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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
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