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:(adsbygoogle = window.adsbygoogle || []).push({});

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

[itex] y^2 = x^3 - d^2 x [/itex]

has rational solutions for x and y with

(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 dif and only ifthe equation:

[itex] y^2 = x^3 - d^2 x [/itex]

has rational solutions for x and y with [itex] y \ne 0 [/itex]"

Peter

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

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