A generalization of a theorem of Erdős-Rényi to $m$-fold sums and differences

Kathryn Hare, Shuntaro Yamagishi

Let $m\ge 2$ be a positive integer. Given a set $E(\omega )\subseteq \mathbb{N}$ we define $r_N^{(m)}(\omega )$ to be the number of ways to represent $N\in \mathbb{Z}$ as any combination of…