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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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.


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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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