BY-MO 1999 Problem 2

Let $m, n$ be positive integers. Starting with all positive integers written in a line, we can form a list of numbers in two ways: $(1)$ Erasing every $m$ -th and then, in the obtained list, erasing every $n$ -th number; $(2)$ Erasing every $n$ -th number and then, in the obtained list, erasing every $m$ -th number.

A pair $(m,n)$ is called good if, whenever some positive integer $k$ occurs in both these lists, then it occurs in both lists on the same position.

(a) Show that the pair $(2, n)$ is good for any $n\in \mathbb{N}$ . (b) Is there a good pair $(m, n)$ with $2<m<n$ ?