Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme
Open Question

Does every runner on a circular track, moving at its own constant and distinct speed, really become lonely at some moment, for every number of runners n?

Open Question

The conjecture is proved individually for up to 13 runners, most recently n = 10 through 13 in 2025 and 2026, and Tao proved an improved general asymptotic bound in 2018, but no argument covers every n at once.

What would resolve this A proof, or a counterexample, covering every number of runners n rather than a further specific value.
OpenCombinatoricsLonely Runner Conjecture (Wikipedia)
Connections

Question On

Source Lonely Runner Conjecture (Wikipedia)
Sources
Lonely Runner Conjecture (Wikipedia)
WikipediaFor specific n section, and Tighter bounds sectionView the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.