List questions from diophantine-equations

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Theory of equations ( Number of positive integral solutions )

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An equation for prime numbers $\frac{p-1}{2}(2^p-1)+1=7k^2$

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$x^5 + y^2 = z^3$

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For all n there exists n distinct integers whose sum is a perfect square and whose product is a perfect cube

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Solving a pair of simultaneous Pell-like equations

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the equation $a^x+(a+1)^y=(a+2)^z$ in natural numbers.

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On $17^7+76271^3=d^2$ and coprime solutions to $x^6+y^3=z^2$?

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Primes of the form $p = (x_1 + x_2 + x_3 + x_4)\cdot(x_1 + x_2 - x_3 - x_4)\cdot(x_1 - x_2 + x_3 - x_4)\cdot(x_1 - x_2 - x_3 + x_4) $

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Does the interval $[x, x + 10 x^{1/4})$ contain a sum of two squares?

Published on 15 Apr 2026 - 5:46

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On simple integer solutions of $2^{(yp-2)/(p-2)!}=px+1,$ where $p$ is a fixed prime $\equiv 1\text{ mod }4$

Published on 16 Apr 2026 - 3:18

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Tough Mordell equation $x^3+9=y^2$

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Numbers of the form $\frac{xyz}{x+y+z}$

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Numbers of the form $\frac{xyz}{x+y+z}$, second question

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Three Variable Nonlinear Diophantine Equation

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List Question

perfect powers of the form $\frac{x^2-1}{y^2-1}$

Theory of equations ( Number of positive integral solutions )

An equation for prime numbers $\frac{p-1}{2}(2^p-1)+1=7k^2$

$x^5 + y^2 = z^3$

For all n there exists n distinct integers whose sum is a perfect square and whose product is a perfect cube

Solving a pair of simultaneous Pell-like equations

the equation $a^x+(a+1)^y=(a+2)^z$ in natural numbers.

On $17^7+76271^3=d^2$ and coprime solutions to $x^6+y^3=z^2$?

Primes of the form $p = (x_1 + x_2 + x_3 + x_4)\cdot(x_1 + x_2 - x_3 - x_4)\cdot(x_1 - x_2 + x_3 - x_4)\cdot(x_1 - x_2 - x_3 + x_4) $

Does the interval $[x, x + 10 x^{1/4})$ contain a sum of two squares?

On simple integer solutions of $2^{(yp-2)/(p-2)!}=px+1,$ where $p$ is a fixed prime $\equiv 1\text{ mod }4$

Tough Mordell equation $x^3+9=y^2$

Numbers of the form $\frac{xyz}{x+y+z}$

Numbers of the form $\frac{xyz}{x+y+z}$, second question

Three Variable Nonlinear Diophantine Equation

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