For what positive integers n does 15|M

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Homework Statement



For what positive integers n does [tex]15|2^{2n}-1[/tex]

Homework Equations



We know [itex]2^{2n}\equiv1mod15[/itex]

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

The Attempt at a Solution



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

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