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!

Number theory: primitive roots

  1. Dec 16, 2009 #1
    Find a primitive root modulo 101. What integers mod 101 are 5th powers? 7th powers?

    -I tested 2.
    -2 and 5 are the prime factors dividing phi(101)=100 so i calculated 2^50 is not congruent to 1 mod 101 and 2^20 is not congruent to 1 mod 101.
    -Therefore 2 is a primitive root modulo 101

    I guess this means to find find all m such that there exists x such that
    x^5 = m (mod 101)

    If this is the case, then how do I find these solutions?
    I found that the congruence x^5 = 1 (mod 101) has gcd(5,100)=5 solutions. I also know that 2^100 = 1 (mod 101) so that ((2^20)^5) = 1 (mod 101).
    I don't know where to go from there.
     
    Last edited: Dec 16, 2009
  2. jcsd
  3. Dec 16, 2009 #2
    To ask what integers modulo 101 are 5th or 7th powers does not mean to find all [tex]x[/tex] such that [tex]x^5 \equiv 1 \pmod{101}[/tex] (or 7), but to find all [tex]m[/tex] such that there exists [tex]x[/tex] such that [tex]x^5 \equiv m \pmod{101}[/tex] (or 7).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Number theory: primitive roots
  1. Primitive roots (Replies: 1)

  2. Primitive root (Replies: 1)

Loading...