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Cute nt from Switzerland

Source: Swiss IMO TST 2020 P2

September 28, 2021
number theorycoprime

Problem Statement

Find all positive integers nn such that there exists an infinite set AA of positive integers with the following property: For all pairwise distinct numbers a1,a2,…,an∈Aa_1, a_2, \ldots , a_n \in A, the numbers a1+a2+…+an and a1⋅a2⋅…⋅ana_1 + a_2 + \ldots + a_n \text{ and } a_1\cdot a_2\cdot \ldots\cdot a_n are coprime.
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