I'm wondering if anyone knows of results counting or bounding the number of relatively prime pairs in two subsets of positive integers. In particular:
Given $A = \{a \in \mathbb{Z} | m_1 \leq a \leq m_2 \}$ and $B = \{b \in \mathbb{Z} | n_1 \leq b \leq n_2 \}$, is there a formula for or a bound on the size of the set $P = \{(a,b)|a \in A, b \in B,$ and $a$ and $b$ are relatively prime$\}$.
Thanks!