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LCM of numbers

Source: IOM 2017 day2 p5

September 6, 2017
number theory

Problem Statement

Let xx and yy be positive integers such that [x+2,y+2]−[x+1,y+1]=[x+1,y+1]−[x,y][x+2,y+2]-[x+1,y+1]=[x+1,y+1]-[x,y].Prove that one of the two numbers xx and yy divide the other.
(Here [a,b][a,b] denote the least common multiple of aa and bb ).
Proposed by Dusan Djukic.
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