On Fibonacci Numbers of Order r Which Are Expressible as Sum of Consecutive Factorial Numbers

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018119" target="_blank" >RIV/62690094:18470/21:50018119 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2227-7390/9/9/962" target="_blank" >https://www.mdpi.com/2227-7390/9/9/962</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math9090962" target="_blank" >10.3390/math9090962</a>

Result language

angličtina

Original language name

On Fibonacci Numbers of Order r Which Are Expressible as Sum of Consecutive Factorial Numbers

Original language description

Let (t(n)((r)))(n &gt;= 0) be the sequence of the generalized Fibonacci number of order r, which is defined by the recurrence t(n)((r)) = t(n-1)((r)) +... + t(n-r)((r)) for n &gt;= r, with initial values t(0)((r)) = 0 and t(i)((r)) = 1, for all 1 &lt;= i &lt;= r. In 2002, Grossman and Luca searched for terms of the sequence (t(n)((2)))(n), which are expressible as a sum of factorials. In this paper, we continue this program by proving that, for any l &gt;= 1, there exists an effectively computable constant C = C(l) &gt; 0 (only depending on l), such that, if (m, n, r) is a solution of t(m)((r)) = n! + (n + 1)! +... + (n + l)!, with r even, then max{m, n, r} &lt; C. As an application, we solve the previous equation for all 1 &lt;= l &lt;= 5.

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

—

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

9

Country of publishing house

CH - SWITZERLAND

Number of pages

9

Pages from-to

"Article Number: 962"

UT code for WoS article

000650581400001

EID of the result in the Scopus database

2-s2.0-85105321726