8

Part of 2002 Austrian-Polish Competition

Problems(1)

Number of solutions of a system

Source: 2002 Austrian-Polish, problem 8

Determine the number of real solutions of the system

\left\{ \begin{aligned}\cos x_{1}&= x_{2}\\ &\cdots \\ \cos x_{n-1}&= x_{n}\\ \cos x_{n}&= x_{1}\\ \end{aligned}\right.

trigonometrylimitinequalitiesalgebra unsolvedalgebra