Results 1 to 2 of 2

Math Help - Primitive Root Question

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    152

    Primitive Root Question

    Show that if p is a prime and p=2q+1, where q is an odd prime and a is a positive integer with 1 < a < p-1, then p- a^2 is a primitive root modulo p.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member PaulRS's Avatar
    Joined
    Oct 2007
    Posts
    571
    Note that p \equiv 3 (\bmod. 4) what does this tell you about -1 ? and about p-a^2 ?

    Next, prove that all non-quadratic residues module p (except for -1) must be primitive roots module p.
    Hint : Count

    Link the two parts.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Primitive root question
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: November 10th 2011, 12:18 AM
  2. Primitive Root Question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 18th 2010, 05:46 PM
  3. primitive root question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 17th 2009, 07:33 PM
  4. one more primitive root question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: July 11th 2009, 04:59 AM
  5. Primitive root question
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: November 5th 2007, 11:19 PM

Search Tags


/mathhelpforum @mathhelpforum