IOM 2017 Problem 5

Let $x$ and $y$ be positive integers such that $[x+2,y+2]-[x+1,y+1]=[x+1,y+1]-[x,y]$ .Prove that one of the two numbers $x$ and $y$ divide the other.

(Here $[a,b]$ denote the least common multiple of $a$ and $b$ ).

Proposed by Dusan Djukic.