Let u_n be a nondegenerate linear recurrence of integers, and let A be the set of positive integers n such that u_n and n are relatively prime. We prove that A has an asymptotic density, and that this density is positive unless u_n / n is a linear recurrence.
On numbers n relatively prime to the nth term of a linear recurrence
Sanna, Carlo
2019-01-01
Abstract
Let u_n be a nondegenerate linear recurrence of integers, and let A be the set of positive integers n such that u_n and n are relatively prime. We prove that A has an asymptotic density, and that this density is positive unless u_n / n is a linear recurrence.
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