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AUSTRIAN-POLISH 1999 Problem 6

    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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