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Number theory - primes

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Let n and k be integers with n>=2 and k>=2. Prove that (n-1)|(n^k - 1).
    Hence prove that if n^k - 1 is prime then n=2 and k is prime.

    2. Relevant equations

    3. The attempt at a solution

    I think you go about this question by using proof by induction. However im really not sure how to do this. Any help would be great! Thanks
  2. jcsd
  3. Mar 17, 2009 #2
    Hint: [tex](n-1)(n^{k-1}+n^{k-2}+\ldots+n+1)=n^k-1[/tex]
  4. Mar 17, 2009 #3
    its supposed to be n^(k) - 1
  5. Mar 17, 2009 #4
    Isn't that the same as the RHS of the formula I wrote?
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