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Dividing a set into pairs

Source: Iran second round 2020 ,Day 2 ,P5

July 15, 2020
number theoryPerfect Square

Problem Statement

Call a pair of integers aa and bb square makers , if ab+1ab+1 is a perfect square. Determine for which nn is it possible to divide the set {1,2,…,2n}\{1,2, \dots , 2n\} into nn pairs of square makers.
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