A note on the lonely runner conjecture. (English) Zbl 1233.11026

Pandey, Ram Krishna

J. Integer Seq. 12, No. 4, Article ID 09.4.6, 4 p. (2009).

The paper gives a simple proof of the lonely runner conjecture for speeds \(r_1, r_2,\ldots ,r_n\) with \(r_{i+1}\geq 2(1+2/(n-1))r_i\). The result can also be found in [I. Z. Ruzsa, Zs. Tuza and M. Voigt, J. Comb. Theory, Ser. B 85, No. 1, 181–187 (2002; Zbl 1027.05036)] and a slight improvement in [J. Barajas and O. Serra, Discrete Math. 309, No. 18, 5687–5696 (2009; Zbl 1213.05064)]. An asymptotic improvement close to optimal is given in [A. Dubickas, Glas. Mat., III. Ser. 46, No. 1, 25–30 (2011; Zbl 1253.11073)].

Reviewer: Oriol Serra (Barcelona)

MSC:

11B75	Other combinatorial number theory
11J71	Distribution modulo one

Keywords:

Lonely Runner Conjecture

Citations:

Zbl 1027.05036; Zbl 1213.05064; Zbl 1253.11073