Does there exist an infinite subset $S$ of the natural numbers such that for every $a$, $b \in S$, the number $(ab)^2$ is divisible by $a^2-ab+b^2$?
Source: MOP 2005 Homework - Blue Group #26
Tags: number theory unsolved, number theory
Does there exist an infinite subset $S$ of the natural numbers such that for every $a$, $b \in S$, the number $(ab)^2$ is divisible by $a^2-ab+b^2$?