So I'm trying to use mathematical induction to show that for all integers $n \ge 1$ ,

$$ 8|(3^{2n} - 1)$$

(is divisible by 8)

I have my base case:
[P(1)], $3^2 - 1 = 9 - 1 = 8$, since $8|8$, the base case proves true

Assume [P(k)], $ 8 | (3^{2k} - 1)$.

I know that I need to show [P(k+1)], $ 8| (3^{2(k+1)}-1) $, but I'm not sure how to prove this. I've only been using induction for summation, so how could I prove divisibility?