2}=0$ and define $$c=\sum_{k=\binom{16}{0}-1}^{n_{2}} (-1)^{k}\binom{n_{2}}{k}.$$ Let $n_{1}=0$ and define $$e=\sum_{k=0}^{n_{1}} (-1)^{k}\binom{n_{1}}{k}.$$ Let $$n=N\c...
86,703
graphs = [ Graph( let={ "_m": Const(89273), "_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))), "n2": Const(0), "c": Summation(var="k1", start=Sub(Binom(n=Const(16), k=Con...
COMB
null
COUNT
sympy
COUNT_CARTESIAN
[ "COUNT_CARTESIAN/COMB1/BINOMIAL_ALTERNATING", "LIN_FORM/COMB1", "ZERO_BINOM_0" ]
0fdb62
comb_count_permutations_fixed_v1
null
6
2
[ "BINOMIAL_ALTERNATING", "COMB1", "COUNT_CARTESIAN", "LIN_FORM", "ZERO_BINOM_0" ]
5
0.006
2026-02-08T15:18:34.745605Z
{ "verified": true, "answer": 86703, "timestamp": "2026-02-08T15:18:34.751435Z" }
b7db2f
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 440, "completion_tokens": 3196 }, "timestamp": "2026-02-24T20:21:34.393Z", "answer": 86703 }, { "...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok_later" }, { "lemma": "COMB1", "status": "ok_later" }, { "lemma": "COUNT_CARTESIAN", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { ...
{ "lo": -2.43, "mid": 1.2, "hi": 4.84 }
bb0dc7
diophantine_fbi2_min_v1_1742523217_630
Let $k = 27$, $a = 4$, $b = 2$, and $u = 37$. Find the smallest positive integer $d$ such that $d \geq 5$, $d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Compute the value of $d$.
9
graphs = [ Graph( let={ "k": Const(27), "a": Const(4), "b": Const(2), "upper": Const(37), "result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref...
NT
null
EXTREMUM
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC", "COPRIME_PAIRS" ]
ac053f
diophantine_fbi2_min_v1
null
2
0
[ "COPRIME_PAIRS", "SUM_ARITHMETIC" ]
2
0.025
2026-02-08T03:09:19.426168Z
{ "verified": true, "answer": 9, "timestamp": "2026-02-08T03:09:19.451597Z" }
6e08de
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 188, "completion_tokens": 208 }, "timestamp": "2026-02-09T20:30:16.664Z", "answer": 9 }, { "id": ...
2
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "DS2", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V1", "status": "no" }, ...
{ "lo": -10, "mid": -7.73, "hi": -5.46 }
dc8493
diophantine_fbi2_count_v1_397696148_2444
Let $k = 1260$. Consider the set of integers $d$ such that $4 \leq d \leq 203$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 201$. Let $r$ be the number of such integers $d$. Compute the sum $\sum_{n=1}^{|r|} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$.
84
graphs = [ Graph( let={ "k": Const(1260), "a": Const(3), "b": Const(1), "upper": Const(200), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(203)), Divides(divisor=Var("d"), dividend=...
NT
null
COUNT
sympy
MAX_PRIME_BELOW
[ "ONE_PHI_2", "C2" ]
d7864f
diophantine_fbi2_count_v1
null
4
0
[ "C2", "MAX_PRIME_BELOW", "ONE_PHI_2" ]
3
0.097
2026-02-08T13:20:06.036440Z
{ "verified": true, "answer": 84, "timestamp": "2026-02-08T13:20:06.133055Z" }
ec3804
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 143, "completion_tokens": 3300 }, "timestamp": "2026-02-15T14:34:17.781Z", "answer": 84 }, { ...
1
[ { "lemma": "C2", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "s...
{ "lo": -5.49, "mid": 0.22, "hi": 6.51 }
f5c4d0
nt_count_divisible_v1_1918700295_3795
Let $n$ be a positive integer such that $1 \leq n \leq 49729$. Let $d$ be the number of integers $t$ with $7 \leq t \leq 39$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 7$, $1 \leq b \leq 5$, and $t = 2a + 5b$. Suppose that $n$ satisfies $$ n \equiv \sum_{k=0}^{7} (-1)^k \binom{7}{k} \pmod{d}. $...
1,714
graphs = [ Graph( let={ "_n": Const(7), "upper": Const(49729), "divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'...
COMB
null
COUNT
sympy
BINOMIAL_ALTERNATING
[ "BINOMIAL_ALTERNATING", "LIN_FORM" ]
10f694
nt_count_divisible_v1
null
5
0
[ "BINOMIAL_ALTERNATING", "LIN_FORM" ]
2
1.601
2026-02-08T08:57:22.302032Z
{ "verified": true, "answer": 1714, "timestamp": "2026-02-08T08:57:23.902561Z" }
99cb7d
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 259, "completion_tokens": 2084 }, "timestamp": "2026-02-24T10:12:47.286Z", "answer": 1714 }, { "i...
1
[ { "lemma": "BINOMIAL_ALTERNATING", "status": "ok" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { ...
{ "lo": -2.35, "mid": 1.22, "hi": 4.84 }
688392
nt_count_divisors_in_range_v1_717093673_1711
Let $n = 7560$, $a = 29$, and $b = 365$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let this number be $k$. Compute $k + 2^{k \bmod 15} \bmod 82900$.
31
graphs = [ Graph( let={ "n": Const(7560), "a": Const(29), "b": Const(365), "result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))), "Q": S...
NT
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
nt_count_divisors_in_range_v1
null
4
0
[ "LIN_FORM" ]
1
0.05
2026-02-08T16:16:21.541119Z
{ "verified": true, "answer": 31, "timestamp": "2026-02-08T16:16:21.591353Z" }
1e3eb0
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": 3527 }, "timestamp": "2026-02-17T00:45:18.431Z", "answer": 31 }, { ...
1
[ { "lemma": "K5", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V5", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
985719
nt_count_coprime_and_v1_784195855_959
Let $N = 80880$. Find the number of positive integers $n$ such that $1 \leq n \leq N$, $\gcd(n, 4) = 1$, and $\gcd(n, 9) = 1$. Let $c$ be the largest prime number less than or equal to $26$. Compute the remainder when $c$ minus the number of such integers $n$ is divided by $58613$.
31,676
graphs = [ Graph( let={ "_n": Const(26), "upper": Const(80880), "k1": Const(4), "k2": Const(9), "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("k1")...
NT
null
COUNT
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW" ]
2ed1de
nt_count_coprime_and_v1
negation_mod
4
0
[ "MAX_PRIME_BELOW" ]
1
12.795
2026-02-08T04:43:24.687473Z
{ "verified": true, "answer": 31676, "timestamp": "2026-02-08T04:43:37.482947Z" }
45c28b
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 205, "completion_tokens": 877 }, "timestamp": "2026-02-11T21:59:05.837Z", "answer": 31676 }, { "...
1
[ { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "MOD_SUB", "status": "no...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
553824
nt_count_gcd_equals_v1_1915831931_184
Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16129$. Let $S$ be the set of positive integers $n$ from 1 to 10201, inclusive, such that $\gcd(n, k) = 2$. Compute the number of elements in $S$, and then find the remainder when this number is divided by 73831...
5,060
graphs = [ Graph( let={ "_n": Const(73831), "upper": Const(10201), "k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16129...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
nt_count_gcd_equals_v1
null
4
0
[ "B3" ]
1
0.811
2026-02-08T15:13:13.382803Z
{ "verified": true, "answer": 5060, "timestamp": "2026-02-08T15:13:14.193410Z" }
d37b30
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 141, "completion_tokens": 966 }, "timestamp": "2026-02-16T02:00:48.867Z", "answer": 5060 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V8_SUM", "status": "no" ...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
698461
nt_count_intersection_v1_898971024_1766
Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $N$ be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $5$ divides $n$, and $\gcd(n, 6) = 1$.
333
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(6250000)))), expr=Sum(Var("x"), Var("y")))), "a": Const(5), ...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
nt_count_intersection_v1
null
4
0
[ "B3" ]
1
0.576
2026-02-08T16:19:00.965517Z
{ "verified": true, "answer": 333, "timestamp": "2026-02-08T16:19:01.541849Z" }
ff9b4d
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 140, "completion_tokens": 1797 }, "timestamp": "2026-02-17T01:24:06.978Z", "answer": 333 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
5260e5
algebra_quadratic_discriminant_v1_1218484723_2154
Let $R$ be the number of integers $v$ with $0 \le v \le 1274$ such that $26d^2 + 26x^2 - 52dx = v$ for some integers $d, x$ with $1 \le d, x \le 8$. Let $D = R^2 - 64$. Compute $2\cdot[D > 0] + [D = 0]$, where $[\cdot]$ is the Iverson bracket.
1
graphs = [ Graph( let={ "_n": Const(2), "a": Const(-1), "b": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(0)), Leq(Var("v"), Const(1274)), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), rig...
ALG
null
COMPUTE
sympy
QF_PSD_DISTINCT
[ "QF_PSD_DISTINCT" ]
a8f9cb
algebra_quadratic_discriminant_v1
null
2
0
[ "QF_PSD_DISTINCT" ]
1
0.05
2026-02-25T03:55:16.744621Z
{ "verified": true, "answer": 1, "timestamp": "2026-02-25T03:55:16.794215Z" }
19846c
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 218, "completion_tokens": 797 }, "timestamp": "2026-03-29T03:17:20.777Z", "answer": 1 }, { "id": ...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_DISTINCT", "status": "ok" } ]
{ "lo": -2.45, "mid": 1.37, "hi": 5.29 }
d82f5e
comb_count_derangements_v1_1915831931_3085
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 $pq = 52920$. Let $!n$ denote the number of derangements of $n$ objects. Compute the value of $!n$.
14,833
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=52920)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))...
