{"paper":{"title":"Some remarks on the lonely runner conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Terence Tao","submitted_at":"2017-01-09T01:29:03Z","abstract_excerpt":"The lonely runner conjecture of Wills and Cusick, in its most popular formulation, asserts that if $n$ runners with distinct constant speeds run around a unit circle ${\\bf R}/{\\bf Z}$ starting at a common time and place, then each runner will at some time be separated by a distance of at least $\\frac{1}{n+1}$ from the others. In this paper we make some remarks on this conjecture. Firstly, we can improve the trivial lower bound of $\\frac{1}{2n}$ slightly for large $n$, to $\\frac{1}{2n} + \\frac{c \\log n}{n^2 (\\log\\log n)^2}$ for some absolute constant $c>0$; previous improvements were roughly of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02048","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}