The lonely runner conjecture holds for eight runners
Combinatorics
2025-10-17 v2 Discrete Mathematics
Number Theory
Abstract
We prove that the lonely runner conjecture holds for eight runners. Our proof relies on a computer verification and on recent results that allow bounding the size of a minimal counterexample. We note that our approach also applies to the known cases with 4, 5, 6, and 7 runners. We expect that minor improvements to our approach could be enough to solve the cases of 9 or 10 runners.
Cite
@article{arxiv.2509.14111,
title = {The lonely runner conjecture holds for eight runners},
author = {Matthieu Rosenfeld},
journal= {arXiv preprint arXiv:2509.14111},
year = {2025}
}