NT
COMB
COUNT
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
comb_count_derangements_v1
null
6
0
[ "COPRIME_PAIRS" ]
1
0.002
2026-02-08T17:21:20.057284Z
{ "verified": true, "answer": 14833, "timestamp": "2026-02-08T17:21:20.059711Z" }
ad52bc
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": 2126 }, "timestamp": "2026-02-18T01:07:18.441Z", "answer": 14833 }, ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V1", "status...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
f0c313
alg_poly4_count_v1_601307018_9044
Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 434$ such that $337 \cdot b^4 = 122221116432$.
434
graphs = [ Graph( let={ "result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(434)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(434)), Eq(Mul(Const(337), Pow(Var("b"), Const(4))), Const(122221116432))))), ...
ALG
null
COUNT
sympy
POLY_ORBIT_LEGENDRE
[ "POLY_ORBIT_LEGENDRE" ]
7c2be8
alg_poly4_count_v1
null
3
null
[ "POLY_ORBIT_LEGENDRE" ]
1
10.892
2026-03-10T09:27:44.255069Z
{ "verified": true, "answer": 434, "timestamp": "2026-03-10T09:27:55.146634Z" }
781952
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 154, "completion_tokens": 1948 }, "timestamp": "2026-04-19T10:31:10.760Z", "answer": 434 }, { "i...
1
[ { "lemma": "POLY_ORBIT_LEGENDRE", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
f77394
modular_product_range_v1_601307018_9834
Let $N = \prod_{i=16}^{104} i$. Find the remainder when $N$ is divided by $11423$.
7,539
graphs = [ Graph( let={ "prod": MathProduct(expr=Var("i"), var="i", start=Const(16), end=Const(104)), "result": Mod(value=Ref("prod"), modulus=Const(11423)), }, goal=Ref("result"), ) ]
NT
null
COMPUTE
sympy
POLY_ORBIT_HENSEL
[ "POLY_ORBIT_HENSEL/POLY3_MIN", "QUADRATIC_INEQ" ]
d182a9
modular_product_range_v1
null
4
0
[ "POLY3_MIN", "POLY_ORBIT_HENSEL", "QUADRATIC_INEQ" ]
3
0.086
2026-03-10T10:13:58.392902Z
{ "verified": true, "answer": 7539, "timestamp": "2026-03-10T10:13:58.479163Z" }
85c99e
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 139, "completion_tokens": 9086 }, "timestamp": "2026-04-19T12:13:02.239Z", "answer": 7539 }, { "...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY3_MIN", "status": "ok_later" }, { "lemma": "POLY_ORBIT_HENSEL", "stat...
{ "lo": -5.34, "mid": 1.1, "hi": 7.53 }
acabb6
alg_poly4_sum_v1_1419126231_1468
Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $17a^2 - 8ab + 16b^2 \le 22633$. Find the remainder when $$ \sum_{\substack{a_1=1 \\ b_1=1}}^{100} \left( \min_{\substack{a_2=1 \\ b_2=1}}^{26} \left( 26a_2^2 + 41b_2^2 + 30a_2b_2 \right) \cdot a_1^4 - 1280a_1b_1^3 +...
10,115
graphs = [ Graph( let={ "_m": Const(2), "_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Sum(Mul(Const(-8), Var("a"), Var("b")), Mul(Co...
ALG
null
COMPUTE
sympy
QF_PSD_COUNT_LEQ
[ "QF_PSD_COUNT_LEQ/QF_PSD_MIN" ]
7f6761
alg_poly4_sum_v1
null
6
0
[ "QF_PSD_COUNT_LEQ", "QF_PSD_MIN" ]
2
0.041
2026-02-25T10:56:05.498920Z
{ "verified": true, "answer": 10115, "timestamp": "2026-02-25T10:56:05.540304Z" }
3dc0fb
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": 17683 }, "timestamp": "2026-03-30T12:44:11.131Z", "answer": 10115 }, { ...
1
[ { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_COUNT_LEQ", "status": "ok" }, { "lemma": "QF_PSD_MIN", "status": "ok_later" } ]
{ "lo": 1.5, "mid": 4.69, "hi": 7.23 }
7d8dbd
comb_count_partitions_v1_1520064083_6253
Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 6$, $1 \leq j \leq 10$, and $\gcd(i,j) = 1$. Compute the number of integer partitions of $n$.
26,015
graphs = [ Graph( let={ "n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(10))))), "re...
NT
COMB
COUNT
sympy
COUNT_COPRIME_GRID
[ "COUNT_COPRIME_GRID" ]
20ec03
comb_count_partitions_v1
null
5
0
[ "COUNT_COPRIME_GRID" ]
1
0.001
2026-02-08T07:58:37.089475Z
{ "verified": true, "answer": 26015, "timestamp": "2026-02-08T07:58:37.090242Z" }
c70c12
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 106, "completion_tokens": 1280 }, "timestamp": "2026-02-13T13:56:23.001Z", "answer": 26015 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "ok" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "V5", "status": "n...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
0db94a
modular_mod_compute_v1_2051736721_5318
Let $a = -20449$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6718464$. Let $m$ be the minimum value of $x + y$ over all such pairs. Define $r$ to be the remainder when $a$ is divided by $m$, so that $0 \leq r < m$ and $r \equiv a \pmod{m}$. Let $Q$ be the smallest positive integ...
