On the sum of squares of consecutive k-bonacci numbers which are l-bonacci numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50015448" target="_blank" >RIV/62690094:18470/19:50015448 - isvavai.cz</a>
Result on the web
<a href="https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/156/1/112828/on-the-sum-of-squares-of-consecutive-k-bonacci-numbers-which-are-l-bonacci-numbers" target="_blank" >https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/156/1/112828/on-the-sum-of-squares-of-consecutive-k-bonacci-numbers-which-are-l-bonacci-numbers</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/cm7272-6-2018" target="_blank" >10.4064/cm7272-6-2018</a>

Result language
angličtina
Original language name
On the sum of squares of consecutive k-bonacci numbers which are l-bonacci numbers
Original language description
Let (F-n)(n >= 0) be the Fibonacci sequence given by Fm+2 = Fm+1 + F-m, for m >= 0, where F-0 = 0 and F-1 = 1. A well-known generalization of the Fibonacci sequence is the k-generalized Fibonacci sequence (F-n((k)))(n) which is defined by the initial values 0, 0, ..., 0, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In 2014, Chaves and Marques solved the Diophantine equation (F-n((k)))(2) + (F-n+1((k)))(2) = F-m((k)) in integers m, n and k >= 2. In this paper, we generalize this result by proving that the Diophantine equation (F-n((k)))(2) + (F-n+1((k)))(2) = F-m((l)) has no solution in positive integers n, m, k, l with 2 <= k < l and n > 1.
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
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OECD FORD branch
10101 - Pure mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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