On Lucac and Frobenius pseudoprimes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00644189" target="_blank" >RIV/67985840:_____/25:00644189 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.5281/zenodo.17711593" target="_blank" >https://doi.org/10.5281/zenodo.17711593</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5281/zenodo.17711593" target="_blank" >10.5281/zenodo.17711593</a>
Alternative languages
Result language
angličtina
Original language name
On Lucac and Frobenius pseudoprimes
Original language description
Consider the Lucas sequences U(P, Q) and V (P, Q) which satisfy the linear recurrence relation Wn+2 = P Wn+1 −QWn with initial terms U0 = 0, U1 = 1, and V0 = 2, V1 = P, respectively, where P and Q are integers. We consider pseudoprimes with parameters P and Q related to U(P, Q) and V (P, Q). We extend results obtained by Somer and Křížek (2022) regarding pseudoprimes with parameters P and Q, where P is odd and greater than 0 to those in which the parameter P can also be less than 0 or even. We also obtain infinitely many new examples of pseudoprimes, called the Lucas pseudoprimes with parameters P and Q. We further present results on Frobenius pseudoprimes, which are generalizations of Lucas pseudoprimes.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS 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
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Integers. Electronic Journal of Combinatorial Number Theory
ISSN
1553-1732
e-ISSN
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Volume of the periodical
25
Issue of the periodical within the volume
November
Country of publishing house
DE - GERMANY
Number of pages
32
Pages from-to
A107
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-105025055789