Let us suppose there are runners running at speeds around a field of circumference . Take any runner from the runners- say , who runs with speed . Say we pair him up with another runner who runs with speed . Then for time , the distance between them is , and for , the distance between them is .
The Lonely Runner Conjecture can be stated in the following way: there exists a time such that .
Here are the smallest positive values found after successively determining , where , and