153
graphs = [ Graph( let={ "a": Const(-20449), "m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6718464)))), expr=Sum(Var("x"), Var("y")...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
modular_mod_compute_v1
null
5
0
[ "B3" ]
1
0.003
2026-02-08T18:29:38.880970Z
{ "verified": true, "answer": 153, "timestamp": "2026-02-08T18:29:38.884252Z" }
9a632d
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 175, "completion_tokens": 2707 }, "timestamp": "2026-02-18T17:23:59.974Z", "answer": 153 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
d3be1e
nt_count_intersection_v1_397696148_964
Let $ a $ be the number of ordered pairs of positive integers $ (i, j) $ such that $ i + j = 7 $, $ 1 \leq i \leq 5 $, and $ 1 \leq j \leq 6 $. Let $ b = 12 $. Determine the number of positive integers $ n \leq 50000 $ such that $ a $ divides $ n $ and $ \gcd(n, b) = 1 $.
3,333
graphs = [ Graph( let={ "_n": Const(7), "N": Const(50000), "a": 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(5)), right=Integer...
NT
null
COUNT
sympy
COUNT_SUM_EQUALS
[ "COUNT_SUM_EQUALS" ]
75ab0f
nt_count_intersection_v1
null
4
0
[ "COUNT_SUM_EQUALS" ]
1
2.917
2026-02-08T11:58:18.904818Z
{ "verified": true, "answer": 3333, "timestamp": "2026-02-08T11:58:21.822130Z" }
ea7bd1
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 144, "completion_tokens": 1318 }, "timestamp": "2026-02-14T23:43:24.464Z", "answer": 3333 }, {...
1
[ { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "ok" }, { "lemma": "K5", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_VAL", "status": "no...
{ "lo": -5.14, "mid": 0.32, "hi": 6.51 }
485997
algebra_poly_eval_v1_784195855_8235
Let $c = 19$. Let $m$ be the smallest divisor of 6125 that is at least 2. Let $n$ be the largest prime number not exceeding $c$. Let $b$ be the largest prime number not exceeding $n$. Compute the value of $9b^3 + m b^2 - 8b - 1$.
63,383
graphs = [ Graph( let={ "_c": Const(19), "_m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6125))))), "_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(V...
NT
null
COMPUTE
sympy
MIN_PRIME_FACTOR
[ "MIN_PRIME_FACTOR/MAX_PRIME_BELOW", "MAX_PRIME_BELOW/MAX_PRIME_BELOW" ]
f15075
algebra_poly_eval_v1
null
4
0
[ "MAX_PRIME_BELOW", "MIN_PRIME_FACTOR" ]
2
0.006
2026-02-08T15:58:03.985255Z
{ "verified": true, "answer": 63383, "timestamp": "2026-02-08T15:58:03.991238Z" }
318b32
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 123, "completion_tokens": 621 }, "timestamp": "2026-02-16T17:44:35.602Z", "answer": 63383 }, {...
1
[ { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MIN_PRIME_FACTOR"...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
ba19a7_n
alg_telescope_v1_1419126231_346
A rectangular garden has area $724201$ square meters, with side lengths $x$ and $y$ in meters, both positive integers. The architect wants to minimize the perimeter, so they choose the pair $(x, y)$ that minimizes $x + y$. Let $s$ be this minimal sum. A fountain is placed along a walkway with $s + 1$ tiles numbered $0$...
3,013
ALG
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
alg_telescope_v1
null
4
null
[ "B3" ]
1
0.138
2026-02-25T09:51:30.007845Z
null
985489
ba19a7
narrative
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 242, "completion_tokens": 9592 }, "timestamp": "2026-03-31T03:34:29.005Z", "answer": 3013 }, { "i...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" } ]
{ "lo": -5.37, "mid": 0.23, "hi": 5.22 }
d168bd
comb_count_derangements_v1_124444284_3517
Let $m = 11$ and $n = 2$. Define $d_{\text{min}}$ to be the smallest integer $d \geq n$ that divides $77077$. Let $D = !d_{\text{min}}$, the number of derangements of $d_{\text{min}}$ elements. Let $P_{\text{max}}$ be the largest prime number $p$ such that $2 \leq p \leq m$. Compute the remainder when $D$ is divided by...
203
graphs = [ Graph( let={ "_m": Const(11), "_n": Const(2), "n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77077))))), "result": Subfactorial(arg=Ref(name='n')), "Q": Bel...
NT
COMB
COUNT
sympy
MAX_PRIME_BELOW
[ "MAX_PRIME_BELOW", "MIN_PRIME_FACTOR" ]
114c7a
comb_count_derangements_v1
bell_mod
4
0
[ "MAX_PRIME_BELOW", "MIN_PRIME_FACTOR" ]
2
0.002
2026-02-08T05:26:09.201004Z
{ "verified": true, "answer": 203, "timestamp": "2026-02-08T05:26:09.202690Z" }
bef374
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": 1351 }, "timestamp": "2026-02-12T08:34:29.283Z", "answer": 203 }, { ...
