Results 1 to 4 of 4

Math Help - mod equations problem...

  1. #1
    Member
    Joined
    May 2008
    Posts
    86

    mod equations problem...

    Hi!
    I need to prove that there is *no* solution to the equation:
    x^2 + y^2 = 3(mod4)

    I tried to assume there is a solution, meaning, there are X,Y in Z so that:
    x^2 + y^2 = 3 + 4*k.

    I tried to reach a contradiction, but alas, I did not succeed :-\

    Help?
    Thank you very much, in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Quote Originally Posted by aurora View Post
    Hi!
    I need to prove that there is *no* solution to the equation:
    x^2 + y^2 = 3(mod4)

    I tried to assume there is a solution, meaning, there are X,Y in Z so that:
    x^2 + y^2 = 3 + 4*k.

    I tried to reach a contradiction, but alas, I did not succeed :-\

    Help?
    Thank you very much, in advance!
    Find all the possibilities.

    mod equations problem...-mods.jpg

    The numbers are the modulus with respect to 4
    Does it help ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by aurora View Post
    Hi!
    I need to prove that there is *no* solution to the equation:
    x^2 + y^2 = 3(mod4)

    I tried to assume there is a solution, meaning, there are X,Y in Z so that:
    x^2 + y^2 = 3 + 4*k.

    I tried to reach a contradiction, but alas, I did not succeed :-\

    Help?
    Thank you very much, in advance!
    If x is even then x^2\equiv 0.
    If x is odd then x^2 \equiv 1.
    Thus, x^2+y^2 \equiv 0,1,2(\bmod 4).
    Thus, it is impossible.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2008
    Posts
    86
    Thank you very much, both of you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equations problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 15th 2010, 09:06 PM
  2. system of equations problem
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: September 21st 2009, 08:05 PM
  3. Replies: 3
    Last Post: February 27th 2009, 08:05 PM
  4. Differential Equations Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 6th 2008, 06:05 AM
  5. Equations Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 12th 2008, 01:26 AM

Search Tags


/mathhelpforum @mathhelpforum