Problem

Source: Iran 3rd round 2013 - Number Theory Exam - Problem 3

Tags: modular arithmetic, number theory proposed, number theory



Let $p>3$ a prime number. Prove that there exist $x,y \in \mathbb Z$ such that $p = 2x^2 + 3y^2$ if and only if $p \equiv 5, 11 \; (\mod 24)$ (20 points)