1
[ { "lemma": "K15", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "L3c", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "...
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
e4f8c5
nt_count_intersection_v1_1439011603_1444
Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 6250000$. Let $b$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = 121$. Compute the number of positive integers $n \leq N$ such that $n$ is divisible by 3 and $\...
757
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(6250000)))), expr=Sum(Var("x"), Var("y")))), "a": Const(3), ...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
nt_count_intersection_v1
null
6
0
[ "B3" ]
1
0.24
2026-02-08T16:06:07.349577Z
{ "verified": true, "answer": 757, "timestamp": "2026-02-08T16:06:07.590070Z" }
efefba
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 161, "completion_tokens": 1778 }, "timestamp": "2026-02-16T21:25:55.100Z", "answer": 757 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_DIVISOR_COUNT", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "L3b", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
a783a2
nt_count_with_divisor_count_v1_458359167_1230
Let $n$ range over the integers from $2$ to $12$. Among these values, let $d$ be the largest prime $n$. Let $N = 12544$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$ and the number of positive divisors of $n$ is equal to $d$.
1
graphs = [ Graph( let={ "_n": Const(12), "upper": Const(12544), "div_count": 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("n"), ...
NT
null
COUNT
sympy
LIN_FORM
[ "MAX_PRIME_BELOW" ]
dc3ad3
nt_count_with_divisor_count_v1
null
4
0
[ "LIN_FORM", "MAX_PRIME_BELOW" ]
2
2.419
2026-02-08T04:30:11.373979Z
{ "verified": true, "answer": 1, "timestamp": "2026-02-08T04:30:13.792664Z" }
1a7aed
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 188, "completion_tokens": 932 }, "timestamp": "2026-02-10T16:54:09.423Z", "answer": 1 }, { "id":...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "LTE_DIFF", "status": "no" }, { "lemma": "MAX_PRIME_BELOW", "status": "ok" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_ADD", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -8.32, "mid": -5.11, "hi": -2.37 }
1220a9
nt_max_prime_below_v1_1742523217_1390
Let $d$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p,q) = 1$, and $p < q$. Compute the largest prime number $n$ such that $d \leq n \leq 44100$.
44,089
graphs = [ Graph( let={ "upper": Const(44100), "result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V...
NT
null
EXTREMUM
sympy
COPRIME_PAIRS
[ "COPRIME_PAIRS" ]
2bb3aa
nt_max_prime_below_v1
null
4
0
[ "COPRIME_PAIRS" ]
1
1.06
2026-02-08T03:41:59.315162Z
{ "verified": true, "answer": 44089, "timestamp": "2026-02-08T03:42:00.375491Z" }
6e4ce3
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 180, "completion_tokens": 2761 }, "timestamp": "2026-02-10T14:57:05.851Z", "answer": 44089 }, { ...
1
[ { "lemma": "COPRIME_PAIRS", "status": "ok" }, { "lemma": "K15", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "LTE_SUM", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V5", "status": "no" } ...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
695503
sequence_lucas_compute_v1_153355830_1016
Let $ n $ be the sum $ \sum_{k=1}^{6} k $. Define $ a = L_n $, where $ L_n $ denotes the $ n $th Lucas number. Compute the value of $$ a + \phi(|a| + 1) + \tau(|a| + 1), $$ where $ \phi(n) $ denotes Euler's totient function and $ \tau(n) $ denotes the number of positive divisors of $ n $.
40,324
graphs = [ Graph( let={ "_n": Const(6), "n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")), "result": Lucas(arg=Ref(name='n')), "Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(nam...
NT
null
COMPUTE
sympy
SUM_ARITHMETIC
[ "SUM_ARITHMETIC" ]
eb34f0
sequence_lucas_compute_v1
null
3
0
[ "SUM_ARITHMETIC" ]
1
0.002
2026-02-08T04:21:17.178638Z
{ "verified": true, "answer": 40324, "timestamp": "2026-02-08T04:21:17.180372Z" }
8eff8d
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 211, "completion_tokens": 1766 }, "timestamp": "2026-02-10T16:12:00.464Z", "answer": 40324 }, { ...
1
[ { "lemma": "K13", "status": "no" }, { "lemma": "LTE_DIFF_P2", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V8_SUM", "status...
{ "lo": -3.42, "mid": 1.86, "hi": 7.55 }
261bb7
modular_count_residue_v1_1978505735_3330
Let $r$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 4$. Let $m = 18$. Find the number of positive integers $n$ such that $1 \le n \le 33489$ and $n \equiv r \pmod{m}$. Compute the remainder when $44121$ times this number is divided by $77186$.
60,463
graphs = [ Graph( let={ "_n": Const(77186), "upper": Const(33489), "m": Const(18), "r": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var(...
NT
null
COUNT
sympy
B3
[ "B3" ]
0cd20d
modular_count_residue_v1
null
3
0
[ "B3" ]
1
1.114
2026-02-08T17:34:05.125377Z
{ "verified": true, "answer": 60463, "timestamp": "2026-02-08T17:34:06.238995Z" }
bf3170
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 139, "completion_tokens": 1695 }, "timestamp": "2026-02-18T04:42:01.067Z", "answer": 60463 }, ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_FIB_DIVISIBLE", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "DS2", "status": "no" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status":...
