  Let $p$ a large enough prime number. When $A$ is a subset of
$\mathbb{F}_p\smallsetminus\{0\}$ of cardinality $|A|> (p+1)/3$, then an
application of Cauchy-Davenport Theorem gives
$\mathbb{F}_p\smallsetminus\{0\}\subset A(A+A)$. In this note, we improve on
this and we show that if $|A|\ge 0.3051 p$ implies
$A(A+A)\supseteq\mathbb{F}_p\smallsetminus\{0\}$. In the opposite direction we
show that there exists a set $A$ such that $|A| > (1/8+o(1))p$ and
$\mathbb{F}_p\smallsetminus\{0\}\not\subseteq A(A+A)$.

Number Theory