The Lonely Runner Conjecture, Linear Relations of Speeds

  • Fosheng Wang
Cite this:
Wang, F. (2017). The Lonely Runner Conjecture, Linear Relations of Speeds. Asian Journal of Current Engineering and Maths, 6(1), 1–4. https://doi.org/10.15520/ajcem.2017.vol6.iss1.68.pp1-4.
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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.

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