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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On sequences not containing a large sum-free subsequence


Author: S. L. G. Choi
Journal: Proc. Amer. Math. Soc. 41 (1973), 415-418
MSC: Primary 10L05
MathSciNet review: 0325563
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Abstract: A subsequence of a sequence of integers is said to be sum-free if no integer of the subsequence is the sum of distinct integers of this same subsequence. In this paper we shall prove, provided $ n$ is sufficiently large, that there exists a sequence of $ n$ integers whose largest sum-free subsequence has at most $ cn{(\log \log n)^{ - 1/2}}$ integers, where $ c$ is an absolute constant.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0325563-X
PII: S 0002-9939(1973)0325563-X
Keywords: Sum-free, subsequence, arithmetic progressions
Article copyright: © Copyright 1973 American Mathematical Society