On the x-coordinates of Pell equations which are k-generalized Fibonacci numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F20%3AA210248I" target="_blank" >RIV/61988987:17310/20:A210248I - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022314X19302598" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022314X19302598</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2019.07.006" target="_blank" >10.1016/j.jnt.2019.07.006</a>

Result language
angličtina
Original language name
On the x-coordinates of Pell equations which are k-generalized Fibonacci numbers
Original language description
For an integer k >= 2, let {F-n(k)}(n >= 2-k) be the k-generalized Fibonacci sequence which starts with 0, ..., 0, 1 (a total of k terms) and for which each term afterwards is the sum of the k preceding terms. In this paper, for an integer d >= 2 which is square-free, we show that there is at most one value of the positive integer x participating in the Pell equation x(2) - dy(2) = +/- 1, which is a k-generalized Fibonacci number, with a couple of parametric exceptions which we completely characterize. This paper extends previous work from [18] for the case k = 2 and [17] for the case k = 3.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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