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4

Part of 2009 IMAR Test

Problems(1)

exists a subsequence of consecutive terms, with product perfect square

Source: IMAR 2009 p4

9/27/2018
Given any nn positive integers, and a sequence of 2n2^n integers (with terms among them), prove there exists a subsequence made of consecutive terms, such that the product of its terms is a perfect square. Also show that we cannot replace 2n2^n with any lower value (therefore 2n2^n is the threshold value for this property).
number theoryPerfect Squarenumber theory with sequencesSequence