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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.

References [Enhancements On Off] (What's this?)

  • [1] P. Erdős, Extremal problems in number theory, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., Providence, R.I., 1965, pp. 181–189. MR 0174539
  • [2] P. Varnavides, On certain sets of positive density, J. London Math. Soc. 34 (1959), 358–360. MR 0106865

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Keywords: Sum-free, subsequence, arithmetic progressions
Article copyright: © Copyright 1973 American Mathematical Society