# For what positive integers n does 15|M

1. Oct 17, 2012

### maximus101

1. The problem statement, all variables and given/known data

For what positive integers n does $$15|2^{2n}-1$$

2. Relevant equations

We know $2^{2n}\equiv1mod15$

I was thinking this might be helpful but not sure
$x^{2} ≡ −1 (mod p)$ is solvable if and only if $p ≡ 1 (mod 4)$

3. The attempt at a solution

I think that the answer is for all $n=2k$ where $k$ is an integer
from plugging in various values of n, however I am not sure how to prove it? Any suggestions