List questions from diophantine-equations

Published on 12 Apr 2026 - 3:04

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To any given positive integer $m$ there exists a positive integer $x,$ such that $x^3+x+m^2$ is a square

Published on 16 Apr 2026 - 17:35

136

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Solving the equation $yz=y^z-2$

Published on 13 Apr 2026 - 18:54

135

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Find all positive integers such that $m+n+mn=2016$

Published on 14 Apr 2026 - 18:51

391

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Diophantine equation negative sign

Published on 12 Apr 2026 - 10:22

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Solve the Diophantine equation $x^6 + 3x^3 + 1 = y^4$

Published on 16 Apr 2026 - 15:46

98

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Solve $\frac{1}{x}+\frac{1}{y}=\frac{1}{2}+\frac{1}{z}$

Published on 16 Apr 2026 - 11:43

137

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Computing greatest common divisor and determining whether Diophantine equation has solutions

Published on 09 Apr 2026 - 4:27

144

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Solutions of Exponential Diophantine Equations $a^x=b^y$

Published on 13 Apr 2026 - 10:08

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Most even numbers is a sum $a+b+c+d$ where $a^2+b^2+c^2=d^2$

Published on 15 Apr 2026 - 12:57

195

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Method for Expressing an Integer as the Sum of Three Cubes

Published on 11 Apr 2026 - 15:52

267

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How prove infinitely many postive integers triples $(x,y,z)$ such $(x+y+z)^2+2(x+y+z)=5(xy+yz+zx)$

Published on 25 Mar 2026 - 18:57

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Applications of Mordell-Weil's theorem

Published on 12 Apr 2026 - 5:26

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$(a^2+b^2-ab)(a^2+b^2-2ab)$ is a perfect square

Published on 13 Apr 2026 - 4:47

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Infinitely many solutions to $a^x+b^y=c^z$ for given $ x, y, z \in \mathbb{N}$?

Published on 15 Apr 2026 - 3:10

List Question

First 30 solutions of Pell's equation.

To any given positive integer $m$ there exists a positive integer $x,$ such that $x^3+x+m^2$ is a square

Solving the equation $yz=y^z-2$

Find all positive integers such that $m+n+mn=2016$

Diophantine equation negative sign

Solve the Diophantine equation $x^6 + 3x^3 + 1 = y^4$

Solve $\frac{1}{x}+\frac{1}{y}=\frac{1}{2}+\frac{1}{z}$

Computing greatest common divisor and determining whether Diophantine equation has solutions

Solutions of Exponential Diophantine Equations $a^x=b^y$

Most even numbers is a sum $a+b+c+d$ where $a^2+b^2+c^2=d^2$

Method for Expressing an Integer as the Sum of Three Cubes

How prove infinitely many postive integers triples $(x,y,z)$ such $(x+y+z)^2+2(x+y+z)=5(xy+yz+zx)$

Applications of Mordell-Weil's theorem

$(a^2+b^2-ab)(a^2+b^2-2ab)$ is a perfect square

Infinitely many solutions to $a^x+b^y=c^z$ for given $ x, y, z \in \mathbb{N}$?

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