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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&apos; 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