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Arithmetic progressions in finite sets of real numbers

Published online by Cambridge University Press:  18 May 2009

W. Klotz
W. Klotz
Affiliation:
Institut Für Mathematik, Technische Universität, 3392 Clausthal, Germany
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In this paper we investigate the structure of a set of n reals that contains a maximal number of l-term arithmetic progressions. This problem has been indicated by J. Riddell. Let l and n be positive integers with 2 ≦ l ≦ n. By F1(n) we denote the maximal number of l-term arithmetic progressions that a set of n reals can contain. A set of n reals containing F1(n)l-progressions will be called an Fl,(n)-set.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 101 - 104
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCE

1.Riddell, J., On sets of numbers containing no l terms in arithmetic progression, Nieuw Arch. Wisk. (3) 17 (1969), 204–209.Google Scholar