Question 165
Let $a, b, c$ be pairwise distinct prime natural numbers. Prove that the number
$$
(a b)^{c-1} + (b c)^{a-1} + (c a)^{b-1} - 1
$$
is a multiple of the product $a b c$.
$$
(a b)^{c-1} + (b c)^{a-1} + (c a)^{b-1} - 1
$$
is a multiple of the product $a b c$.