Max Alekseyev on Mon, 07 Nov 2016 20:37:27 +0100

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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.


On Sun, Nov 6, 2016 at 6:51 PM, Charles Greathouse <> 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