Let $x,y \in \mathbb{R}$ such that the set $\{\cos{(n\pi x)} + \cos{(n\pi y)} | n \in \mathbb{N} \}$ is finite. Show that $x$ and $y$ are rational.
I have been trying to consider a graph of this set and maybe an argument by contradiction....
Let $x,y \in \mathbb{R}$ such that the set $\{\cos{(n\pi x)} + \cos{(n\pi y)} | n \in \mathbb{N} \}$ is finite. Show that $x$ and $y$ are rational.
I have been trying to consider a graph of this set and maybe an argument by contradiction....