### Abstract

We prove that if A is a subset of at least cn ^{1/2} elements of {1,..., n}, where c is a sufficiently large constant, then the collection of subset sums of A contains an arithmetic progression of length n. As an application, we confirm a long standing conjecture of Erdös and Folkman on complete sequences.

Original language | English |
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Pages (from-to) | 1-35 |

Number of pages | 35 |

Journal | Annals of Mathematics |

Volume | 163 |

Issue number | 1 |

DOIs | |

Publication status | Published - júl. 24 2006 |

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Szemerédi, E., & Vu, V. H. (2006). Finite and infinite arithmetic progressions in sumsets.

*Annals of Mathematics*,*163*(1), 1-35. https://doi.org/10.4007/annals.2006.163.1