Fixed points and upper bounds for the rank of appearance in Lucas sequences

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Fixed points and upper bounds for the rank of appearance in Lucas sequences

Original language description

Let U(P,Q) denote the Lucas sequence satisfying the recursion relation Un+2 = PUn+1 QUn, where U0 = 0, U1 = 1, and P and Q are integers. Let z(n), called the rank of appearance of n in U(P,Q), denote the least positive integer m such that Um 0 (mod n). We find all fixed points n for the rank of appearance such that z(n) = n. We also show that z(n) 2n when z(n) exists. This paper improves results considered by Diego Marques regarding the Fibonacci sequence.

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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

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

Name of the periodical

Fibonacci Quarterly

ISSN

0015-0517

e-ISSN

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Volume of the periodical

51

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

16

Pages from-to

291-306

UT code for WoS article

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EID of the result in the Scopus database

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