On the lonely runner conjecture

Ram Krishna Pandey

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 1, page 63-68
  • ISSN: 0862-7959

Abstract

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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 ≤ 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.

How to cite

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Pandey, Ram Krishna. "On the lonely runner conjecture." Mathematica Bohemica 135.1 (2010): 63-68. <http://eudml.org/doc/38111>.

@article{Pandey2010,
abstract = {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 ($k \le 6$) 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.},
author = {Pandey, Ram Krishna},
journal = {Mathematica Bohemica},
keywords = {congruences; arithmetic progression; bi-arithmetic progression; congruence; arithmetic progression; bi-arithmetic progression},
language = {eng},
number = {1},
pages = {63-68},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the lonely runner conjecture},
url = {http://eudml.org/doc/38111},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Pandey, Ram Krishna
TI - On the lonely runner conjecture
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 1
SP - 63
EP - 68
AB - 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 ($k \le 6$) 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.
LA - eng
KW - congruences; arithmetic progression; bi-arithmetic progression; congruence; arithmetic progression; bi-arithmetic progression
UR - http://eudml.org/doc/38111
ER -

References

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  12. Pandey, R. K., A note on the lonely runner conjecture, J. Integer Sequences 12 (2009), Article 09.4.6. (2009) Zbl1233.11026MR2511224
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