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On Non-Averaging Sets of Integers

Published online by Cambridge University Press:  20 November 2018

Leo Moser
Leo Moser*
Affiliation:
University of Alberta
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Let 5 be a set of positive integers no three of which are in arithmetical progression, i.e., if A, B, C are distinct elements of S, A + B ≠ 2C. We call such a set a non-averaging set. Let v(n) denote the maximum number of elements not exceeding n in any non-averaging set. The problem of finding bounds for v(n) has been treated by several authors [1, 3, 5, 6, 7]. The question first arose in connection with a theorem of van der Waerden [8].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 245 - 252
Copyright
Copyright © Canadian Mathematical Society 1953

References

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