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3 Variable equation that i'm stuck on .

  1. May 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the following equation in N^3:

    x^2+y^2+z^2=xyz-1



    3. The attempt at a solution

    I moved all the terms to one side, but I don't know what to do from there on.
     
  2. jcsd
  3. May 18, 2012 #2

    HallsofIvy

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    That's a cubic Diophantine equation and those are notoriously difficult!
     
  4. May 18, 2012 #3
    Do you have any idea on how i can start it? I think i should make x=t and x=s as my two parameters and i'll get an equation in z. Is that a good idea???
     
  5. May 18, 2012 #4
    Consider the possibilities mod 2, then mod 4, on the two sides of the equation as originally given.
     
  6. May 19, 2012 #5
    yea that's what i did i got lhs=1mod4 and rhs is -1mod4 thus this equation has no solution.
     
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