New posts in Diophantine Equations

number of integer solutions to $2x_1 + x_2 + x_3 = n$

$x^2+y^2=2z^2$, positive integer solutions

Show that $x^2 + y^2$ and $x^2 - y^2$ cannot both be perfect squares at the same time where $x, y \in \mathbb{Z}^+$.

Does the Pell-like equation $X^2-dY^2=k$ have a simple recursion like $X^2-dY^2=1$?

Prove that the equation $3^k = m^2 + n^2 + 1$ has infinitely many solutions in positive integers.

On equations $m^2+1=5^n$

Does the equation $x^2+23y^2=2z^2$ have integer solutions?

Chinese New Year Equation 2016

How many answers to $|3^x-2^y|=5$?

A diophantine equation with only "titanic" solutions