A Solution to the Lonely Runner Conjecture for Almost All Points

Details A Solution to the Lonely Runner Conjecture for Almost All Points A Solution to the Lonely Runner Conjecture for Almost All Points

2011-03-08

arxiv.org/abs/1103.1662v1

Mathematics

Number Theory

5 pages

Scientific paper

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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