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Number of solutions of a system

Source: 2002 Austrian-Polish, problem 8

September 23, 2006
trigonometrylimitinequalitiesalgebra unsolvedalgebra

Problem Statement

Determine the number of real solutions of the system {cos⁡x1=x2⋯cos⁡xn−1=xncos⁡xn=x1\left\{ \begin{aligned}\cos x_{1}&= x_{2}\\ &\cdots \\ \cos x_{n-1}&= x_{n}\\ \cos x_{n}&= x_{1}\\ \end{aligned}\right.
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