I am given two distinct primes $p$ and $q$, where $$m = p*q$$ Also,
$$ \begin{cases} r\equiv 1\mod p-1\\ r\equiv 1\mod q-1 \end{cases} $$
I have to show that given an integer a, show that $$a^r \equiv a \mod (m)$$
I'm not sure how to get started. I know I can tie this in to Fermat's Little Theorem and I've found something here CRT + Fermat's Little Theorem that was somewhat related to my question but I had a hard time seeing where to go. Just need a little hint to get me in the right direction! Thanks.