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(a^m^2 + 1) | (a^n^2 - 1) ?

  1. Oct 17, 2005 #1
    (a^m^2 + 1) | (a^n^2 - 1) ???

    I'm sure there is a quick trick I'm missing somewhere... but anyone have any ideas on how to prove:

    (a^m^2 + 1) | (a^n^2 - 1) , for n > m.

    [Show [a^(n^2) -1] is divisible by [a^(m^2) +1]

    Thanks a lot. . .

    (I've tried letting k=n-m, and other stuff like that... kept going in circles. I'm guessing Fermat's Little Thm comes in somewhere?)
     
  2. jcsd
  3. Oct 17, 2005 #2
    It's not true. A counterexample exists among the very small integers...
     
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