IMO Shortlist 1993 problem A4


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2. travnja 2012.
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Solve the following system of equations, in which a is a given number satisfying |a| > 1:

\begin{matrix}x_{1}^{2}= ax_{2}+1\\ x_{2}^{2}= ax_{3}+1\\ \ldots\\ x_{999}^{2}= ax_{1000}+1\\ x_{1000}^{2}= ax_{1}+1\\ \end{matrix}
Izvor: Međunarodna matematička olimpijada, shortlist 1993