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AUSTRIAN-POLISH 1986 Problem 5

    Find all real solutions of the system of equations {x2+y2+u2+v2=4xu+yv+xv+yu=0xyu+yuv+uvx+vxy=−2xyuv=−1\begin{cases} x^2 + y^2 + u^2 + v^2 = 4 xu + yv + xv + yu = 0 xyu + yuv + uvx + vxy = - 2 xyuv = -1 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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