MathNet 2016-part-04 — 184 problems (EN–VI) Question 171

Let $a$ be a positive integer. Find all prime numbers $p$ with the following property: there exist exactly $p$ ordered pairs of integers $(x, y)$, with $0 \leq x, y \leq p-1$, such that $p$ divides $y^{2}-x^{3}-a^{2} x$.