The maximum number of odd integral distances between points in the plane
P. Erdös asked for the maximum number of odd integral distances occurring between \(n\) points in the plane [Oral communication, Conference on Graph Theory, Combinatorics and Compuratation (1994), Boca Raton, FL]. The author here proves that this number is \(n^2/3 + r(r-3)/6\) for all \(n\), where \(r=1, 2, 3\) and \(n \equiv r \pmod 3\).
scientific article; zbMATH DE number 919858