## Submission + - The lonely runner conjecture might have been solved (arxiv.org)

Paxinum writes:

*Today, a preprint appeared on arxiv, claiming to solve the famous Lonely runner conjecture, which has been open since the 60s.*

The conjecture states that if k runners are running with different speed on a race track of length 1, then each runner is lonely some time, meaning the distance to the closest other runner is at least 1/k.

The submission is only four pages long, and solves the problem by first restating it in terms of a view-obstruction problem, and then giving an explicit construction of polyhedral cones covering every integer point in the k-dimensional integer lattice. This implies the conjecture.The conjecture states that if k runners are running with different speed on a race track of length 1, then each runner is lonely some time, meaning the distance to the closest other runner is at least 1/k.

The submission is only four pages long, and solves the problem by first restating it in terms of a view-obstruction problem, and then giving an explicit construction of polyhedral cones covering every integer point in the k-dimensional integer lattice. This implies the conjecture.