Problem

Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade

Tags: algebra, number theory, prime numbers



Find all prime numbers $p$, for which there exist $x, y \in \mathbb{Q}^+$ and $n \in \mathbb{N}$, satisfying $x+y+\frac{p}{x}+\frac{p}{y}=3n$.