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The Lonely Runner Conjecture, Linear Relations of Speeds

Fosheng Wang

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Abstract


Let  be an integer and let  be distinct nonzero real numbers (also called speeds). The Lonely Runner Conjecture states that there exists  such that  for all . Viewing  as an abelian group, we prove that the conjecture holds for speeds  if the speeds are linearly independent or “almost linearly independent” in the group , and we give a measure of “how lonely the runners are” in these cases.

 

Mathematics Subject Classification: 11B75.




DOI: http://dx.doi.org/10.15520/ajcem.2017.vol6.iss1.68.pp1-4.

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