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a_1+a_2+... +a_n=a_1a_2 ... a_n=n

Source: Argentina 2006 OMA L3 p6

May 12, 2024
number theory

Problem Statement

We will say that a natural number nn is adequate if there exist nn integers a1,a2,…,ana_1,a_2,\ldots ,a_n (which are not necessarily positive and can be repeated) such thata1+a2+⋯+an=a1a2⋯an=n.a_1+a_2+\cdots +a_n=a_1a_2 \cdots a_n=n.Determine all adequate numbers.
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