MathDB

Vietnamese System Of Equation

Source: IMO Shortlist 1993, Vietnam 1

October 24, 2005

linear algebramatrixalgebrasystem of equationsIMO Shortlist

Problem Statement

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}