Geodesic
Arithmetic progressions in finite sets of real numbers
Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 101-104

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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. 
Klotz, W. Arithmetic progressions in finite sets of real numbers. Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 101-104. doi: 10.1017/S0017089500001828
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[1] 1.Riddell, J., On sets of numbers containing no l terms in arithmetic progression, Nieuw Arch. Wisk. (3) 17 (1969), 204–209. Google Scholar

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