A Solution to the Lonely Runner Conjecture for Almost All Points

C. Harold Horvat; Matthew Stoffregen

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arXiv · 1103.1662

A Solution to the Lonely Runner Conjecture for Almost All Points

C. Harold Horvat·Matthew Stoffregen

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Abstract

The Lonely Runner Conjecture is a number theory problem, dating to 1964. Using dynamical systems theory, we show almost all sets of velocities solve the conjecture. Furthermore, any "traditional" approach of Diophantine approximation cannot solve the problem, and we offer a short list of reformulations of the problem.

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C. Harold Horvat, Matthew Stoffregen. 2011-03-08. A Solution to the Lonely Runner Conjecture for Almost All Points. https://arxiv.org/abs/1103.1662

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