1. On the lonely runner conjecture
- Creator:
- Pandey, Ram Krishna
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- congruences, arithmetic progression, and bi-arithmetic progression
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public