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for each n, exactly 1 of n,2n,3n is element of A, 2 \in A, prove 13824 \notin A

Source: Dutch BxMO/EGMO TST 2012 p5

August 24, 2019
number theorycombinatoricsset

Problem Statement

Let AA be a set of positive integers having the following property: for each positive integer nn exactly one of the three numbers n,2nn, 2n and 3n3n is an element of AA. Furthermore, it is given that 2∈A2 \in A. Prove that 13824∉A13824 \notin A.
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