Results 1 to 2 of 2

Math Help - primitive root

  1. #1
    Banned
    Joined
    Mar 2010
    From
    India
    Posts
    10

    primitive root

    For which prime p does the congruence (x^2 + 4x + 5) mod p =0 have
    a solution? some hint about this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by fyw891105 View Post
    For which prime p does the congruence (x^2 + 4x + 5) mod p =0 have
    a solution? some hint about this.

    1) if p = 2 then x^2+4x+5=x^2+1=(x+1)^2\!\!\!\pmod 2 and we have a double root;

    2) If p > 2 then the equation has a solution iff the quadratic's determinant is a square modulo p, i.e. \Delta=16-20=-4 is a square modulo p \Longleftrightarrow -1 is a square modulo p.

    For example, for p = 5,13,17,29, 97 we have a solution, pero not for p = 3, 7, 19, 31

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 27th 2011, 06:59 PM
  2. Primitive root of 2^n + 1
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: May 9th 2010, 01:34 PM
  3. primitive root
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 10th 2009, 06:53 PM
  4. Primitive root
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 29th 2008, 08:47 PM
  5. primitive root
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: December 30th 2006, 03:21 PM

Search Tags


/mathhelpforum @mathhelpforum