All Random Solved Random Open
Let $A$ be a finite set of integers. Is it true that, for every $k$, if $\lvert A\rvert$ is sufficiently large depending on $k$, then there are least $\lvert A\rvert^k$ many integers which are either the sum or product of distinct elements of $A$?
Asked by Erdős and Szemerédi [ErSz83]. Solved in this form by Chang [Ch03].