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NL-BXMO-TST 2016 Problem 2

    Determine all triples (x, y, z) of non-negative real numbers that satisfy the following system of equations {x2−y=(z−1)2y2−z=(x−1)2z2−x=(y−1)2\begin{cases} x^2 - y = (z - 1)^2 y^2 - z = (x - 1)^2 z^2 - x = (y -1)^2 \end{cases} .

    Dataset text AI-MO AoPS. Quoted with source.

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