### Abstract

It is shown that if p > 2 and C is a subset of F_{p} with |C|≥p-C_{1} p/log p then there are A∈F_{p}, B∈F_{p} with C=A+B, |A|≥2, |B|≥2. On the other hand, for every prime p there is a subset C F_{p} with |C|>p-C_{2}loglogp/(logp)^{1/2}p such that there are no A, B with these properties.

Original language | English |
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Pages (from-to) | 2374-2397 |

Number of pages | 24 |

Journal | Journal of Number Theory |

Volume | 133 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2013 |

### Fingerprint

### Keywords

- Reducible set
- Sumset

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

*133*(7), 2374-2397. https://doi.org/10.1016/j.jnt.2013.01.002

**On the reducibility of large sets of residues modulo p.** / Gyarmati, Katalin; Konyagin, Sergei; Sárközy, A.

Research output: Contribution to journal › Article

*Journal of Number Theory*, vol. 133, no. 7, pp. 2374-2397. https://doi.org/10.1016/j.jnt.2013.01.002

}

TY - JOUR

T1 - On the reducibility of large sets of residues modulo p

AU - Gyarmati, Katalin

AU - Konyagin, Sergei

AU - Sárközy, A.

PY - 2013/7

Y1 - 2013/7

N2 - It is shown that if p > 2 and C is a subset of Fp with |C|≥p-C1 p/log p then there are A∈Fp, B∈Fp with C=A+B, |A|≥2, |B|≥2. On the other hand, for every prime p there is a subset C Fp with |C|>p-C2loglogp/(logp)1/2p such that there are no A, B with these properties.

AB - It is shown that if p > 2 and C is a subset of Fp with |C|≥p-C1 p/log p then there are A∈Fp, B∈Fp with C=A+B, |A|≥2, |B|≥2. On the other hand, for every prime p there is a subset C Fp with |C|>p-C2loglogp/(logp)1/2p such that there are no A, B with these properties.

KW - Reducible set

KW - Sumset

UR - http://www.scopus.com/inward/record.url?scp=84875234768&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875234768&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2013.01.002

DO - 10.1016/j.jnt.2013.01.002

M3 - Article

VL - 133

SP - 2374

EP - 2397

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 7

ER -