A note on the set $\mathbf{A}(\mathbf{A}+\mathbf{A})$

Pierre-Yves Bienvenu, François Hennecart, Ilya Shkredov

Let $p$ a large enough prime number. When $A$ is a subset of ${\mathbb{F}}_p\setminus \{0\}$ of cardinality $|A|>(p+1)/3$, then an application of Cauchy-Davenport Theorem gives…