On Fibonacci numbers as sum of powers of two consecutive Tribonacci numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019196" target="_blank" >RIV/62690094:18470/22:50019196 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007/s13398-022-01252-2.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/s13398-022-01252-2.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-022-01252-2" target="_blank" >10.1007/s13398-022-01252-2</a>

Result language
angličtina
Original language name
On Fibonacci numbers as sum of powers of two consecutive Tribonacci numbers
Original language description
For k >= 2, the sequence (F-n((k)))(n >=-(k-2)) of k-generalized Fibonacci numbers is defined by the initial values 0, ..., 0, 1 = F-1((k)) and such that each term afterwards is the sum of the k preceding ones. There are many recent results about the Diophantine equation (F-n((k)))(s) + (F-n+1((k)))(s) = F-m((l)), most of them dealing with the case k = l. In 2018, Bednarik et al. solved the equation for k <= l, but with s = 2. The aim of this paper is to continue this line of investigation by solving this equation for all s >= 2, but with (k, l) = (3, 2).
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
ISSN
1578-7303
e-ISSN
1579-1505
Volume of the periodical
116
Issue of the periodical within the volume
3
Country of publishing house
IT - ITALY
Number of pages
16
Pages from-to
"Article Number: 119"
UT code for WoS article
000800800400003
EID of the result in the Scopus database
2-s2.0-85130802133

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