### 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 - 2006 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Annals of Mathematics*,

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

**Finite and infinite arithmetic progressions in sumsets.** / Szemerédi, E.; Vu, V. H.

Research output: Contribution to journal › Article

*Annals of Mathematics*, vol. 163, no. 1, pp. 1-35. https://doi.org/10.4007/annals.2006.163.1

}

TY - JOUR

T1 - Finite and infinite arithmetic progressions in sumsets

AU - Szemerédi, E.

AU - Vu, V. H.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33746079267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746079267&partnerID=8YFLogxK

U2 - 10.4007/annals.2006.163.1

DO - 10.4007/annals.2006.163.1

M3 - Article

VL - 163

SP - 1

EP - 35

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 1

ER -