The Proof of a Conjecture on the Density of Sets Related to Divisibility Properties of z(n)

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018677" target="_blank" >RIV/62690094:18470/21:50018677 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2227-7390/9/22/2912" target="_blank" >https://www.mdpi.com/2227-7390/9/22/2912</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math9222912" target="_blank" >10.3390/math9222912</a>

Result language

angličtina

Original language name

The Proof of a Conjecture on the Density of Sets Related to Divisibility Properties of z(n)

Original language description

Let (F-n)(n) be the sequence of Fibonacci numbers. The order of appearance (in the Fibonacci sequence) of a positive integer n is defined as z(n)=min{k &amp; GE;1:n divide F-k}. Very recently, Trojovska and Venkatachalam proved that, for any k &amp; GE;1, the number z(n) is divisible by 2(k), for almost all integers n &amp; GE;1 (in the sense of natural density). Moreover, they posed a conjecture that implies that the same is true upon replacing 2(k) by any integer m &amp; GE;1. In this paper, in particular, we prove this conjecture.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematics

ISSN

2227-7390

e-ISSN

—

Volume of the periodical

9

Issue of the periodical within the volume

22

Country of publishing house

CH - SWITZERLAND

Number of pages

7

Pages from-to

"Article Number: 2912"

UT code for WoS article

000726222600001

EID of the result in the Scopus database

2-s2.0-85119626328