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Iterative system of equations

Source: Korean Summer Program Practice Test 2016 1

August 17, 2016
algebrasystem of equations

Problem Statement

Find all real numbers x1,…,x2016x_1, \dots, x_{2016} that satisfy the following equation for each 1≤i≤20161 \le i \le 2016. (Here x2017=x1x_{2017} = x_1.) xi2+xi−1=xi+1 x_i^2 + x_i - 1 = x_{i+1}
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