The Ramanujan Journal

, Volume 9, Issue 1–2, pp 77–82 | Cite as

Sum-Avoiding Subsets



We estimate the maximal number of elements that can be selected from a set of n numbers so that the sum of two selected elements are never in the original set. We improve Choi’s upper bound of n2/5 to ec√log n n.


sumset combinatorial number theory 


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  1. 1.
    S.L.G. Choi, “On a combinatorial problem in number theory,” Proc. London Math. Soc. 23 (1971), 629–641.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of MathematicsHungary

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