Let pairwise different positive integers $a,b, c$ with gcd$(a,b,c) = 1$ are such that $a | (b - c)^2, b | (c- a)^2, c | (a - b)^2$. Prove, that there is no non-degenerate triangle with side lengths $a, b$ and $c$.
Source: 2019 Saudi Arabia March Camp Test 2.1
Tags: number theory
Let pairwise different positive integers $a,b, c$ with gcd$(a,b,c) = 1$ are such that $a | (b - c)^2, b | (c- a)^2, c | (a - b)^2$. Prove, that there is no non-degenerate triangle with side lengths $a, b$ and $c$.