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AUSTRIAN-POLISH 2002 Problem 8

    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.

    Dataset text AI-MO AoPS. Quoted with source.

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