IMO 1985 LL CZS21

Let A be a set of positive integers such that for any two elements

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IMO 1985 LL CZS21

Origin: CZS

Problem

Let A be a set of positive integers such that for any two elements x, y of A, |x−y| \geqxy 25 . Prove that A contains at most nine elements. Give an example of such a set of nine elements.