IMC 2020 Problem 6

Find all prime numbers $p$ such that there exists a unique $a \in \mathbb{Z}_p$ for which $a^3 - 3a + 1 = 0.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.