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The lonely runner conjecture holds for eight runners

Published 17 Sep 2025 in math.CO, cs.DM, and math.NT | (2509.14111v1)

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.

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