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arXiv · 1703.10478

On numbers $n$ relatively prime to the $n$th term of a linear recurrence

Carlo Sanna
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Abstract

Let $(u_n)_{n \geq 0}$ be a nondegenerate linear recurrence of integers, and let $\mathcal{A}$ be the set of positive integers $n$ such that $u_n$ and $n$ are relatively prime. We prove that $\mathcal{A}$ has an asymptotic density, and that this density is positive unless $(u_n / n)_{n \geq 1}$ is a linear recurrence.

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Carlo Sanna. 2017-03-30. On numbers $n$ relatively prime to the $n$th term of a linear recurrence. https://doi.org/10.1007/s40840-017-0514-8

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