RIOPLATENSE 2014 Problem 4

A pair (a,b) of positive integers is Rioplatenseif it is true that $b + k$ is a multiple of $a + k$ for all $k \in\{ 0 , 1 , 2 , 3 , 4 \}$ . Prove that there is an infinite set $A$ of positive integers such that for any two elements $a$ and $b$ of $A$ , with $a < b$ , the pair $(a,b)$ is Rioplatense.