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.
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Communicated by Emrah Kilic.
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Sanna, C. On Numbers n Relatively Prime to the nth Term of a Linear Recurrence. Bull. Malays. Math. Sci. Soc. 42, 827–833 (2019). https://doi.org/10.1007/s40840-017-0514-8
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DOI: https://doi.org/10.1007/s40840-017-0514-8