Question 20
Let $m$ and $n$ be positive integers, and let $A_1, \dots, A_m$ be pairwise disjoint $n$-element sets of positive integers such that no member of $A_i$ is divisible by one of $A_{i+1}$, whatever $i$ (indices are reduced modulo $m$). Determine the largest number of ordered pairs $(a, b)$, where $a$ and $b$ are members of distinct $A_i$'s, and $b$ is divisible by $a$.