Date: Apr 29, 2012 9:36 AM
Author: Terry M
Subject: Re: Pell type equations
"Helmut Richter" <firstname.lastname@example.org> wrote in message
> 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.
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