Let $x$ and $y$ be positive integers such that $\frac{x^2-1}{y+1}+\frac{y^2-1}{x+1}$ is integer. Prove that numbers $\frac{x^2-1}{y+1}$ and $\frac{y^2-1}{x+1}$ are integers
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009
Tags: number theory, Integer