List questions from diophantine-equations

Published on 10 May 2026 - 12:34

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Solutions for $65x^2-57y^2=8 \cdot 61$

Published on 17 Apr 2026 - 19:47

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What is the minimum n to get a prime pythagorean n-tuple?

Published on 10 May 2026 - 12:33

132

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Is "$a^p + b^p = c^p + d^p \Rightarrow (a+b) \equiv (c+d) \mod p$" true?

Published on 25 Mar 2026 - 6:28

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About the solutions of the equation $ay^p-bx^q=k$

Published on 13 Apr 2026 - 13:09

205

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Bounded Solution for Linear Diophantine Equation problem

Published on 08 Apr 2026 - 22:31

237

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Solve the equation in positive integers $k^m+m^n=kmn$

Published on 26 Mar 2026 - 16:00

112

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Show that $x^2-dy^2 = -2$ with $d = m^2+2$ has infinitetly many integer solutions

Published on 18 Apr 2026 - 13:51

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Solve in $\mathbb{Z}$ the equation $x^4 + 1 = 2y^2$.

Published on 05 May 2026 - 2:05

42

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Theorem on diophantine equations in $\mathbb Z_n$ and in $\mathbb Z$

Published on 11 Apr 2026 - 22:06

320

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On integer solutions to $a^3+b^3+c^3+d^3=3$

Published on 15 Apr 2026 - 16:08

112

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Find $a, b \in \mathbb{N} $ such that $\frac{1}{a}+\frac{1}{b} +\frac{1}{(a,b)}+\frac{1}{[a,b]}=\frac{1}{2}$

Published on 29 Mar 2026 - 6:49

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Show: if $k = x^3 - y^3$, where $x, y \in \mathbb{Q}_{>0}$, then $k = u^3 + v^3$ with $u, v \in \mathbb{Q}_{>0}$

Published on 15 Apr 2026 - 20:47

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Number of non-integer solutions in an diophantine equation of order 2

Published on 16 Apr 2026 - 10:28

367

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Diophantine quadratic $(5m+3)(3m+1)=n^2$

Published on 16 Apr 2026 - 8:03

List Question

Find the natural solutions of $a^3-b^3=999$

Solutions for $65x^2-57y^2=8 \cdot 61$

What is the minimum n to get a prime pythagorean n-tuple?

Is "$a^p + b^p = c^p + d^p \Rightarrow (a+b) \equiv (c+d) \mod p$" true?

About the solutions of the equation $ay^p-bx^q=k$

Bounded Solution for Linear Diophantine Equation problem

Solve the equation in positive integers $k^m+m^n=kmn$

Show that $x^2-dy^2 = -2$ with $d = m^2+2$ has infinitetly many integer solutions

Solve in $\mathbb{Z}$ the equation $x^4 + 1 = 2y^2$.

Theorem on diophantine equations in $\mathbb Z_n$ and in $\mathbb Z$

On integer solutions to $a^3+b^3+c^3+d^3=3$

Find $a, b \in \mathbb{N} $ such that $\frac{1}{a}+\frac{1}{b} +\frac{1}{(a,b)}+\frac{1}{[a,b]}=\frac{1}{2}$

Show: if $k = x^3 - y^3$, where $x, y \in \mathbb{Q}_{>0}$, then $k = u^3 + v^3$ with $u, v \in \mathbb{Q}_{>0}$

Number of non-integer solutions in an diophantine equation of order 2

Diophantine quadratic $(5m+3)(3m+1)=n^2$

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