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set with \lfloor x\rfloor =\lfloor y\rfloor , for any x,y

Source: Danube 2014 p2

July 22, 2019
floor functionsetalgebraProduct

Problem Statement

Let SS be a set of positive integers such that ⌊x⌋=⌊y⌋\lfloor \sqrt{x}\rfloor =\lfloor \sqrt{y}\rfloor for all x,y∈Sx, y \in S. Show that the products xyxy, where x,y∈Sx, y \in S, are pairwise distinct.
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