Question 3
Let pairwise different positive integers $a$, $b$, $c$ with $\operatorname{gcd}(a, b, c) = 1$ be such that
$$
a \mid (b - c)^2, \quad b \mid (c - a)^2, \quad c \mid (a - b)^2.
$$
Prove that there is no non-degenerate triangle with side lengths $a$, $b$ and $c$.
$$
a \mid (b - c)^2, \quad b \mid (c - a)^2, \quad c \mid (a - b)^2.
$$
Prove that there is no non-degenerate triangle with side lengths $a$, $b$ and $c$.