Re:

[Max Alekseyev <maxale@gmail.com>]

Hi Charles, 

You can transform your equation into a Fermat-Pell one: 

Y^2 - 8*A*x^2 = B^2

where Y=2*A*y+B.

Then you need to consider its solutions Y modulo 2*A (they will be periodic) to figure out if there are those that are congruent to -B.

Regards,

Max

On Sun, Nov 6, 2016 at 6:51 PM, Charles Greathouse <charles.greathouse@case.edu> wrote:

I'm trying to determine if Diphantine equations of the form 2x^2 = Ay^2 + By have any solutions, where A and B are constant. Can I do this with gp?

I remmeber Max Alekseyev asked about general quadratic Diophantine equations some years ago but I don't know if there are scripts or other resources for this. If the equation was of the form Ax^2 + Bxy + Cy^2 = D I could use bnfisintnorm or qfbsolve (or Denis Simon's script), but I don't know of a way to do more general equations.

Charles Greathouse
Case Western Reserve University