Solution to the Lonely Runner Conjecture

Pat Devlin — Sat, 20 Oct 2012 15:29:10 +0200

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Subject: Number Theory

Consider n runners on a circular track of unit length. At time t = 0, all runners are at the same position and start to run; the runners' speeds are pair-wise distinct. A runner is said to be lonely if at distance of at least 1/n from each other runner. The Lonely Runner Conjecture states that every runner gets lonely at some time.

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Solution to the Lonely Runner Conjecture