IMO 1988 LL VIE94

Let n + 1 (n \geq1) positive integers be given such that for each

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IMO 1988 LL VIE94

Origin: VIE

Problem

Let n + 1 (n \geq1) positive integers be given such that for each integer, the set of all prime numbers dividing this integer is a subset of the set of n given prime numbers. Prove that among these n + 1 integers one can find numbers (possibly one number) whose product is a perfect square.