IMO 1987 LL FIN13

A be an infinite set of positive integers such that every n \inA is

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IMO 1987 LL FIN13

Origin: FIN

Problem

A be an infinite set of positive integers such that every n \inA is the product of at most 1987 prime numbers. Prove that there is an infinite set B \subsetA and a number p such that the greatest common divisor of any two distinct numbers in B is b.