On primes in Lucas sequences

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00441527" target="_blank" >RIV/67985840:_____/15:00441527 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On primes in Lucas sequences

Original language description

Consider the Lucas sequence u(a, b) = (un(a, b)) and the companion Lucas sequence v(a, b) = (vn(a, b)) which both satisfy the second order recursion relation wn+2 = awn+1 bwn with initial terms u0 = 0, u1 = 1, and v0 = 2, v1 = a, respectively. We give both necessary and sufficient tests and also necessary tests for the primality of |un| and |vn|. For those tests which are only necessary, we show that these tests are not sufficient by means of a simple criterion using the Legendre symbol. These results are specialized to the Fibonacci numbers (Fn) and to the Lucas numbers (Ln). In particular, we generalize a result of Drobot giving criteria for Fp not to be prime, where p is a prime, to the Lucas numbers (Ln).

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

<a href="/en/project/GA14-02067S" target="_blank" >GA14-02067S: Advanced methods for flow-field analysis</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

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

53

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

23

Pages from-to

1-23

UT code for WoS article

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EID of the result in the Scopus database

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