Homogeneous structures in subset sums and non-averaging sets

David Conlon, Jacob Fox, Huy Tuan Pham

We show that for every positive integer $k$ there are positive constants $C$ and $c$ such that if $A$ is a subset of $\{1,2,\dots ,n\}$ of size at least $C{n}^{1/k}$, then, for so…