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arXiv · 2111.07157

Coprime matchings

Carl Pomerance
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Abstract

We prove that there is a matching between 2 intervals of positive integers of the same even length, with corresponding pairs coprime, provided the intervals are in $[n]$ and their lengths are $>c(\log n)^2$, for a positive constant $c$. This improves on a recent result of Bohman and Peng. As in their paper, the result has an application to the lonely runner conjecture.

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Carl Pomerance. 2021-11-13. Coprime matchings. https://arxiv.org/abs/2111.07157

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