Question

Are there any non-trival positive integer solutions to $n^{k}+k=2025!$?

score 101 · Answer 1 · 2023-12-25 14:20:06

101

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Are there any non-trival positive integer solutions to $n^{k}+k=2025!$?

Published on 25 Dec 2023 - 14:20

score 560 · Answer 2 · 2023-12-27 19:57:23

560

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When can products of linear terms differ by a constant?

Published on 27 Dec 2023 - 19:57

score 173 · Answer 3 · 2023-12-29 13:29:19

173

Views

Proving that $2444_b$ is not a perfect square in any base $b$

Published on 29 Dec 2023 - 13:29

score 132 · Answer 4 · 2026-04-02 21:14:32

132

Views

Reference request : The smallest integer solution to $313(x^3+y^3)=z^3$ has more than $1000$ digits!

Published on 02 Apr 2026 - 21:14

score 85 · Answer 5 · 2026-03-30 09:30:12

85

Views

What subjects should I learn to understand the proof of Fermat's Last Theorem?

Published on 30 Mar 2026 - 9:30

score 187 · Answer 6 · 2026-02-23 13:38:40

187

Views

Can the sequence $\{\lfloor \alpha n \rfloor\}$ be divided into two parts with equal sums, for all $\alpha \in \mathbb{R}$?

Published on 23 Feb 2026 - 13:38

score 100 · Answer 7 · 2026-03-25 09:49:30

100

Views

Infinitely many Ramanujan-type sum of cubes and unimodular matrices?

Published on 25 Mar 2026 - 9:49

score 99 · Answer 8 · 2024-01-05 13:41:51

99

Views

How can I show that $a^2 + b^2 \equiv 3(\mod 4)$ has no integer solutions?

Published on 05 Jan 2024 - 13:41

score 255 · Answer 9 · 2026-03-30 03:19:14

255

Views

When does $(a+b\sqrt n)^3+(a-b\sqrt n)^3=c^3$ have integer solutions $(a,b,c,n)$?

Published on 30 Mar 2026 - 3:19

score 123 · Answer 10 · 2026-03-27 07:46:53

123

Views

Four rational Pythagorean triples in a square

Published on 27 Mar 2026 - 7:46

score 63 · Answer 11 · 2024-01-06 15:48:26

63

Views

how to find the number of integral solutions when exponential functions are involved?

Published on 06 Jan 2024 - 15:48

score 295 · Answer 12 · 2024-01-07 18:37:00

295

Views

Solve for $a,b,c$ such that $2^a+2^b+2^c=148$ where $a,b,c$ are positive integers

Published on 07 Jan 2024 - 18:37

score 165 · Answer 13 · 2026-03-26 07:59:03

165

Views

Are there rational solutions $r,s \in \mathbb{Q}$ to the equation $\tan^2(\pi r) + \tan^2(\pi s) = 1$

Published on 26 Mar 2026 - 7:59

score 216 · Answer 14 · 2024-01-15 04:48:13

216

Views

Why do the lattice points of these ellipses obey a curious relationship?

Published on 15 Jan 2024 - 4:48

score 258 · Answer 15 · 2024-01-16 08:24:16

258

Views

What is the relation between these pairs of triangles on an ellipse for $x^3+y^3+z^3 = (z+1)^3$?

Published on 16 Jan 2024 - 8:24

List Question

Are there any non-trival positive integer solutions to $n^{k}+k=2025!$?

When can products of linear terms differ by a constant?

Proving that $2444_b$ is not a perfect square in any base $b$

Reference request : The smallest integer solution to $313(x^3+y^3)=z^3$ has more than $1000$ digits!

What subjects should I learn to understand the proof of Fermat's Last Theorem?

Can the sequence $\{\lfloor \alpha n \rfloor\}$ be divided into two parts with equal sums, for all $\alpha \in \mathbb{R}$?

Infinitely many Ramanujan-type sum of cubes and unimodular matrices?

How can I show that $a^2 + b^2 \equiv 3(\mod 4)$ has no integer solutions?

When does $(a+b\sqrt n)^3+(a-b\sqrt n)^3=c^3$ have integer solutions $(a,b,c,n)$?

Four rational Pythagorean triples in a square

how to find the number of integral solutions when exponential functions are involved?

Solve for $a,b,c$ such that $2^a+2^b+2^c=148$ where $a,b,c$ are positive integers

Are there rational solutions $r,s \in \mathbb{Q}$ to the equation $\tan^2(\pi r) + \tan^2(\pi s) = 1$

Why do the lattice points of these ellipses obey a curious relationship?

What is the relation between these pairs of triangles on an ellipse for $x^3+y^3+z^3 = (z+1)^3$?

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