Cauchy-Davenport theorem

Statement

Suppose $p$ is a prime number. Denote by $G=\mathbb {Z} /p\mathbb {Z}$ the group of prime order $p$. Then, for any subsets $A$ and $B$ of $G$, we have the following lower bound on the size of the sumset $A+B$of $A$ and $B$:

$|A+B|\geq \min\{p,|A|+|B|-1\}$

Related facts

• Erdos-Heilbronn conjecture
• Kneser's theorem
• Kemperman's theorem