Cauchy-Davenport theorem

In additive number theory and combinatorics, a restricted sumset has the form

where ${\displaystyle A_{1},\ldots ,A_{n}}$ are finite nonempty subsets of a field F and ${\displaystyle P(x_{1},\ldots ,x_{n})}$ is a polynomial over F.

When ${\displaystyle P(x_{1},\ldots ,x_{n})=1}$, S is the usual sumset ${\displaystyle A_{1}+\cdots +A_{n}}$ which is denoted by nA if ${\displaystyle A_{1}=\cdots =A_{n}=A}$; when

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