@MISC{Solymosi01distinctdistances, author = {J. Solymosi and Cs. D. Toth}, title = {Distinct Distances in the Plane}, year = {2001} }

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Abstract

It is shown that every set of n points in the plane has an element from which there are at least cn 6/7 other elements at distinct distances, where c > 0 is a constant. This improves earlier results of Erdos, Moser, Beck, Chung, Szemeredi, Trotter, and Szekely. 1.