8. Let $a_1, \dots, a_m$ and $b_1, \dots, b_m$ be any two permutations of $1, 2, \dots, m$.
(a) Show that if $m > 1$ is a prime, then there exist $i$ and $j$, $i \neq j$ satisfying
$m | (a_i b_i - a_j b_j)$.
(b) Prove the same assertion of $m$ is composite.