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On sum-free subsequences


Author: David G. Cantor
Journal: Proc. Amer. Math. Soc. 43 (1974), 67-68
MSC: Primary 10L10
DOI: https://doi.org/10.1090/S0002-9939-1974-0374078-2
MathSciNet review: 0374078
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Abstract: A sequence of real numbers is said to be sum-free if no number of the sequence is the sum of distinct elements of the same sequence. In this paper we show that a sequence $ S$ of $ n$ positive real numbers has a sum-free subsequence containing at least $ {(2n)^{1/2}} - {\log _2}(4n)$ elements.


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

  • [1] S. Choi, The largest sum-free subsequence from a sequence of $ n$ numbers, Proc. Amer. Math. Soc. 39 (1973), 42-44. MR 0313216 (47:1771)
  • [2] P. Erdös, Extremal problems in number theory, Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc., Providence, R.I., 1965, pp. 181-189. MR 30 #4740. MR 0174539 (30:4740)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0374078-2
Article copyright: © Copyright 1974 American Mathematical Society

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