Unique Differences in Symmetric Subsets of ${\mathbb{F}}_p$

Abstract

Let $p$ be a prime and let $A$ be a subset of ${\mathbb{F}}_p$ with $A=-A$ and $|A\setminus \{0\}|\le 2{\log }_3(p)$. Then there is an element of ${\mathbb{F}}_p$ which has a unique representation as a difference of two elements of $A$.