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Math Help - How does one solve a quadratic Diophantine equation?

  1. #1
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    How does one solve a quadratic Diophantine equation?

     <br />
x^2 - Dy^2 = 1<br />

    For D = 2, x = 3 and y = 2.

    What is the best way to go about solving an equation like this, where D is a known value, and x and y are variables?

    Thanks,
    Patrick
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  2. #2
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    Quote Originally Posted by PatrickFoster View Post
     <br />
x^2 - Dy^2 = 1<br />

    For D = 2, x = 3 and y = 2.

    What is the best way to go about solving an equation like this, where D is a known value, and x and y are variables?

    Thanks,
    Patrick
    Google "Pell's equation" to learn a little about these equations, which in general have no trivial solution and require some thorough knowledge of some rather nice quadratic number fields and their integer rings.

    Tonio
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