Results 1 to 3 of 3

Thread: resolve in N...

  1. #1
    Newbie
    Joined
    Dec 2008
    From
    France
    Posts
    10
    the equation :

    $\displaystyle
    x^2-3y^2+4z^2=0
    $

    good luck

    sorry, it's not in N but in Z
    there isn't any difference ^^
    Last edited by mr fantastic; Dec 22nd 2008 at 02:54 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member PaulRS's Avatar
    Joined
    Oct 2007
    Posts
    571
    First, we obviously have the trivial solution $\displaystyle (x,y,z)=(0,0,0)$

    Now suppose there's another solution $\displaystyle (x,y,z)$

    If $\displaystyle x$ and $\displaystyle z$ are not multiples of 3 then $\displaystyle x^2+4z^2\equiv{5}(\bmod.3)$ a contradiction.

    Again if only one of them ( x or z) is multiple of 3 we get a contradiction ( try it).

    So both, $\displaystyle x$ and $\displaystyle z$ are multiples of 3. And thus $\displaystyle 3y^2$ is multiple of 9, so it must be that $\displaystyle y$ is multiple of 3. Now set $\displaystyle x=3x'$; $\displaystyle y=3y'$; $\displaystyle z=3z'$

    We get: $\displaystyle x'^2-3y'^2+4z'^2=0$ (dividing by 9)

    And it follows by infinite descent that there can be no other solution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    From
    France
    Posts
    10
    yes good, i post an other equation ^^
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help me resolve this...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Mar 1st 2012, 07:41 PM
  2. Hey can someone help? I just can't resolve this problem !
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: Feb 2nd 2010, 05:32 PM
  3. Resolve into factors
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Dec 8th 2009, 01:15 AM
  4. How do you resolve this mechanics equation?
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: Apr 1st 2009, 11:46 AM
  5. Resolve triangle
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Aug 1st 2007, 02:07 PM

Search Tags


/mathhelpforum @mathhelpforum