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

You can check for contributions to this problem on the solutions page.

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