Journal of Integer Sequences, Vol. 13 (2010), Article 10.9.3

A Note on Lacunary Lonely Runners

This paper has been withdrawn by the author. See the erratum below.

Stefan Steinerberger
Department of Financial Mathematics
University of Linz
Altenbergstraße 69
4040 Linz


We give a simple argument proving the lonely runner conjecture in the case where the speed of the runners forms a certain lacunary sequence. This improves an earlier result by Pandey, and is then used to derive that for each number of runners the lonely runner conjecture is true for a set of nonzero measure in a natural probability space.

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Received September 9 2010; revised version received September 19 2010. Published in Journal of Integer Sequences, December 6 2010. Withdrawn, January 3 2011.

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