On Diophantine Equations Related to Order of Appearance in Fibonacci Sequence
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50016196" target="_blank" >RIV/62690094:18470/19:50016196 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/7/11/1073" target="_blank" >https://www.mdpi.com/2227-7390/7/11/1073</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math7111073" target="_blank" >10.3390/math7111073</a>
Alternative languages
Result language
angličtina
Original language name
On Diophantine Equations Related to Order of Appearance in Fibonacci Sequence
Original language description
Let Fn be the n-th Fibonacci number. Order of appearance z(n) of a natural number n is defined as smallest natural number k, such that n divides Fk. In 1930, Lehmer proved that all solutions of equation z(n)=n+/-1 are prime numbers. In this paper, we solve equation z(n)=n+l for the absolute value of l is from the set {1,…,9}. Our method is based on the p-adic valuation of Fibonacci numbers.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - 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
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
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
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Volume of the periodical
7
Issue of the periodical within the volume
11
Country of publishing house
CH - SWITZERLAND
Number of pages
10
Pages from-to
"Article Number: 1073"
UT code for WoS article
000502288700070
EID of the result in the Scopus database
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