# 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.
Title Cauchy-Davenport theorem CauchyDavenportTheorem 2013-03-22 13:32:13 2013-03-22 13:32:13 bbukh (348) bbukh (348) 7 bbukh (348) Theorem msc 11B05 Sumset