Multiplicative Subgroups of Prime Fields Are Not Sumsets

Misha Rudnev, Fred Tyrrell

Let $H\le {\mathbb{F}}_p^{\ast }$ be a proper multiplicative subgroup, and suppose that $H=A+B$ for some $A,B\subseteq {\mathbb{F}}_p$. We prove that either one of the summands is a sin…