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }
51f63a
alg_qf_psd_sum_v1_1218484723_6345
Consider all ordered quadruples $(a,b,c,d)$ of positive integers satisfying \[1 \le a \le 25, \quad 1 \le b \le 25,\] \[1 \le c \le \min\bigl\{-6a1 \cdot b1 + b1^{2} + 34 \cdot a1^{2} : (a1, b1),\, 1 \le a1 \le 14,\, 1 \le b1 \le 14 \bigr\},\] \[1 \le d \le \left|\bigl\{ (a2, b2) : 1 \le a2 \le 30,\, 1 \le b2 \le 30,\,...
67,172
graphs = [ Graph( let={ "_c": Const(16), "_m": Const(15), "_n": Const(25), "result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n...
ALG
null
COMPUTE
sympy
QF_PSD_ORBIT
[ "QF_PSD_ORBIT", "POLY4_COUNT", "QF_PSD_MIN" ]
588cb2
alg_qf_psd_sum_v1
null
7
0
[ "POLY4_COUNT", "QF_PSD_MIN", "QF_PSD_ORBIT" ]
3
1.864
2026-02-25T07:53:40.681601Z
{ "verified": true, "answer": 67172, "timestamp": "2026-02-25T07:53:42.545355Z" }
f0d845
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 527, "completion_tokens": 14879 }, "timestamp": "2026-03-30T01:16:37.668Z", "answer": 67284 }, { ...
1
[ { "lemma": "POLY4_COUNT", "status": "ok" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "QF_PSD_MIN", "status": "ok" }, { "lemma": "QF_PSD_ORBIT", "status": "ok" } ]
{ "lo": 1.53, "mid": 4.7, "hi": 7.23 }
d9e0f8
comb_count_permutations_fixed_v1_1218484723_5470
Let $D_n$ denote the number of derangements of $n$ elements. Let $M = \sum_{k=1}^{2} k$, $k = \sum_{j=1}^{M} j$, and $n = 9$. Compute $66666 - \binom{n}{k} \cdot D_{n-k}$.
66,498
graphs = [ Graph( let={ "_n": Summation(var="k1", start=Const(1), end=Const(2), expr=Var("k1")), "n": Const(9), "k": Summation(var="k2", start=Const(1), end=Ref("_n"), expr=Var("k2")), "result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(...
COMB
null
COUNT
sympy
POLY_ORBIT_LEGENDRE
[ "SUM_ARITHMETIC/SUM_ARITHMETIC" ]
2a57af
comb_count_permutations_fixed_v1
null
3
0
[ "POLY_ORBIT_LEGENDRE", "SUM_ARITHMETIC" ]
2
0.269
2026-02-25T07:01:05.523169Z
{ "verified": true, "answer": 66498, "timestamp": "2026-02-25T07:01:05.791713Z" }
942d35
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": 790 }, "timestamp": "2026-03-29T21:14:51.832Z", "answer": 66498 }, { "i...
2
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_CARTESIAN", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "SUM_ARITHMETIC", "status": "ok" }, { "lemma": "V8", "...
{ "lo": -10, "mid": -6.24, "hi": -2.48 }
6b0124
comb_count_derangements_v1_784195855_5985
Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 21$ and the $k$-th Fibonacci number is divisible by $2$. Compute the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements.
1,854
graphs = [ Graph( let={ "_n": Const(2), "n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(21)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))), "result": Subfactorial(arg=Ref(name='n')), ...
NT
COMB
COUNT
sympy
COUNT_FIB_DIVISIBLE
[ "COUNT_FIB_DIVISIBLE" ]
66de3c
comb_count_derangements_v1
null
4
0
[ "COUNT_FIB_DIVISIBLE" ]
1
0.001
2026-02-08T08:15:02.019352Z
{ "verified": true, "answer": 1854, "timestamp": "2026-02-08T08:15:02.020089Z" }
d14852
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 113, "completion_tokens": 775 }, "timestamp": "2026-02-13T15:57:48.170Z", "answer": 1854 }, { ...
1
[ { "lemma": "COUNT_FIB_DIVISIBLE", "status": "ok" }, { "lemma": "K18", "status": "no" }, { "lemma": "L3b", "status": "no" }, { "lemma": "V1", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "VAL_SUM_EQ", "status": "no" } ]
{ "lo": -5.55, "mid": -3.01, "hi": 0.32 }
8b0392
lin_form_endings_v1_124444284_4874
Let $a = 30$, $b = 18$, $A = 46$, and $B = 18$. Let $g = \gcd(a,b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define $T$ to be a set whose size is $a' \cdot A + b' \cdot B - a' \cdot b'$. The total number of elements in a certain structure is $a \cdot A + b \cdot...
