2006 USAMO Problems/Problem 4

Problem

Find all positive integers $n$ such that there are $k\ge 2$ positive rational numbers $a_1,a_2,\ldots a_k$ satisfying $a_1+a_2+...+a_k = a_1 \cdot a_2 \cdot \cdots a_k = n$ .

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2006 USAMO Problems/Problem 4

Problem

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