Problem

Source: 2022 Turkey JBMO TST P1

Tags: number theory, Integers, Divisibility



For positive integers $a$ and $b$, if the expression $\frac{a^2+b^2}{(a-b)^2}$ is an integer, prove that the expression $\frac{a^3+b^3}{(a-b)^3}$ is an integer as well.