Finite and infinite arithmetic progressions in sumsets

E. Szemerédi, V. H. Vu

Research output: Contribution to journalArticle

20 Citations (Scopus)


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 languageEnglish
Pages (from-to)1-35
Number of pages35
JournalAnnals of Mathematics
Issue number1
Publication statusPublished - Jul 24 2006


ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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