The Lonely Runner Conjecture, Linear Relations of Speeds
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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.
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Mathematics Subject Classification: 11B75.
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