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a_1 + a_2 + .. + a_k = a_1a_2 . . . a_k = n , a_i \in Q

Source: Danube 2018 junior p3

July 22, 2019
number theorySumProductrationalpositive integers

Problem Statement

Find all the positive integers nn with the property: there exists an integer k>2k > 2 and the positive rational numbers a1,a2,...,aka_1, a_2, ..., a_k such that a1+a2+..+ak=a1a2...ak=na_1 + a_2 + .. + a_k = a_1a_2 . . . a_k = n.
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