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AUSTRIAN-POLISH 1991 Problem 2

    Find all solutions (x,y,z)(x,y,z) to the system {(x2−6x+13)y=20(y2−6y+13)z=20(z2−6z+13)x=20\begin{cases}(x^2 - 6x + 13)y = 20 (y^2 - 6y + 13)z = 20 (z^2 - 6z + 13)x = 20 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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