IMO 1989 LL KOR61

Let A be a set of positive integers such that no positive integer

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IMO 1989 LL KOR61

Origin: KOR

Problem

Let A be a set of positive integers such that no positive integer greater than 1 divides all the elements of A. Prove that any sufficiently large positive integer can be written as a sum of elements of A. (Elements may occur several times in the sum.)