# Cauchy-Davenport theorem

If $A$ and $B$ are non-empty subsets of ${\mathbb{Z}}_{p}$, then

$$\left|A+B\right|\ge \mathrm{min}(\left|A\right|+\left|B\right|-1,p),$$ |

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^{} |
---|---|

Canonical name | CauchyDavenportTheorem |

Date of creation | 2013-03-22 13:32:13 |

Last modified on | 2013-03-22 13:32:13 |

Owner | bbukh (348) |

Last modified by | bbukh (348) |

Numerical id | 7 |

Author | bbukh (348) |

Entry type | Theorem |

Classification | msc 11B05 |

Related topic | Sumset |