Date: Apr 29, 2012 9:36 AM
Author: Terry M
Subject: Re: Pell type equations

"Helmut Richter" <hhr-m@web.de> wrote in message

news:alpine.LNX.2.00.1204291311200.5595@badwlrz-clhri01.ws.lrz.de...

> On Sun, 29 Apr 2012, Terry M wrote:

>

>> correction: so 3x² + 7y² is never 1, 5 or 6 (Mod 8)

>

> This is 100% correct.

>

> I mentioned only the 6 as example but the others are correct as well.

> The 1 and 5 could have been caught modulo 4, but for the 6 it is necessary

> to check modulo 8.

>

ok.

The equation I am working on is (a^2 + b^2)(c^2 + d^2) = x^2

with d > c >= b > a > 0, a and b are coprime, c and d are coprime

and I am aware of the Brahmagupta-Fibonacci identity.

If a and b are known, what (if anything) can be deduced about c and d.

My original examples were where a=1, b=2 and c=2 and 3 respectively

It has now been shown that where c=2 there are many (infinite) values for d

and where c=3 there are no possible values for d within the constraints.

> --

> Helmut Richter