Name: Central binomial coefficients divisible by or coprime to their indices
Creator: Sanna, Carlo
Keywords: 2. Zero hunger, 1. No poverty, central binomial coefficient, divisibility, upper and lower densities, 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article 01 May 2018 English Publisher:World Scientific Pub Co Pte LtdJournal:International Journal of Number Theory, volume 14, pages 1,135-1,141 (issn: 1793-0421, eissn: 1793-7310,

Authors: Sanna, Carlo;

doi: 10.1142/s1793042118500707

handle: 11583/2722660 , 2318/1651940

Central binomial coefficients divisible by or coprime to their indices

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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].

Related Organizations

Polytechnic University of Turin
Italy
University of Turin
Italy

Keywords

central binomial coefficient, divisibility, upper and lower densities

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