2006 Romanian NMO Problems/Grade 7/Problem 4
From AoPSWiki
Problem
Let 
be a set of positive integers with at least 2 elements. It is given that for any numbers 
, 
we have ![\frac{ [a,b] }{ a- b } \in A](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/7/9/07935dec710c231788b09807c717d0418bf2332d.gif)
, where by ![[a,b]](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/1/4/7/1475c39442659c6febe03b2e1809dbde6ec5fb5a.gif)
we have denoted the least common multiple of 
and 
. Prove that the set has exactly two elements.
Marius Gherghu, Slatina
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
