List questions from diophantine-equations

Published on 14 Apr 2026 - 3:29

173

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An identity form: $x_1^3+x_2^3+x_3^3+x_4^3=y_1^3+y_2^3+y_3^3+y_4^3$

Published on 16 Apr 2026 - 19:42

189

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How to solve $n^2+1 \mid 2^n+1$ for positive integer $n$?

Published on 16 Apr 2026 - 0:16

111

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A conjecture on diophantine equation

Published on 25 Mar 2026 - 11:18

92

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rational solutions of $r^n-s^n=1$?

Published on 15 Apr 2026 - 1:59

342

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Prove there are no integer solutions

Published on 10 Apr 2026 - 23:59

108

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Find all solutions of $9^x-4^y=5^z$ over the naturals

Published on 15 Apr 2026 - 7:28

87

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Prove that $4bc+3b+3c+2$ is never a perfect square

Published on 14 Apr 2026 - 18:08

223

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Find the integral solution of a given equation while minimizing the integral sum of solution

Published on 12 Apr 2026 - 8:04

81

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Integer solutions to $x^2+1=ay$

Published on 16 Apr 2026 - 12:12

95

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Solve an equation for natural numbered ordered pairs

Published on 10 Apr 2026 - 23:03

190

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About the absolute value and the place on a number field

Published on 17 Apr 2026 - 4:16

194

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Positive integer solutions of $x^2-1 = y^p$

Published on 15 Apr 2026 - 4:04

300

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Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$

Published on 16 Apr 2026 - 22:40

869

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Let $x$, $y$ and $z$ be natural numbers satisfying $x^2 + y^2 + 1 = xyz$. Prove that $z = 3$.

Published on 25 Mar 2026 - 18:59

List Question

number of solutions of a quadric diophantine equation

An identity form: $x_1^3+x_2^3+x_3^3+x_4^3=y_1^3+y_2^3+y_3^3+y_4^3$

How to solve $n^2+1 \mid 2^n+1$ for positive integer $n$?

A conjecture on diophantine equation

rational solutions of $r^n-s^n=1$?

Prove there are no integer solutions

Find all solutions of $9^x-4^y=5^z$ over the naturals

Prove that $4bc+3b+3c+2$ is never a perfect square

Find the integral solution of a given equation while minimizing the integral sum of solution

Integer solutions to $x^2+1=ay$

Solve an equation for natural numbered ordered pairs

About the absolute value and the place on a number field

Positive integer solutions of $x^2-1 = y^p$

Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$

Let $x$, $y$ and $z$ be natural numbers satisfying $x^2 + y^2 + 1 = xyz$. Prove that $z = 3$.

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