List questions from diophantine-equations

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Integer solutions of equation $x^3+10x-1=y^3+6y$?

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How to solve $p^{2a+1}+p^a+1=b^2$ in integers?

Published on 14 Apr 2026 - 1:06

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There don't exist $a, b$ positive integers such that $a^2 + b^2$ and $a^2 - b^2$ are perfect squares

Published on 11 Apr 2026 - 23:47

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Prove that $ax + by = a + c$ has solutions if and only if $ax + by = c$ has solutions

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On the arithmetic differential equation $n''=n'$

Published on 16 Apr 2026 - 8:16

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About the equation $m^4+n^4=10m^2n^2+1$

Published on 15 Apr 2026 - 5:56

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Show that $x^3-x^2+8=y^2$ has no integer solution

Published on 16 Apr 2026 - 10:27

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fermat's last theorem by elementary methods

Published on 12 Apr 2026 - 16:52

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Solving $(a-1)^{p+1}+a^p=(a+1)^{p-1}$

Published on 17 Apr 2026 - 4:46

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Proving that $\Bigl[\frac{-4+\sqrt{26+20y+4y^2}}{2},\frac{-3+\sqrt{23+20y+4y^2}}{2}\Bigl]$ contains no integer

Published on 16 Apr 2026 - 23:23

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Parametric Diophantine solutions of $kx^4+1=y^2$.

Published on 14 Apr 2026 - 2:10

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Equation $x = \tau(2^x - 1)$

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$x^2+y^3 = z^4$ for positive integers

Published on 17 Apr 2026 - 9:18

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Find integral solutions - rational points of $4p=x^2+27y^2$ for $p>3$ prime

Published on 17 Apr 2026 - 9:57

List Question

General integer solutions of the equation $a^{2} = (b+c)^{2}$?

Integer solutions of equation $x^3+10x-1=y^3+6y$?

How to solve $p^{2a+1}+p^a+1=b^2$ in integers?

There don't exist $a, b$ positive integers such that $a^2 + b^2$ and $a^2 - b^2$ are perfect squares

Prove that $ax + by = a + c$ has solutions if and only if $ax + by = c$ has solutions

On the arithmetic differential equation $n''=n'$

About the equation $m^4+n^4=10m^2n^2+1$

Show that $x^3-x^2+8=y^2$ has no integer solution

fermat's last theorem by elementary methods

Solving $(a-1)^{p+1}+a^p=(a+1)^{p-1}$

Proving that $\Bigl[\frac{-4+\sqrt{26+20y+4y^2}}{2},\frac{-3+\sqrt{23+20y+4y^2}}{2}\Bigl]$ contains no integer

Parametric Diophantine solutions of $kx^4+1=y^2$.

Equation $x = \tau(2^x - 1)$

$x^2+y^3 = z^4$ for positive integers

Find integral solutions - rational points of $4p=x^2+27y^2$ for $p>3$ prime

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