Find all pairs of integers $(x,y)$ satisfying the following condition: each of the numbers $x^3 + y$ and $x + y^3$ is divisible by $x^2 + y^2$ Tournament of Towns
Source: 2013 Romania JBMO TST 5.1
Tags: number theory, divides, divisible
Find all pairs of integers $(x,y)$ satisfying the following condition: each of the numbers $x^3 + y$ and $x + y^3$ is divisible by $x^2 + y^2$ Tournament of Towns