1. Prove, by induction, that for every positive integer n, $\displaystyle 4^n +14 \equiv 0 (mod 6)$

Base case, n=1, $\displaystyle 6 \mid 18-0$

Assume: $\displaystyle 4^{n+1} +14 \equiv 0 (mod 6) $

Then I could write is as $\displaystyle 4^n * 4 +14 \equiv 0 (mod 6) $

I have no idea how to proceed.