I'm trying to solve $y^2=3x^2+3x+1$ for integers, which transforms into $(2y)^2-3(2x+1)^2=1$. I know how to solve pell's equation, but how can we extract only (odd,even) pair from the solutions of the diophantine equation $y^2-3x^2=1$? Any help would be appreciated.
2026-04-08 08:10:18.1775635818
How to extract solutions to a Pell's equation satisfying certain congruences?
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There is a recursion, with each solution a linear combination of an earlier solution. That should help decide which are even, which are odd.