ILL 1988 Problem 28

Find a necessary and sufficient condition on the natural number $n$ for the equation $x^n + (2 + x)^n + (2 - x)^n = 0$ to have a integral root.

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.