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: Primitive roots

  1. Dec 7, 2004 #1
    let g be a primitive root of the odd prime p
    show that -g is a primitive root or not according as
    p==1 ( mod 4) or p==3(mod4)

    how would i start in solving this problem
  2. jcsd
  3. Dec 7, 2004 #2
    For p==1 Mod 4, there exists an X such that X^2 ==-1 Mod p. This is not true for p==3 Mod 4. If x is a primitive root then x^((p-1)/2) = -1 since the smallest power of x that is 1 Mod p is x^(p-1). So, those are the facts needed.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Primitive roots Date
Length of primitive cell Jul 7, 2012
Using primitives to integrate moments of Inertia Nov 5, 2005
Primitive roots? Sep 4, 2005
Primitive function Jun 7, 2005
Primitive roots, specifically of 18 Mar 11, 2005