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ag.algebraic geometry – How many options are there to the equation $x^2 + 3y^2 equiv 1 pmod{p}$? Answer

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ag.algebraic geometry – How many options are there to the equation $x^2 + 3y^2 equiv 1 pmod{p}$?

Let $p$ breathe a main. How many options $(x, y)$ are there to the equation $x^2 + 3y^2 equiv 1 pmod{p}$? Here $x, y in {0, 1, ldots p-1}$. This paper (https://arxiv.org/abs/1404.4214) appears love it could give some concepts, however focuses on equations of the figure $sum_{i = 1}^n x_i^2 equiv 1 pmod{p}$, i.e. it doesn’t enable for the opportunity of coefficients on the variables.

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