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Math Help - Equation of two variables

  1. #1
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    Equation of two variables

    How do i solve this equation of two variables?

    I need to find out how many solutions in \mathbb{Z}\times\mathbb{Z} the quation has, x^4-x^3y-8y^4=0

    I don't know how to solve equations of two or more variables :-s.
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  2. #2
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    Quote Originally Posted by Utherr View Post
    How do i solve this equation of two variables?

    I need to find out how many solutions in \mathbb{Z}\times\mathbb{Z} the quation has, x^4-x^3y-8y^4=0

    I don't know how to solve equations of two or more variables :-s.

    By mere inspection, (2,1) is one solution, and since the left hand polynomial is a homogeneous one (of degree 4), t(2,1)=(2t,t) is again a solution for any t\in\mathbb{Z} , so there are infinite (i.e., \aleph_0 solutions).

    Tonio
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  3. #3
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    So there's no actual calculation here? just thinking? Can you elaborate ? :-s the part after "the left hand polynomial"
    Last edited by Utherr; July 16th 2010 at 08:10 AM.
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