Second-order linear recurrences having arbitrarily large defect modulo p

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542416" target="_blank" >RIV/67985840:_____/21:00542416 - isvavai.cz</a>
Result on the web
<a href="http://hdl.handle.net/11104/0319826" target="_blank" >http://hdl.handle.net/11104/0319826</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Second-order linear recurrences having arbitrarily large defect modulo p
Original language description
Let (w) = w(a, b) denote the second-order linear recurrence satisfying wn+2 =awn+1 +bwn, where w0, w1, and a are integers, b = 1, and D = a2 +4b is the discriminant. We distinguish the Lucas sequences u(a, b) and v(a, b) with initial terms u0 = 0, u1 = 1, and v0 = 2, v1 = a, respectively. Let p be a prime. Given the recurrence w(a, b), let w(p), called the defect of w(a, b) modulo p, denote the number of residues not appearing in (w) modulo p. It is known that for the recurrence w(a, 1), w(p) 1 if p > 7 and p - D. Given the xed recurrence w(a, 1), where w(a, 1) = u(a, 1) or v(a, 1), we will show that limp!1 w(p) = 1. Further, given the arbitrary recurrence w(a,????1), we will demonstrate that limp!1 w(p) = 1 and limp!1 w(p)=p 1 2. We will also prove that for the arbitrary recurrence w(a, 1), we have that lim supp!1 w(p)=p = 1.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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