Identically distributed second-order linear recurrences modulo p, II
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00462797" target="_blank" >RIV/67985840:_____/16:00462797 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Identically distributed second-order linear recurrences modulo p, II
Original language description
Let p be an odd prime and let u(a, 1) and u(a′, 1) be two Lucas sequences whose discriminants have the same nonzero quadratic character modulo p and whose periods modulo p are equal. We prove that there is then an integer c such that for all d 2 Zp, the frequency with which d appears in a full period of u(a, 1) (mod p) is the same frequency as cd appears in u(a′, 1) (mod p). Here u(a, 1) satisfies the recursion relation un+2 = aun+1 + un with initial terms u0 = 0 and u1 = 1. Similar results are obtained for the companion Lucas sequences v(a, 1) and v(a′, 1). We also explicitly determine the exact distribution of esidues of u(a, 1)(mod p) when u(a, 1) has a maximal period modulo p.
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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fibonacci Quarterly
ISSN
0015-0517
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
217-234
UT code for WoS article
000399398200004
EID of the result in the Scopus database
2-s2.0-85039857772