Results 1 to 3 of 3

Math Help - Show that there exist no positive integers ...

  1. #1
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Show that there exist no positive integers ...

    Show that there exist no positive integers m and n such that m^2+n^2 and m^2-n^2 are both perfect squares.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jun 2010
    From
    Israel
    Posts
    148

    Re: Show that there exist no positive integers ...

    There's a theorem by Fermat: The equation x^4-y^4=z^2 is not solvable in nonzero integers.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: Show that there exist no positive integers ...

    Quote Originally Posted by melese View Post
    There's a theorem by Fermat: The equation x^4-y^4=z^2 is not solvable in nonzero integers.
    Thanks!

    So, m^2+n^2=a^2 and m^2-n^2=b^2.

    (m^2+n^2)(m^2-n^2)=a^2b^2

    m^4-n^4=(ab)^2, which has no solution.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 1st 2011, 05:24 AM
  2. Replies: 1
    Last Post: November 20th 2011, 10:13 AM
  3. show that limit exist
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 1st 2010, 03:53 PM
  4. if x and n are positive integers....
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 7th 2009, 12:07 AM
  5. Replies: 2
    Last Post: September 22nd 2007, 03:03 PM

Search Tags


/mathhelpforum @mathhelpforum