## A Proof of the Lonely Runner Conjecture for Any n, with Rational Values Approximating Any Set of Arbitrary Integers with Infinite Precision

**Authors:** Patrick A Devlin

In number theory, and especially the study of the diophantine approximation, the Lonely Runner Conjecture is a conjecture with important and widespread applications in mathematics.
A previous paper by this author proved the lonely runner conjecture for any n, for the special case of integers with particularly correlated prime factors. In this paper we attempt to extend this work to the general case of n arbitrary integers. The paper demonstrates that a set of integers with correctly correlated prime factors, such that they satisfy the conjecture, can be modified to approximate any set of arbitrary integers with infinite precision.

**Comments:** 17 Pages.

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### Submission history

[v1] 2012-10-25 06:02:32

[v2] 2012-10-25 10:11:22

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