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Math Help - Area of a Triangle and Elliptic Curves - Birch and Swinnerton Dyer Conjecture

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    Area of a Triangle and Elliptic Curves - Birch and Swinnerton Dyer Conjecture

    In the book by Keith Devlin on the Millenium Problems - in Chapter 6 on the Birch and Swinnerton-Dyer Conjecture we find the following text:

    "It is a fairly straightforward piece of algebraic reasoning to show that there is a right triangle with rational sides having an area d if and only the equation:

     y^2 = x^3 - d^2 x

    has rational solutions for x and y with  y \ne 0 "

    (Note: Devlin has defined d as a positive whole number earlier on)

    Can someone please supply the straightforward algebra to show that:

    There is a right triangle with rational sides having an area d if and only the equation:

     y^2 = x^3 - d^2 x

    has rational solutions for x and y with  y \ne 0 "



    Peter
    Last edited by Bernhard; March 27th 2012 at 02:25 AM.
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