Second-order linear recurrences with identically distributed residues modulo p^e
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00583475" target="_blank" >RIV/67985840:_____/24:00583475 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.7546/nntdm.2024.30.1.47-66" target="_blank" >https://doi.org/10.7546/nntdm.2024.30.1.47-66</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7546/nntdm.2024.30.1.47-66" target="_blank" >10.7546/nntdm.2024.30.1.47-66</a>
Alternative languages
Result language
angličtina
Original language name
Second-order linear recurrences with identically distributed residues modulo p^e
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 dinmathbb Z_p, the frequency with which d appears in a full period of u(a,-1)pmod p is the same frequency as cd appears in u(a',-1)pmod p. Here u(a,b) satisfies the recursion relation u_{n+2}=au_{n+1}+bu_n with initial terms u_0=0 and u_1=1. Similar results are obtained for the companion Lucas sequences v(a,-1) and v(a',-1). This paper extends analogous statements for Lucas sequences of the form u(a,1)pmod p given in a previous article. We further generalize our results by showing for a certain class of primes p that if e>1, b=pm 1, and u(a,b) and u(a',b) are Lucas sequences with the same period modulo p, then there exists an integer c such that for all residues dpmod{p^e}, the frequency with which d appears in u(a,b)pmod{p^e} is the same frequency as cd appears in u(a',b)pmod{p^e}.
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
<a href="/en/project/GA24-10586S" target="_blank" >GA24-10586S: Analytical and numerical modeling of hysteresis phenomena</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Notes on Number Theory and Discrete Mathematics
ISSN
1310-5132
e-ISSN
2367-8275
Volume of the periodical
30
Issue of the periodical within the volume
1
Country of publishing house
BG - BULGARIA
Number of pages
20
Pages from-to
47-66
UT code for WoS article
001221794100003
EID of the result in the Scopus database
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