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On subsets of abelian groups with no 3-term arithmetic progression

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Abstract

A short proof of the following result of Brown and Buhler is given: For any ϵ > 0 there exists n0 = n0(ϵ) such that if A is an abelian group of odd order |A| > n0 and BA with |B| > ϵ|A|, then B must contain three distinct elements x, y, z satisfying x + y = 2z.

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This work was performed while the authors were visiting AT&T Bell Laboratories.