Results 1 to 5 of 5

Math Help - prove there is no primitive root mod 3p

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    israel
    Posts
    13

    prove there is no primitive root mod 3p

    when p odd , p>3.

    ---------
    I don't know how to cintinue:

    a^(p-1)=1(modp)
    a^2=1(mod3)

    ....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Kanwar245's Avatar
    Joined
    Jun 2011
    From
    Canada
    Posts
    68
    Thanks
    2

    Re: prove there is no primitive root mod 3p

    Is there a condition on p that is is prime?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2013
    From
    israel
    Posts
    13

    Re: prove there is no primitive root mod 3p

    yes, p is a prime
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member Kanwar245's Avatar
    Joined
    Jun 2011
    From
    Canada
    Posts
    68
    Thanks
    2

    Re: prove there is no primitive root mod 3p

    Okay so this might help
    Suppose a is a primitive root of \{Z}_{3p}^X

    Also, \phi(3p) = \phi(3)\phi(p) = 2(p-1)
    Last edited by Kanwar245; March 27th 2013 at 05:44 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2013
    From
    israel
    Posts
    13

    Re: prove there is no primitive root mod 3p

    I solved this. thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 27th 2011, 05:59 PM
  2. Prove that 2 is a primitive root modulo p.
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 21st 2010, 05:51 PM
  3. primitive root
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 8th 2010, 08:49 AM
  4. Primitive root
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: October 5th 2008, 07:08 PM
  5. primitive root
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: April 28th 2008, 08:36 AM

Search Tags


/mathhelpforum @mathhelpforum