The number of rational numbers determined by large sets of integers

Javier Cilleruelo, D. S. Ramana, Olivier Ramare

When $A$ and $B$ are subsets of the integers in $[1,X]$ and $[1,Y]$ respectively, with $|A|\ge \alpha X$ and $|B|\ge \beta X$, we show that the number of rational numbers expressible as $…