Find $4$ primes that divide $14^{60} - 33^{60}$
okay, so the easiest thing to do was to re-write that as $7^{60}2^{60} - 11^{60}3^{60}$. However, that doesn't really help. Next step is the little Fermat's theorem, makes sense to try with modulo $2, 3, 7, 11$. However I don't remember how to do that, how to start. Would appreciate any help.
$$33^{60}-14^{60}$$ is immediately divisible by $33^2-14^2=(33-14)(33+14)$ which are primes
Using Fermat's little theorem $a^{60}\equiv1\pmod p$ for $(a,p)=1$ and if $\phi(p)=p-1$ divides $60$
$\implies a^{60}\equiv b^{60}\pmod p$ for $(ab,p)=1$
Clearly two possible values of $p$ are $31,61$