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x_n^2 + x_nx_{n-1} + x_{n-1}^4 = 1 for n = 1,2,..., 1999, x_0 = x_{1999}.

Source: Austrian - Polish 1999 APMC

May 4, 2020
algebrasystem of equations

Problem Statement

Solve in the nonnegative real numbers the system of equations {xn2+xnxn−1+xn−14=1    for    n=1,2,...,1999 x0=x1999\begin{cases} x_n^2 + x_nx_{n-1} + x_{n-1}^4 = 1 \,\,\,\, for \,\,\,\, n = 1,2,..., 1999 \\\ x_0 = x_{1999} \end{cases}
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