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Number Theory - divisibility and primes

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that any integer n >= 2 such that n divides (n-1)! + 1 is prime.


    2. Relevant equations



    3. The attempt at a solution
    I'm having trouble getting started, I have no idea how to approach this, can someone give a hint on where to begin maybe because I'm just not seeing it.
     
  2. jcsd
  3. Jan 22, 2009 #2
    Assuming that n divides [tex](n-1) \cdot (n-2) \cdots 2 + 1[/tex]. Show that this entails [tex](n-1), (n-2), \cdots 2[/tex] do not divide [tex]n[/tex]. In other words, nothing less than n divides n (except the trivial case).
     
    Last edited: Jan 22, 2009
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