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

I have tried many times, but failed, please help me

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    $\begingroup$ What attempts have you made so far? If you add them to the question, then people may be able to point out where you are going wrong $\endgroup$ – lioness99a Mar 22 '17 at 9:26

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 $q$?


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