Extend the n=4 method of Cusick and Pomerance

Ascertain whether the proof technique of Cusick and Pomerance for establishing κ(4) = 1/5 can be extended to prove the Lonely Runner Conjecture for n ≥ 5.

Background

The case n = 4 was settled by Cusick and Pomerance using an argument that involved computer assistance and discrete-time considerations. This approach successfully confirmed the conjecture for n = 4 and identified tight instances.

It is unknown whether the method scales to larger n, as increased combinatorial complexity may obstruct direct generalization.