1,388
graphs = [ Graph( let={ "a_coeff": Const(30), "b_coeff": Const(18), "A_val": Const(46), "B_val": Const(18), "g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")), "ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))), "bp_node": ...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
4
null
[ "LIN_FORM" ]
1
0.002
2026-02-08T06:16:36.710440Z
{ "verified": true, "answer": 1388, "timestamp": "2026-02-08T06:16:36.712196Z" }
57d81c
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 0, "correct": { "strict": false, "boxed": false, "relaxed": false }, "usage": { "prompt_tokens": 214, "completion_tokens": 451 }, "timestamp": "2026-02-15T17:23:53.990Z", "answer": 1387 }, { "id": 11,...
1
[ { "lemma": "COUNT_CARTESIAN", "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": -7.01, "mid": -4.68, "hi": -2.15 }
cab665
antilemma_k3_v1_124444284_3575
Let $n = 44062$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$. Compute the value of the Bell number $B_{|x| \bmod 11}$.
877
graphs = [ Graph( let={ "_n": Const(44062), "x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), "Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))), }, goal=Ref("Q"), ) ]
NT
COMB
COMPUTE
sympy
K13
[ "K3" ]
54c41e
antilemma_k3_v1
null
4
0
[ "K13", "K3" ]
2
0.007
2026-02-08T05:27:44.058555Z
{ "verified": true, "answer": 877, "timestamp": "2026-02-08T05:27:44.065860Z" }
aa73ce
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 106, "completion_tokens": 495 }, "timestamp": "2026-02-12T09:35:50.945Z", "answer": 877 }, { ...
1
[ { "lemma": "K14", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "K18", "status": "no" }, { "lemma": "K3", "status": "ok" }, { "lemma": "MOD_FACTORIAL", "status": "no" }, { "lemma": "V5", "status": "no" } ]
{ "lo": -3.44, "mid": 1.34, "hi": 6.56 }
7d81ef
lin_form_endings_v1_971394319_1700
Compute the value of $ \left\lfloor \frac{20}{\gcd(20, 16)} \right\rfloor $. Multiply this value by $15001$, then find the remainder when the result is divided by $90980$.
75,005
graphs = [ Graph( let={ "a_coeff": Const(20), "b_coeff": Const(16), "_inner_result": Floor(Div(Const(20), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))), "_scale_k": Const(15001), "_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")), "_mod_...
COMB
NT
COMPUTE
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
lin_form_endings_v1
null
3
null
[ "LIN_FORM" ]
1
0.001
2026-02-08T13:51:57.853469Z
{ "verified": true, "answer": 75005, "timestamp": "2026-02-08T13:51:57.854035Z" }
4d1cfa
CC BY 4.0
[ { "id": 8, "model": "mathstral", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 117, "completion_tokens": 307 }, "timestamp": "2026-02-16T05:07:44.919Z", "answer": 75005 }, { "id": 11, ...
2
[ { "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": -10, "mid": -7.27, "hi": -4.54 }
3cc7a7
diophantine_fbi2_min_v1_784195855_3972
Let $k = 96$, $a = 2$, $b = 3$, and $\text{upper} = 106$. Consider the set of all integers $d$ such that $d \geq 3$, $d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Let $r$ be the minimum value of $d$ in this set. Compute $r$.
3
graphs = [ Graph( let={ "k": Const(96), "a": Const(2), "b": Const(3), "upper": Const(106), "result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Re...
NT
null
EXTREMUM
sympy
K2
[ "B3" ]
0cd20d
diophantine_fbi2_min_v1
null
2
0
[ "B3", "K2" ]
2
0.123
2026-02-08T06:43:44.790694Z
{ "verified": true, "answer": 3, "timestamp": "2026-02-08T06:43:44.913691Z" }
2fb6b4
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 142, "completion_tokens": 728 }, "timestamp": "2026-02-13T03:48:09.716Z", "answer": 3 }, { ...
1
[ { "lemma": "B3", "status": "ok" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "MOD_SUB", "status": "no" }, { "lemma": "V7", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -5.55, "mid": -3.01, "hi": 0.32 }
1e06fa
nt_sum_divisors_compute_v1_124444284_805
Let $n = 21787$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $c$ be the largest integer such that $7^c$ divides $11634!$. Compute the remainder when $c - \sigma(n)$ is divided by $58441$.
38,589
graphs = [ Graph( let={ "_n": Const(58441), "n": Const(21787), "result": SumDivisors(n=Ref("n")), "_c": MaxKDivides(target=Factorial(Const(11634)), base=Const(7)), "Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Ref("_n")), }, ...
NT
null
COMPUTE
sympy
C3
[ "V1" ]
574795
nt_sum_divisors_compute_v1
negation_mod
5
0
[ "C3", "V1" ]
2
0.017
2026-02-08T03:31:51.352016Z
{ "verified": true, "answer": 38589, "timestamp": "2026-02-08T03:31:51.369137Z" }
deac17
CC BY 4.0
[ { "id": 1, "model": "openai/gpt-oss-20b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 175, "completion_tokens": 3704 }, "timestamp": "2026-02-09T22:19:49.568Z", "answer": 38589 }, { "...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K15", "status": "no" }, { "lemma": "K5", "status": "same_pattern_wrong" }, { "lemma": "POLY_PADIC_VAL_CONST", "status": "no" }, { "lemma": "V1", "status": ...
