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