Identically distributed second-order linear recurrences modulo p

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

Identically distributed second-order linear recurrences modulo p

Original language description

Let w(a,1) denote the second-order linear recurrence satisfying the recursion relation wn+2 = awn+1 wn, where a and the initial terms w0, w1 are all integers. Let p be an odd prime. The restricted period hw(p) of w(a,1) modulo p is the least positive integer r such that wn+r Mwn (mod p) for all n 0 and some nonzero residue M modulo p. We distinguish two recurrences, the Lucas sequence of the first kind u(a,1) and the Lucas sequence of the second kind v(a,1), satisfying the above recursion relation and having initial terms u0 = 0, u1 = 1 and v0 = 2, v1 = a, respectively. We show that if u(a1,1) and u(a2,1) both have the same restricted period modulo p, or equivalently, the same period modulo p, then u(a1,1) and u(a2,1) have the same distribution of residues modulo p. Similar results are obtained for Lucas sequences of the second kind.

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

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

4

Country of publishing house

US - UNITED STATES

Number of pages

23

Pages from-to

290-312

UT code for WoS article

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EID of the result in the Scopus database

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