### Abstract

It is proved that for any two subsets A and B of an arbitrary finite field $ \mathbb{F}_q $Fqsuch that |A||B| > q, the identity 10AB = $ \mathbb{F}_q $Fqholds. Under the assumption |A||B| ⩾2q, this improves to 8AB = $ \mathbb{F}_q $Fq.

Translated title of the contribution | On additive properties of product sets in an arbitrary finite field |
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Original language | English |

Pages (from-to) | 159 - 170 |

Number of pages | 12 |

Journal | Journal d'Analyse Mathématique |

Volume | 108 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 2009 |

### Bibliographical note

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## Cite this

Glibichuk, A., & Rudnev, M. (2009). On additive properties of product sets in an arbitrary finite field.

*Journal d'Analyse Mathématique*,*108*(1), 159 - 170. https://doi.org/10.1007/s11854-009-0021-4