Problem

Source: Romanian IMO Team Selection Test TST 1996, problem 3

Tags: trigonometry, algebra unsolved, algebra



Let $ x,y\in \mathbb{R} $. Show that if the set $ A_{x,y}=\{ \cos {(n\pi x)}+\cos {(n\pi y)} \mid n\in \mathbb{N}\} $ is finite then $ x,y \in \mathbb{Q} $. Vasile Pop