Cauchy-davenport

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The Cauchy-Davenport Theorem states that for all nonempty sets $A,B \subseteq \mathbb{Z}/p\mathbb{Z}$ , we have that \[|A+B| \geq \min\{|A|+|B|-1,p\},\] where $A+B$ is defined as the set of all $c \in \mathbb{Z}/p\mathbb{Z}$ that can be expressed as $a+b$ for $a \in A$ and $b \in B$.

Proof of the Cauchy-Davenport Theorem by the Combinatorial Nullstellensatz

Proof by Induction

Applications of the Cauchy-Davenport Theorem