On prime factors of the sum of two k-Fibonacci numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901Y0Q" target="_blank" >RIV/61988987:17310/18:A1901Y0Q - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1142/S1793042118500720" target="_blank" >http://dx.doi.org/10.1142/S1793042118500720</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S1793042118500720" target="_blank" >10.1142/S1793042118500720</a>

Result language
angličtina
Original language name
On prime factors of the sum of two k-Fibonacci numbers
Original language description
We consider for integers k >= 2 the k-generalized Fibonacci sequences F-(k) := (F-n((k)))(n >= 2-k), whose first k terms are 0,..., 0, 1 and each term afterwards is the sum of the preceding k terms. We give a lower bound for the largest prime factor of the sum of two terms in F(k). As a consequence of our main result, for every fixed finite set of primes S, there are only finitely many positive integers k and S-integers which are a non-trivial sum of two k-Fibonacci numbers, and all these are effectively computable.
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
—
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
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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