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

Autor:	Van H. Vu, Endre Szemerédi
Rok vydání:	2005
Předmět:	Discrete mathematics Combinatorics Root of unity modulo n Mathematics::Number Theory General Mathematics Modulo ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Arithmetic progression Primes in arithmetic progression Mathematics
Zdroj:	Proceedings of the London Mathematical Society. 90:273-296
ISSN:	1460-244X 0024-6115
DOI:	10.1112/s0024611504015059
Popis:	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 $n$.
Databáze:	OpenAIRE
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