Home›Open Questions›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 QuestionsDoes 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?Citation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "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?." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/open-questions-index/question-lonely-runner-every-n-runners.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). 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?. Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/open-questions-index/question-lonely-runner-every-n-runnersCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-does-every-runner-on-a-circular-track-mo, author = {Mathematics Atlas}, title = {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?}, year = {2026}, url = {https://mathematics.interactiveatlas.org/open-questions-index/question-lonely-runner-every-n-runners}, note = {Accessed August 30, 2026} }Copy BibTeXOpen QuestionCross-Tradition ConnectionsSourcesComments (0)Reader Challenges (0 open reader challenges)Open QuestionThe 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)Cross-Tradition ConnectionsQuestion OnLonely Runner Conjecture, Conjectures Well-attested Source Lonely Runner Conjecture (Wikipedia)tier 2SourcesLonely Runner Conjecture (Wikipedia)tier 2WikipediaFor specific n section, and Tighter bounds sectionView the SourceComments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0 open reader challenges)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.View At A Past YearThe atlas records no dated fact of its own for this entry, so there is no other year to choose.Show This Year