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Infinite subset A of the naturals with coprime condition

Source: Baltic Way 2010

November 19, 2010

inductionnumber theory proposednumber theory

Problem Statement

Determine all positive integers

n

for which there exists an infinite subset

A

of the set

\mathbb{N}

of positive integers such that for all pairwise distinct

a_1,\ldots , a_n \in A

the numbers

a_1+\ldots +a_n

and

a_1a_2\ldots a_n

are coprime.