Talk:Lonely runner conjecture

Only positive speeds needed in reduced case?
Reducing the problem from k+1 runners to k runner by assuming that one of the runner has speed zero imposes on the first spot that some runners may have negative speeds. It is stated that one can restrict to the case of k "positive integers" as proven in the paper of Bohman, Holzman, Kleitman. I cannot see the argument why it is possible to restrict to positive (integer) speeds nor can I find this argument for positivity in Bohman, Holzman, Kleitman. To clarify, the argument why one can restrict to rational (hence integer) speeds is contained in the mentioned paper. — Preceding unsigned comment added by 134.147.253.243 (talk) 15:32, 20 November 2018 (UTC)
 * Adding the same speed to every runner doesn't change the situation. If there is a solution with any integers there is also one with one runner at speed 0 and other runners at positive speed and vice versa. --mfb (talk) 06:56, 21 November 2018 (UTC)

Known results
The table with known results, and the year when they were proved, contradict the dates cited on the page at the Open Problem Garden. In any case, the table needs inline citations. Hermel (talk) 10:17, 20 March 2009 (UTC)
 * I'm working on correcting the table with citations and adding k+1 = 7. This will take a few days, so please bear with me. Gramby (talk) 21:03, 19 April 2011 (UTC)
 * Thanks a lot for your effort. Hermel (talk) 16:57, 22 April 2011 (UTC)

Trivial results
The results for k <= 3 should be added, at least in the "Known results" box. For k = 0 and 1 the result is trivial (t=0 and t=v2-v1), and I can add it myself, but k = 2 could have its own explanatory section. MestreLion (talk) 15:41, 28 February 2013 (UTC)

k+1?
Not substituting k+1 for k is just stupid. I'm changing that shit.

k=3?
Why is it that any proof for k larger than 3, automatically proves it for k=3? - DPizzo (talk) 23:22, 21 August 2013 (UTC) Just add runner speed infinitesimally small. It is trivial. — Preceding unsigned comment added by Mtheorylord (talk • contribs) 02:06, 11 August 2016 (UTC)
 * The distance goes up with k=3 compared to larger numbers. But it is easy to proof directly: Consider speeds relative to runner A, let runner C be faster than B. If the speed of C does not exceed twice the speed of B, then A will be lonely within the first round of both, otherwise A will lonely within the first round of B and the nth round of C. --mfb (talk) 17:51, 13 November 2016 (UTC)

animation/gif
what are the speeds for each of the runners in the gif animation to the right? — Preceding unsigned comment added by 69.171.166.1 (talk) 22:32, 8 September 2013 (UTC)

Non-rational values
With respect to this: it is a true statement. Its truth is the underlying reason that this article begins "in number theory". But (1) it is uncited, and (2) it is certainly not part of the formulation of the problem (which is the topic of the section to which it was added). With a citation, we could certainly try to fit it in somewhere else. --JBL (talk) 00:41, 1 November 2021 (UTC)