"Helmut Richter" <firstname.lastname@example.org> wrote in message news:alpine.LNX.email@example.com... > 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.