{ "lo": -6.51, "mid": -0.31, "hi": 5.43 }
bb21c2
comb_count_partitions_v1_1978505735_2480
Let $ n $ be the number of integers $ t $ with $ 11 \le t \le 68 $ for which there exist positive integers $ a $ and $ b $, with $ 1 \le a \le 10 $ and $ 1 \le b \le 4 $, such that $ t = 4a + 7b $. Let $ \text{result} $ be the number of integer partitions of $ n $. Let $ Q = \sum_{i=0}^{d-1} d_i (i+1)^2 + 32768 $, wher...
33,002
graphs = [ Graph( let={ "_n": Const(2), "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=10)), Geq(left=Var(n...
COMB
null
COUNT
sympy
LIN_FORM
[ "LIN_FORM" ]
7b2633
comb_count_partitions_v1
null
6
0
[ "LIN_FORM" ]
1
0.004
2026-02-08T16:54:54.093453Z
{ "verified": true, "answer": 33002, "timestamp": "2026-02-08T16:54:54.097215Z" }
0211bd
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 229, "completion_tokens": 2107 }, "timestamp": "2026-02-17T15:52:55.982Z", "answer": 33002 }, ...
1
[ { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_COPRIME_GRID", "status": "no" }, { "lemma": "COUNT_INTEGER_RANGE", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "LIN_FORM", "status": "ok" }, { "lemma": "V8", "st...
{ "lo": -2.38, "mid": 1.74, "hi": 6.59 }
a18d4e
comb_bell_compute_v1_865884756_2430
Let $N = 33344$. Define $n$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq N$ and $\binom{33344}{j}$ is odd. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements.
4,140
graphs = [ Graph( let={ "_n": Const(33344), "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(33344), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), "r...
COMB
null
COMPUTE
sympy
V8
[ "V8" ]
86348e
comb_bell_compute_v1
null
7
0
[ "V8" ]
1
0.002
2026-02-08T16:46:26.973228Z
{ "verified": true, "answer": 4140, "timestamp": "2026-02-08T16:46:26.975700Z" }
4a1703
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 116, "completion_tokens": 998 }, "timestamp": "2026-02-17T11:10:10.928Z", "answer": 4140 }, { ...
1
[ { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "COUNT_SUM_EQUALS", "status": "no" }, { "lemma": "K17", "status": "no" }, { "lemma": "MAX_VAL", "status": "no" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V8", "status": "ok" } ]
{ "lo": -2.38, "mid": 1.74, "hi": 6.59 }
e51748
algebra_poly_eval_v1_1742523217_1666
Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 121$. Compute $a^2 + 4a$.
572
graphs = [ Graph( let={ "_n": Const(121), "a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))), ...
NT
null
COMPUTE
sympy
B3
[ "B3" ]
0cd20d
algebra_poly_eval_v1
null
4
0
[ "B3" ]
1
0.001
2026-02-08T04:06:00.041882Z
{ "verified": true, "answer": 572, "timestamp": "2026-02-08T04:06:00.043324Z" }
adc614
CC BY 4.0
[ { "id": 2, "model": "openai/gpt-oss-120b", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 153, "completion_tokens": 254 }, "timestamp": "2026-02-10T15:17:40.177Z", "answer": 572 }, { "id...
2
[ { "lemma": "B3", "status": "ok" }, { "lemma": "C2", "status": "no" }, { "lemma": "COUNT_PRIMES", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V8_SUM", "status": "no" } ]
{ "lo": -10, "mid": -7.73, "hi": -5.46 }
878f2a
nt_count_divisible_v1_1978505735_1776
Let $$d = \sum_{k=1}^{6} \varphi(k) \left\lfloor \frac{6}{k} \right\rfloor,$$ where $\varphi$ denotes Euler's totient function. Find the number of positive integers $n \leq 31684$ such that $n$ is divisible by $d$. Then, compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by thi...
150
graphs = [ Graph( let={ "_n": Const(6), "upper": Const(31684), "divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))), "result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq...
NT
null
COUNT
sympy
K2
[ "K2" ]
6897ab
nt_count_divisible_v1
null
6
0
[ "K2" ]
1
6.256
2026-02-08T16:23:42.376556Z
{ "verified": true, "answer": 150, "timestamp": "2026-02-08T16:23:48.632883Z" }
4f64f9
CC BY 4.0
[ { "id": 5, "model": "deepseek-ai/DeepSeek-V3.2", "score": 3, "correct": { "strict": true, "boxed": true, "relaxed": true }, "usage": { "prompt_tokens": 144, "completion_tokens": 2063 }, "timestamp": "2026-02-17T02:29:39.418Z", "answer": 150 }, { ...
1
[ { "lemma": "DS2", "status": "no" }, { "lemma": "K14", "status": "no" }, { "lemma": "K2", "status": "ok" }, { "lemma": "MOD_MUL", "status": "no" }, { "lemma": "V3", "status": "no" }, { "lemma": "V7", "status": "no" } ]
{ "lo": -7.08, "mid": -0.29, "hi": 6.49 }