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