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Question Number 9746 by Yozzias last updated on 30/Dec/16

Find (x,y)∈F_7 ^2  such that x^2 −3y^2 ≡ 0 mod 7.

$$\mathrm{Find}\:\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{F}_{\mathrm{7}} ^{\mathrm{2}} \:\mathrm{such}\:\mathrm{that}\:\mathrm{x}^{\mathrm{2}} −\mathrm{3y}^{\mathrm{2}} \equiv\:\mathrm{0}\:\mathrm{mod}\:\mathrm{7}. \\ $$

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