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AUSTRIAN-POLISH 2000 Problem 3

    For each integer n≥3n \ge 3 solve in real numbers the system of equations: {x13=x2+x3+1...xn−13=xn+x1+1xn3=x1+x2+1\begin{cases} x_1^3 = x_2 + x_3 + 1 ...x_{n-1}^3 = x_n+ x_1 + 1x_{n}^3 = x_1+ x_2 + 1 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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