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Math Help - Fermat's little theorem

  1. #1
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    Fermat's little theorem

    It is possible for a positive integer n not to be prime and still have the property that a^(n-1) congruent to 1 mod n whenever hcf(a,n) = 1. SHow that 561 is such a positive integer n.

    So far i have:
    a^560 congruent to 1 mod 561
    (a^560)-1 = 561k where k is some integer

    I also know that 1 mod 561 is congruent to a^2a^2a^2.......a^2 (280 times)
    I have no idea what to do now?
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