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AUSTRIAN-POLISH 1990 Problem 4

    Find all solutions in positive integers to: {x14+14x1x2+1=y14x24+14x2x3+1=y24...xn4+14xnx1+1=yn4\begin{cases} x_1^4 + 14x_1x_2 + 1 = y_1^4 x_2^4 + 14x_2x_3 + 1 = y_2^4 ... x_n^4 + 14x_nx_1 + 1 = y_n^4 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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