Problem

Source: 2011 Saudi Arabia BMO TST 1.2 - Balkan MO

Tags: number theory



For any positive integer $n$, let $a_n$ be the number of pairs $(x,y)$ of integers satisfying $|x^2-y^2| = n$. (a) Find $a_{1432}$ and $a_{1433}$. (b) Find $a_n$ .