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BG-MO 1964 Problem 2

    Find all nn - tuples of reals x1,x2,…,xnx_1,x_2,\ldots,x_n satisfying the system: {x1x2⋯xn=1x1−x2x3⋯xn=1x1x2−x3x4⋯xn=1⋮x1x2⋯xn−1−xn=1\begin{cases}x_1x_2\cdots x_n=1\\x_1-x_2x_3\cdots x_n=1\\x_1x_2-x_3x_4\cdots x_n=1\\\vdots\\x_1x_2\cdots x_{n-1}-x_n=1\end{cases}

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