Results 1 to 3 of 3

Math Help - Primitive Roots

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    14

    Primitive Roots

    Hello everyone!

    I have a question about primitive roots. I'm just trying to come up with general strategies that would help we remember tricks on how to find all primitive roots. So I came up with a few basic cases and perhaps one of you could explain how to solve them. Here it goes:

    Find all primitive roots for:
    i) 13
    ii) 2 * 13
    iii) 13^2
    iv) 2 * 13^4

    Thanks again for your help. I appreciate it. Happy Easter.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
    From
    Champaign, Illinois
    Posts
    1,163
    Quote Originally Posted by mathmaniac234 View Post
    Hello everyone!

    I have a question about primitive roots. I'm just trying to come up with general strategies that would help we remember tricks on how to find all primitive roots. So I came up with a few basic cases and perhaps one of you could explain how to solve them. Here it goes:

    Find all primitive roots for:
    i) 13
    I claim  2 is a primitive root modulo  13 (I'll let you verify).

    Let's find all other primitive roots:

    Consider  \{2^1,2^2,2^3,\cdots,2^{p-1}\} . All other primitive roots will be of the form  2^m where  (m,\phi(13))=1 .

    This means there are  \phi(\phi(13))=4 primitive roots.

     (1,12)=(5,12)=(7,12)=(11,12)=1

    So our Primitive roots are  \{2, 2^5, 2^7,2^{11}\} = \{2,6,7,11\} .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2010
    Posts
    78
    There's no good way to find primitive roots. There is one computer algorithm which runs in polynomial time *under GRH*, so really I believe that there's no general way to do it.

    However, 2 or 3 usually works. Check these two before you complain about finding primitive roots.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Primitive roots
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: July 10th 2011, 05:15 PM
  2. Primitive Roots
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: November 17th 2008, 08:09 PM
  3. Primitive roots
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 15th 2007, 09:19 AM
  4. Primitive roots
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 21st 2006, 07:05 AM
  5. Primitive Roots
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 18th 2006, 01:43 PM

Search Tags


/mathhelpforum @mathhelpforum