Original scientific paper

https://doi.org/10.3336/gm.46.1.05

The lonely runner problem for many runners

Arturas Dubickas orcid.org/0000-0002-3625-9466 ; Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania

Abstract

The lonely runner conjecture asserts that for any positive integer n and any positive numbers v1 < ... < vn there exists a positive number t such that ||vi t|| ≥ 1/(n+1) for every i=1, ...,n. We verify this conjecture for n ≥ 16342 under assumption that the speeds of the runners satisfy vj+1/vj ≥ 1+33 log n/n for j=1, ...,n-1.

Keywords

Lonely runner conjecture; Diophantine approximation; Lovász local lemma

Hrčak ID:

68865

URI

https://hrcak.srce.hr/68865

Publication date:

13.6.2011.

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