Here is the Wikipedia article on the lonely runner conjecture https://en.m.wikipedia.org/wiki/Lonely_runner_conjecture# I have some inquires about it. Firstly I am right in thinking that "pair wise distinct" means that the speed of all runners are different? Also does every runner have to be at least 1/k (k is the number of runners) from all the other runners simultaneously? Or can runners achieve "loneliness" at a certain time even whilst other runners have not? Furthermore, once a runner achieves "loneliness" is it maintained? In other words say a runner is lonely, does it stay lonely even if the distance between it and the other runners decreases to become smaller than 1/k afterwards?