- #1

- 22

- 0

## 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