On sets of integers not containing long arithmetic progressions
Izabella Laba, Michael T. Lacey
Abstract
We 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 2k+1. This extends a result of Behrend (1946) concerning sets which do not contain aritmetic progressions of length 3.
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