Question 158
Find all positive integers $a, b$ and $c$ such that $\gcd(a, b, c)=1$,
$$
a\mid (b-c)^2, \quad b\mid (a-c)^2, \quad c \mid (a-b)^2
$$
and such that it is possible to construct a non-degenerate triangle whose sides have lengths $a$, $b$ and $c$.
$$
a\mid (b-c)^2, \quad b\mid (a-c)^2, \quad c \mid (a-b)^2
$$
and such that it is possible to construct a non-degenerate triangle whose sides have lengths $a$, $b$ and $c$.