Results 1 to 3 of 3

Math Help - resolve in N...

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

     <br />
x^2-3y^2+4z^2=0<br />

    good luck

    sorry, it's not in N but in Z
    there isn't any difference ^^
    Last edited by mr fantastic; December 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 (x,y,z)=(0,0,0)

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

    If x and z are not multiples of 3 then 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, x and z are multiples of 3. And thus 3y^2 is multiple of 9, so it must be that y is multiple of 3. Now set x=3x'; y=3y'; z=3z'

    We get: 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: March 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: February 2nd 2010, 05:32 PM
  3. Resolve into factors
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 8th 2009, 01:15 AM
  4. How do you resolve this mechanics equation?
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: April 1st 2009, 11:46 AM
  5. Resolve triangle
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: August 1st 2007, 02:07 PM

Search Tags


/mathhelpforum @mathhelpforum