On sets of integers not containing long arithmetic progressions

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62064We construct subsets of {1,...,N} of cardinality at least N exp(-C(log N)^{1/(k+1)}) which do not contain arithmetic progressions of length 2^k+1. This extends a result of Behrend (1946) concerning sets which do not contain aritmetic progressions of length 3.8 pagesCombinatoricsNumber TheoryOn sets of integers not containing long arithmetic progressionstext