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Are there prime numbers n for which S=/0?

  1. Sep 8, 2015 #1
    • Member warned about posting without the homework template
    We have the set:S={1<a<n:gcd(a,n)=1,a^(n-1)=/1(modn)}
    Are there prime numbers n for which S=/0?After this, are there any composite numbers n for which S=0?

    (with =/ i mean the 'not equal' and '0' is the empty set)

    for the first one i know that there are no n prime numbers suh that S to be not empty from Fermat's little theorem.Any ideas or hints for the second one?
     
  2. jcsd
  3. Sep 8, 2015 #2

    Dick

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    Try it for a few small composite values of n. And be careful, 2 is prime.
     
    Last edited: Sep 8, 2015
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