Journal of Integer Sequences, Vol. 12 (2009), Article 09.4.6

A Note on the Lonely Runner Conjecture

Ram Krishna Pandey
Département de Mathématiques
Université Jean Monnet
23, rue Dr. Paul Michelon
42023 Saint-Etienne


Suppose n runners having nonzero distinct constant speeds run laps on a unit-length circular track. The Lonely Runner Conjecture states that there is a time at which all the n runners are simultaneously at least 1/(n+1) units from their common starting point. The conjecture has been already settled up to six (n ≤ 6) runners and it is open for seven or more runners. In this paper the conjecture has been proved for two or more runners provided the speed of the (i+1)th runner is more than double the speed of the ith runner for each i, arranged in increasing order.

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Received April 16 2009; revised version received June 4 2009. Published in Journal of Integer Sequences, June 5 2009.

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