Results 1 to 2 of 2

Math Help - need help by tonight PLEASE!!!

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    13

    need help by tonight PLEASE!!!

    How do I solve these kind of quadratic congruence problems?!

    x^2 is congruent to 53 mod 143

    I said 143=11x13

    so x^2 is congruent to 53 mod 11 AND x^2 is congruent to 53 mod 13


    where do i go from there?! Please any help would be great..My final is tomorrow and this is the only thing that is confusing me!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by kel1487 View Post
    How do I solve these kind of quadratic congruence problems?!

    x^2 is congruent to 53 mod 143

    I said 143=11x13

    so x^2 is congruent to 53 mod 11 AND x^2 is congruent to 53 mod 13


    where do i go from there?! Please any help would be great..My final is tomorrow and this is the only thing that is confusing me!!
    That's the right way to start. Then 53\equiv 9\pmod{11}, and the equation x^2\equiv9\pmod{11} has solutions x\equiv\pm3\pmod{11}. Also, 53\equiv 1\pmod{13}, and the equation x^2\equiv1\pmod{13} has solutions x\equiv\pm1\pmod{13}.

    So we are looking for numbers of the form (multiple of 11) 3, that are also of the form (multiple of 13) 1. The easiest way to find such numbers is simply to go through the multiples of 11, looking at the numbers 3 from these, and seeing if they are within 1 of a multiple of 13.

    The first one we find is 14 (=11+3=13+1).

    Then 25 (=22+3=26-1); 118 (=121-3=117+1); and 129 (=132-3=130-1).

    So there are four solutions, x\equiv 14, 25, 118, 119\pmod{143}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mean Value Theorem- Need help tonight please
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 28th 2009, 07:24 PM
  2. I need help with this before 12am tonight!!
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 3rd 2009, 04:50 PM
  3. I got to figure this out tonight
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 24th 2008, 07:39 PM
  4. Need Help for tonight
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 22nd 2006, 05:06 PM

Search Tags


/mathhelpforum @mathhelpforum