IMO Shortlist 1994 problem N3


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2. travnja 2012.
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Show that there exists a set A of positive integers with the following property: for any infinite set S of primes, there exist two positive integers m in A and n not in A, each of which is a product of k distinct elements of S for some k \geq 2.
Izvor: Međunarodna matematička olimpijada, shortlist 1994