Question

Solving Dudeney's "A Question of Cubes": sum of consecutive cubes is a square

score 685 · Answer 1 · 2026-04-14 21:39:41

685

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Solving Dudeney's "A Question of Cubes": sum of consecutive cubes is a square

Published on 14 Apr 2026 - 21:39

score 354 · Answer 2 · 2026-04-11 10:54:39

354

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Showing a system of equations has no integer solutions using modular arithmetic

Published on 11 Apr 2026 - 10:54

score 129 · Answer 3 · 2026-04-12 05:09:12

129

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Diophantine Equation with 3 Variables example

Published on 12 Apr 2026 - 5:09

score 254 · Answer 4 · 2026-04-26 00:27:14

254

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$ 3^2 + 4^2 = 5^2 $. Are there more of these equations?

Published on 26 Apr 2026 - 0:27

score 150 · Answer 5 · 2026-04-16 16:35:20

150

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The Diophantine equation $5(p^2+q^2+r^2+s^2+t^2)^2 - 7(p^4+q^4+r^4+s^4+t^4) = 90pqrst$

Published on 16 Apr 2026 - 16:35

score 151 · Answer 6 · 2026-04-09 04:06:55

151

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How to find the numbers efficiently given their sum and product?

Published on 09 Apr 2026 - 4:06

score 79 · Answer 7 · 2026-04-12 21:05:48

79

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A system of quadratic diophantine equations

Published on 12 Apr 2026 - 21:05

score 277 · Answer 8 · 2026-04-12 03:18:41

277

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When a number $N$ is expressible as a sum of two squares in EXACTLY three ways

Published on 12 Apr 2026 - 3:18

score 91 · Answer 9 · 2026-04-13 08:52:06

91

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Does the equation $k^k+1=a^2$ have any positive integer solutions?

Published on 13 Apr 2026 - 8:52

score 176 · Answer 10 · 2026-04-16 06:55:44

176

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A Diophantine Equation Related to the Markoff Numbers

Published on 16 Apr 2026 - 6:55

score 82 · Answer 11 · 2026-04-13 13:06:07

82

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How to solve this four variables system of equations?

Published on 13 Apr 2026 - 13:06

score 55 · Answer 12 · 2026-04-16 16:15:31

55

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Prove that, if $a, b, c \in \mathbb{Z}$ then $8a^{3}+8b^{3}+8c^{3}-12a^{2}+6a-24abc+12bc \neq 1$

Published on 16 Apr 2026 - 16:15

score 103 · Answer 13 · 2026-04-11 03:23:08

103

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Help understanding proof for integers than can be expressed as $a^{3} + b^{3} + c^{3} - abc$

Published on 11 Apr 2026 - 3:23

score 51 · Answer 14 · 2026-04-15 21:25:45

51

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Given two natural numbers $a,b$ so that $ab+\left(a+1\right)\left(b+1\right)=2n=fixed,$ find $a\left(a\leq b\right)$ such that $b-a$ at the least.

Published on 15 Apr 2026 - 21:25

score 152 · Answer 15 · 2026-03-30 06:42:21

152

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How to find a pair of solutions of Linear Diophantine equation such that you minimize this expression?

Published on 30 Mar 2026 - 6:42

List Question

Solving Dudeney's "A Question of Cubes": sum of consecutive cubes is a square

Showing a system of equations has no integer solutions using modular arithmetic

Diophantine Equation with 3 Variables example

$ 3^2 + 4^2 = 5^2 $. Are there more of these equations?

The Diophantine equation $5(p^2+q^2+r^2+s^2+t^2)^2 - 7(p^4+q^4+r^4+s^4+t^4) = 90pqrst$

How to find the numbers efficiently given their sum and product?

A system of quadratic diophantine equations

When a number $N$ is expressible as a sum of two squares in EXACTLY three ways

Does the equation $k^k+1=a^2$ have any positive integer solutions?

A Diophantine Equation Related to the Markoff Numbers

How to solve this four variables system of equations?

Prove that, if $a, b, c \in \mathbb{Z}$ then $8a^{3}+8b^{3}+8c^{3}-12a^{2}+6a-24abc+12bc \neq 1$

Help understanding proof for integers than can be expressed as $a^{3} + b^{3} + c^{3} - abc$

Given two natural numbers $a,b$ so that $ab+\left(a+1\right)\left(b+1\right)=2n=fixed,$ find $a\left(a\leq b\right)$ such that $b-a$ at the least.

How to find a pair of solutions of Linear Diophantine equation such that you minimize this expression?

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