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Quick check on Korstelt's Criterion

  1. May 1, 2007 #1
    1. The problem statement, all variables and given/known data
    N is a Carmichael number. It is known that N is square free, show tha tif p is prim and p|N, the (p-1)|(N-1).

    2. Relevant equations
    a^N ≡ a (mod N)

    3. The attempt at a solution
    I want to know if this is good enough or if there is a cleaner way to state it. Thanks!

    Let a be a genrator of Z*p, so a has order (p-1). Now (p|N)|a(a^(N-1)-1) but not p|a, so a^(N-1)=1 mod p, hence (N-1) must be divisible by (p-1), the order of a mod p. QED
  2. jcsd
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