THE ORDER OF APPEARANCE OF THE PRODUCT OF FIVE CONSECUTIVE LUCAS NUMBERS

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F14%3A50002885" target="_blank" >RIV/62690094:18470/14:50002885 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.2478/tmmp-2014-0000" target="_blank" >http://dx.doi.org/10.2478/tmmp-2014-0000</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2478/tmmp-2014-0000" target="_blank" >10.2478/tmmp-2014-0000</a>

Result language

angličtina

Original language name

THE ORDER OF APPEARANCE OF THE PRODUCT OF FIVE CONSECUTIVE LUCAS NUMBERS

Original language description

Let $ F_n$ be the $n$th Fibonacci number and let $L_n$ be the $n$th Lucas number. The order of appearance $z(n)$ of a natural number $n$ is defined as the smallest natural number $k$ such that $n$ divides $F_k$. For instance, $z(F_n)=n=z(L_n)/2$, for all$n>2$. In this paper, among other things, we prove that begin{center} $z(L_{n}L_{n+1}L_{n+2}L_{n+3}L_{n+4})=dfrac{n(n+1)(n+2)(n+3)(n+4)}{12}$, end{center} for all positive integers $nequiv 0,8pmod{12}$.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2014

Confidentiality

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

Name of the periodical

Tatra Mountains Matematical Pulblications

ISSN

1210-3195

e-ISSN

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Volume of the periodical

59

Issue of the periodical within the volume

1

Country of publishing house

SK - SLOVAKIA

Number of pages

13

Pages from-to

1-13

UT code for WoS article

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EID of the result in the Scopus database

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