Finite and infinite arithmetic progressions in sumsets

• Autores: V.H. Vu, B. Szemerédi
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 163, Nº 1, 2006, págs. 1-35
• Idioma: inglés
• DOI: 10.4007/annals.2006.163.1
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• Resumen

  • We prove that if A is a subset of at least cn1/2 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 Erd¿os and Folkman on complete sequences.