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freiman inverse theorem

Proceedings of the London Mathematical Society (1)

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Long arithmetic progressions in sum-sets and the number x-sum-free sets
E. Szemerédi, V. H. Vu
Journal:

Proceedings of the London Mathematical Society / Volume 90 / Issue 2 / March 2005

Published online by Cambridge University Press:

25 February 2005, pp. 273-296

Print publication:

March 2005
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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 $n$.