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On Numbers n Relatively Prime to the nth Term of a Linear Recurrence

  • Carlo SannaEmail author
Article

Abstract

Let \((u_n)_{n \ge 0}\) 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 \((u_n{/}n)_{n \ge 1}\) is a linear recurrence.

Keywords

Linear recurrences Greatest common divisor Divisibility 

Mathematics Subject Classification

Primary 11B37 Secondary 11A07 11B39 11N25 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversità degli Studi di TorinoTurinItaly

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