On Non-Averaging Sets of Integers
- 1 January 1953
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 5, 245-252
- https://doi.org/10.4153/cjm-1953-027-0
Abstract
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].Keywords
This publication has 3 references indexed in Scilit:
- On Sets of Integers Which Contain No Three Terms in Arithmetical ProgressionProceedings of the National Academy of Sciences, 1946
- On Sets of Integers Which Contain No Three Terms in Arithmetical ProgressionProceedings of the National Academy of Sciences, 1942
- On Some Sequences of IntegersJournal of the London Mathematical Society, 1936