Školjka

%V0 Solve the following system of equations, in which $a$ is a given number satisfying $|a| > 1$: $\begin{matrix}x_{1}^{2}= ax_{2}+1\\ x_{2}^{2}= ax_{3}+1\\ \ldots\\ x_{999}^{2}= ax_{1000}+1\\ x_{1000}^{2}= ax_{1}+1\\ \end{matrix}$