1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    Try it for a few small composite values of n. And be careful, 2 is prime.
    Last edited: Sep 8, 2015
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted