- #1

Math Amateur

Gold Member

MHB

- 3,998

- 48

"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 if**the 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 d

**if and only if**the equation:

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

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

Peter