Geodesic
On the lonely runner conjecture
Mathematica Bohemica, Tome 135 (2010) no. 1, pp. 63-68.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Suppose $k+1$ runners having nonzero distinct constant speeds run laps on a unit-length circular track. The Lonely Runner Conjecture states that there is a time at which a given runner is at distance at least $1/(k+1)$ from all the others. The conjecture has been already settled up to seven ($k \leq 6$) runners while it is open for eight or more runners. In this paper the conjecture has been verified for four or more runners having some particular speeds using elementary tools.
DOI : 10.21136/MB.2010.140683
Classification : 11B25, 11B75
Keywords: congruences; arithmetic progression; bi-arithmetic progression 
@article{10_21136_MB_2010_140683,
     author = {Pandey, Ram Krishna},
     title = {On the lonely runner conjecture},
     journal = {Mathematica Bohemica},
     pages = {63--68},
     publisher = {mathdoc},
     volume = {135},
     number = {1},
     year = {2010},
     doi = {10.21136/MB.2010.140683},
     mrnumber = {2643356},
     zbl = {1224.11013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140683/}
}
TY  - JOUR
AU  - Pandey, Ram Krishna
TI  - On the lonely runner conjecture
JO  - Mathematica Bohemica
PY  - 2010
SP  - 63
EP  - 68
VL  - 135
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140683/
DO  - 10.21136/MB.2010.140683
LA  - en
ID  - 10_21136_MB_2010_140683
ER  - 
%0 Journal Article
%A Pandey, Ram Krishna
%T On the lonely runner conjecture
%J Mathematica Bohemica
%D 2010
%P 63-68
%V 135
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140683/
%R 10.21136/MB.2010.140683
%G en
%F 10_21136_MB_2010_140683
Pandey, Ram Krishna. On the lonely runner conjecture. Mathematica Bohemica, Tome 135 (2010) no. 1, pp. 63-68. doi : 10.21136/MB.2010.140683. http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140683/

Cité par Sources :