Results 1 to 3 of 3

Math Help - Solve x^2 - 10y^2 = 2

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    36

    Solve x^2 - 10y^2 = 2

    I want to show that x^2-10y^2 = \pm 2 is insoluble in integers. I've tried factorisation in \mathbb{Z}[\sqrt{10}] but this isn't a UFD so I can't get things to work. I've also tried considering norms. Is there a more elementary idea that can show this? I assume we should look for a contradiction. By simple "odd/even" arguments it's clear that x must be even and y must be odd, but I can't get much further. If anyone's able to give a hint then that would be most appreciated!

    EDIT: OK I've spotted it - just look at the equation modulo 10 ! Incidentally, is there a way of deleting a question of yours so that other people won't waste time trying to answer something you've already done?
    Last edited by Boysilver; February 14th 2010 at 03:41 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,569
    Thanks
    1410
    Try modulo 4. For n any even integer, n^2 is congruent to 0 mod 4. For n any odd integer, n^2 is congruent to 1 mod 4.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Boysilver View Post
    ...Incidentally, is there a way of deleting a question of yours so that other people won't waste time trying to answer something you've already done?
    you are not to delete your problems. simply edit your thread saying you have solved it. or mark the thread as "Solved" using Thread Tools.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. need to solve summation equation to solve sum(x2)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 16th 2010, 10:29 PM
  2. Solve for x
    Posted in the Algebra Forum
    Replies: 6
    Last Post: March 3rd 2010, 06:34 PM
  3. Replies: 1
    Last Post: June 9th 2009, 10:37 PM
  4. how can i solve this
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 6th 2008, 09:11 AM
  5. how do i solve this?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 2nd 2008, 02:58 PM

Search Tags


/mathhelpforum @mathhelpforum