A Note on the Lonely Runner Conjecture
Ram Krishna Pandey
Département de Mathématiques
Université Jean Monnet
23, rue Dr. Paul Michelon
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.
Full version: pdf,
Received April 16 2009;
revised version received June 4 2009.
Published in Journal of Integer Sequences, June 5 2009.
Journal of Integer Sequences home page