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not easy ,i think

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

August 31, 2005
trigonometryalgebra unsolvedalgebra

Problem Statement

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