For some integer n the equation $x^2 + y^2 + z^2 -xy -yz - zx = n$ has an integer solution $x, y, z$. Prove that the equation$ x^2 + y^2 - xy = n$ also has an integer solution $x, y$. Alexandr Yuran
Problem
Source: Tournament of Towns, Junior O-Level Paper, Spring 2020 , p4
Tags: Diophantine equation, diophantine, number theory