ILL 1983 Problem 7

Find all numbers $x \in \mathbb Z$ for which the number $x^4 + x^3 + x^2 + x + 1$ is a perfect square.

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.