Problem Statement
Let $A$ be a finite set of integers such that $\lvert A+A\rvert \ll \lvert A\rvert$. Is it true that\[\lvert AA\rvert \gg \frac{\lvert A\rvert^2}{(\log \lvert A\rvert)^C}\]for some constant $C>0$?
Categories:
Additive Combinatorics
Progress
This was proved by Solymosi [So09d], in the strong form\[\lvert AA\rvert \gg \frac{\lvert A\rvert^2}{\log \lvert A\rvert}.\]See also [52].Source: erdosproblems.com/818 | Last verified: January 16, 2026