Year: 2026
Type: article
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 4 , 5 5 , 6 6 , and 7 7 runners. We expect that minor improvements to our approach could be enough to solve the cases of 9 9 or 10 10 runners.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4243
Author: Matthieu Rosenfeld
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7160985913