Art of Problem Solving

Art of Problem Solving

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The Cauchy-Davenport theorem states that for all nonempty sets <math>A,B \subseteq \mathbb{Z}/p\mathbb{Z}</math> , we have that 
<cmath>|A+B| \geqslant \min\{|A|+|B|-1,p\},</cmath>
where <math>A+B</math> is defined as the set of all <math>c \in \mathbb{Z}/p\mathbb{Z}</math> that can be expressed as <math>a+b</math> for <math>a \in A</math> and <math>b \in B</math>.

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