### Abstract

Let p be a prime. A set A of residues modulo p is said to be sum-free if there axe no solutions to a = a' + a" with a, a', a" is an element of A. We show that there axe 2(p/3+o(p)) such sets. We also count the number of distinct sets of the form B + B, where B is a set of residues modulo p. Once again, there are 2(p/3+o(p)) such sets.

Translated title of the contribution | Counting sumsets and sum-free sets modulo a prime |
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Original language | English |

Pages (from-to) | 285 - 293 |

Journal | Studia Scientiarum Mathematicarum Hungarica |

Volume | 41 (3) |

Publication status | Published - 2004 |

### Bibliographical note

Publisher: Akademiai KiadoOther identifier: IDS Number: 850HM

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## Cite this

Green, BJ., & Ruzsa, IZ. (2004). Counting sumsets and sum-free sets modulo a prime.

*Studia Scientiarum Mathematicarum Hungarica*,*41 (3)*, 285 - 293.