2006 Romanian NMO Problems/Grade 7/Problem 4
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://latex.artofproblemsolving.com/6/5/5/6550f4db3bccfcf0062b37b540bb0c9ecae03777.png)
, where by ![$[a,b]$](http://latex.artofproblemsolving.com/8/e/c/8ecbd1ba3da8f2adef66a63f2ab32c47e63fa734.png)
we have denoted the least common multiple of 
and 
. Prove that the set has exactly two elements.
Marius Gherghu, Slatina
