On the Diophantine Equation $z(n)=(2-1/k),n$ Involving the Order of Appearance in the Fibonacci Sequence
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50016628" target="_blank" >RIV/62690094:18470/20:50016628 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/8/1/124" target="_blank" >https://www.mdpi.com/2227-7390/8/1/124</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math8010124" target="_blank" >10.3390/math8010124</a>
Alternative languages
Result language
angličtina
Original language name
On the Diophantine Equation $z(n)=(2-1/k),n$ Involving the Order of Appearance in the Fibonacci Sequence
Original language description
Let $(F_n)_{ngeq 0}$ be the sequence of the Fibonacci numbers. The order (or rank) of appearance $z(n)$ of a positive integer $n$ is defined as the smallest positive integer $m$ such that $n$ divides $F_m$. In 1975, Sall' e proved that $z(n)leq 2n$, for all positive integers $n$. In this paper, we shall solve the Diophantine equation $z(n)=(2-1/k)n$ for positive integers $n$ and $k$.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
—
Volume of the periodical
8
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
8
Pages from-to
"Article Number: 124"
UT code for WoS article
000515730100049
EID of the result in the Scopus database
2-s2.0-85080142871