Central binomial coefficients divisible by or coprime to their indices-Reference-Cited by-同舟云学术

Central binomial coefficients divisible by or coprime to their indices

Published:2018-05 Issue:04 Volume:14 Page:1135-1141
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Sanna Carlo¹

Affiliation:

1. Department of Mathematics, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

Abstract

Let [Formula: see text] be the set of all positive integers [Formula: see text] such that [Formula: see text] divides the central binomial coefficient [Formula: see text]. Pomerance proved that the upper density of [Formula: see text] is at most [Formula: see text]. We improve this bound to [Formula: see text]. Moreover, let [Formula: see text] be the set of all positive integers [Formula: see text] such that [Formula: see text] and [Formula: see text] are relatively prime. We show that [Formula: see text] for all [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042118500707

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