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(m+1)/(m+1,n+1) \in A => A \equiv N^*

Source: JBMO Shortlist 2007 A3

October 14, 2017
JBMOalgebra

Problem Statement

Let AA be a set of positive integers containing the number 11 and at least one more element. Given that for any two different elements m,nm, n of A the number m+1(m+1,n+1) \frac{m+1 }{(m+1,n+1) } is also an element of AA, prove that AA coincides with the set of positive integers.
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