The lonely runner conjecture holds for eight runners

2025/09/17 by Rosenfeld, Matthieu · 3 citations
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.14111

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.

Citations

• Local obstructions in sequences revisited
• Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants
• The Lonely Runner Conjecture turns 60
• The structure of Lonely Runner spectra
• Some remarks on the lonely runner conjecture
• The Lonely Runner Conjecture
• The lonely runner with seven runners

Cited by

• The lonely runner conjecture holds for nine runners
• Nine and ten lonely runners
• Riesz products and the Lonely Runner Conjecture: A wider gap of loneliness

Related

• The lonely runner conjecture holds for nine runners
• The lonely runner with seven runners
• Nine and ten lonely runners
• On the time for a runner to get lonely
• Some remarks on the lonely runner conjecture