number theory - Using Fermat's little theorem

I have this question:

$a \equiv 12^{772} \pmod{71}$, when $0 \leq a < 71$

and I am having troubles getting it started.

$\frac{772}{71}$ is $10$ with a remainder of $62$;

How do I do this question?

Answer

$12^{772}=12^{71\cdot 10+62}\equiv 12^{10+62}=12^{71+1}\equiv 12\cdot 12=144\equiv 2$ mod $71$. So $a=2$.

Alternately,

$12^{772}=12^{70\cdot 11+2}\equiv 12^2=144\equiv 2$ mod $71$.

The first one uses the form $a^p\equiv a$ mod $p$ and the second uses the form $a^{p-1}\equiv 1$ mod $p$ if $gcd(a,p)=1$ where $p$ is prime.