olymmath

BG-MO 1968 Problem 1

    Find all natural values of kk for which the system {x1+x2+…+xk=91x1+1x2+…+1xk=1\begin{cases}x_1+x_2+\ldots+x_k=9\frac1{x_1}+\frac1{x_2}+\ldots+\frac1{x_k}=1\end{cases} has solutions in positive numbers. Find these solutions.

    I. Dimovski

    Dataset text AI-MO AoPS. Quoted with source.

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