Show that 13 divides $2^{70}+3^{70}$ 
Show that $13$ divides $2^{70} + 3^{70}$.

My main problem here is trying to figure out how to separate the two elements in the sum, and then use Fermat's little theorem. So how can I separate the two?
Thanks!

$2^{12} \equiv 1 \pmod{13}$ and $3^{12} \equiv 1 \pmod{13}$ by Fermat's Little Theorem.
Hence, $2^{72} \equiv 1 \pmod{13}$ and $3^{72} \equiv 1 \pmod{13}$
$2^{72} \equiv 1 \pmod{13} \Rightarrow 2^{72} \equiv 40 \pmod{13} \Rightarrow 2^{70} \equiv 10 \pmod{13}$
$3^{72} \equiv 1 \pmod{13} \Rightarrow 3^{72} \equiv 27 \pmod{13} \Rightarrow 3^{70} \equiv 3 \pmod{13}$
Hence, you get the result.
