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Number theory - primes

  • Thread starter Fairy111
  • Start date
  • #1
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Homework Statement



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.

Homework Equations





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
 

Answers and Replies

  • #2
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Hint: [tex](n-1)(n^{k-1}+n^{k-2}+\ldots+n+1)=n^k-1[/tex]
 
  • #3
73
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its supposed to be n^(k) - 1
 
  • #4
316
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its supposed to be n^(k) - 1
Isn't that the same as the RHS of the formula I wrote?
 

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