TH-TMO 2007 Problem 10

Find the smallest positive integer $n$ such that the equation $\sqrt3 z^{n+1} - z^n - 1 = 0$ has a root on the unit circle.

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.