UNSOLVED PROBLEMS |

In Number Theory, Logic, and Cryptography |

Lonely Runner Conjecture |

Suppose there are k runners, all lined up at the start of a circular running track of length 1. They all start running at constant, but different, speeds.
The Lonely Runner conjecture states that for each runner, there will come a time when he or she will be a distance of at least 1/k along the track from every other runner. The conjecture has been proved for small values of k (<=7). The problem is to prove or disprove the conjecture for the general case, or for cases where k > 7.
For further information, please see: [1] http://en.wikipedia.org/wiki/Lonely_runner_conjecture [2] https://rjlipton.wordpress.com/2012/01/28/the-lonely-runner-conjecture/ [3] https://arxiv.org/abs/1701.02048
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