Question

Follow-up 'Diophantine' question: extrapolating to the general case

score 119 · Answer 1 · 2026-04-22 10:45:52

119

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Follow-up 'Diophantine' question: extrapolating to the general case

Published on 22 Apr 2026 - 10:45

score 276 · Answer 2 · 2026-03-28 11:06:06

276

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one equation three unknowns

Published on 28 Mar 2026 - 11:06

score 63 · Answer 3 · 2026-04-16 13:04:38

63

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A way to solve equations of the form $(\frac{n}{a})! = b$?

Published on 16 Apr 2026 - 13:04

score 127 · Answer 4 · 2026-04-10 09:29:28

127

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Has this family of Diophantine equations ever been studied?

Published on 10 Apr 2026 - 9:29

score 229 · Answer 5 · 2026-04-16 05:49:03

229

Views

Proving that every positive integer is of the form $x^2+y^2-5z^2$

Published on 16 Apr 2026 - 5:49

score 106 · Answer 6 · 2026-04-17 07:42:28

106

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Diophantine question: find two positive numbers a and b such that $a\cdot b+a=c^3$ and $a\cdot b+b=d^3$

Published on 17 Apr 2026 - 7:42

score 31 · Answer 7 · 2026-04-16 17:43:33

31

Views

How many positive integral solutions exist for $2a+3b-c = 0$ where $a$ ranges from $0$ to $5$, $b$ from $0$ to $10$ and $c$ from $0$ to $40$?

Published on 16 Apr 2026 - 17:43

score 79 · Answer 8 · 2026-04-16 08:31:40

79

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Are there coprime integers $x,y$ ( greater than 1 in absolute value) such that $3y(4x^3-y^3)$ is a square?

Published on 16 Apr 2026 - 8:31

score 71 · Answer 9 · 2026-04-14 21:44:41

71

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Finding all integer solutions of $\frac{1}{x} + \frac{1}{y} - \frac{1}{z} = \frac12$

Published on 14 Apr 2026 - 21:44

score 204 · Answer 10 · 2026-04-14 07:19:03

204

Views

Cubic diophantine equation in two variables

Published on 14 Apr 2026 - 7:19

score 183 · Answer 11 · 2026-04-17 13:00:33

183

Views

All solutions $(x, y, z) \in (\mathbb{N},\mathbb{N},\mathbb{N})$ for $3x^2 + 6y^2 = z^2$

Published on 17 Apr 2026 - 13:00

score 305 · Answer 12 · 2026-04-16 02:35:04

305

Views

if $x^2=y^3$, then $x=a^3$ and $y=b^2$

Published on 16 Apr 2026 - 2:35

score 260 · Answer 13 · 2026-04-15 13:16:38

260

Views

Show that $3n^4+3n^2+1$ is never a perfect square

Published on 15 Apr 2026 - 13:16

score 89 · Answer 14 · 2026-04-15 15:20:47

89

Views

Diophantine equations of a certain form

Published on 15 Apr 2026 - 15:20

score 80 · Answer 15 · 2026-04-17 01:05:40

80

Views

Let $m,n \in \mathbb{Z}^+$ and $p$ be an odd prime number. Show that $n=1$ if $2^m = p^n +1$.

Published on 17 Apr 2026 - 1:05

List Question

Follow-up 'Diophantine' question: extrapolating to the general case

one equation three unknowns

A way to solve equations of the form $(\frac{n}{a})! = b$?

Has this family of Diophantine equations ever been studied?

Proving that every positive integer is of the form $x^2+y^2-5z^2$

Diophantine question: find two positive numbers a and b such that $a\cdot b+a=c^3$ and $a\cdot b+b=d^3$

How many positive integral solutions exist for $2a+3b-c = 0$ where $a$ ranges from $0$ to $5$, $b$ from $0$ to $10$ and $c$ from $0$ to $40$?

Are there coprime integers $x,y$ ( greater than 1 in absolute value) such that $3y(4x^3-y^3)$ is a square?

Finding all integer solutions of $\frac{1}{x} + \frac{1}{y} - \frac{1}{z} = \frac12$

Cubic diophantine equation in two variables

All solutions $(x, y, z) \in (\mathbb{N},\mathbb{N},\mathbb{N})$ for $3x^2 + 6y^2 = z^2$

if $x^2=y^3$, then $x=a^3$ and $y=b^2$

Show that $3n^4+3n^2+1$ is never a perfect square

Diophantine equations of a certain form

Let $m,n \in \mathbb{Z}^+$ and $p$ be an odd prime number. Show that $n=1$ if $2^m = p^n +1$.

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