1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: For what positive integers n does 15|M

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant 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]

    3. 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
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted