# Fermats theorem, Euler's phi function application

If $p,q$ are distinct primes and $a$ is any integer,then prove that $$a^{pq} - a^p - a^q + a$$ is divisible by $pq$.

Using Fermat we have $$(a^q)^p-a^p-a^q+a\equiv a^q-a-a^q+a\equiv 0\bmod p.$$ What is the result modulo $q$?