Cauchy-Davenport theorem

If $A$ and $B$ are non-empty subsets of ${\mathbb{Z}}_{p}$ , then

\left\lvert A+B\right\rvert\geq\min(\left\lvert A\right\rvert+\left\lvert B% \right\rvert-1,p),

where $A+B$ denotes the sumset of $A$ and $B$ .

References

1 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry of Sumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.