Results 1 to 2 of 2

Math Help - Congruence Problem

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    59

    Congruence Problem

    This is from chapter on linear congruences:

    Show that if p is an odd prime and a is a positive integer not divisible by p, then the congruence x^2 \equiv a \pmod {p} has either no solution or exactly two incongruent solutions.

    I can see If p \mid x, then there are no solutions. I'm really not sure how to approach the rest of this...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5

    Re: Congruence Problem

    Solving the 'quadratic congruence equation'...

     x^{2} \equiv a (\text{mod}\ p) (1)

    ... is equivalent to find two integers x < p and y so that is...

    a + p\ y = x^{2} (2)

    Now if x_{0} satisfies (2) for some y, then x_{1} = p-x_{0} \ne x_{0} satisfies also (2) for some other y...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. One Congruence Problem
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: September 29th 2010, 10:51 PM
  2. Congruence Problem
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: November 19th 2009, 10:17 AM
  3. congruence problem
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: July 2nd 2009, 11:24 AM
  4. Another congruence problem
    Posted in the Number Theory Forum
    Replies: 10
    Last Post: April 3rd 2009, 06:14 PM
  5. Congruence problem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: September 24th 2008, 11:54 AM

/mathhelpforum @mathhelpforum