# Cusick, Thomas W.

## Lonely runner conjecture ★★★

Author(s): Cusick; Wills

\begin{conjecture} Suppose $k$ runners having distinct constant speeds start at a common point and run laps on a circular track with circumference 1. Then for any given runner, there is a time at which that runner is distance at least $\frac{1}{k}$ (along the track) away from every other runner. \end{conjecture}