A Second-Logarithm Lower Bound for Sets with No Unique Sums

Jiao-Long Cao, Ye Yuan

For an odd prime $p$, let $m(p)$ be the minimum cardinality of a set $A\subseteq \mathbb{Z}/p\mathbb{Z}$, with $|A|\ge 2$, such that no sum in $A+A$ has a unique representation as an…