Long arithmetic progressions in sum-sets and the number x-sum-free sets

• Autores: Endre Szemerédi, Van H. Vu
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 2, 2005, págs. 273-296
• Idioma: inglés
• DOI: 10.1112/s0024611504015059
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• Resumen

  • In this paper we obtain optimal bounds for the length of the longest arithmetic progression in various kinds of sum-sets. As an application, we derive a sharp estimate for the number of sets $A$ of residues modulo a prime $n$ such that no subsum of $A$ equals $x$ modulo $n$, where $x$ is a fixed residue modulo $n$.