A Note on the Lonely Runner Conjecture
Ram Krishna Pandey, Paul Michelon · 2009
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 an increasing order.