Competition problem — Number theory

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Number theory Difficulty 5.2 AIME, harder Find the answer

例题 2
求所有的质数 $p$ , 使得满足 $0 \leq x, y \leq p-1$ 且 $y^{2} \equiv x^{3}-x(\bmod p)$ 的整数对 $(x, y)$ 恰有 $p$ 对.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.