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Find some numbers whose product is a perfect square

Source: IMO LongList 1988, Vietnam 6, Problem 94 of ILL

November 9, 2005
number theoryprime numbersPerfect SquareIMO Longlist

Problem Statement

Let n+1,n≥1n+1, n \geq 1 positive integers be formed by taking the product of nn given prime numbers (a prime number can appear several times or also not appear at all in a product formed in this way.) Prove that among these n+1n+1 one can find some numbers whose product is a perfect square.
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