Original scientific paper

On k- generalized Fibonacci Diophantine triples

Nurettin Irmak orcid.org/0000-0003-0409-4342 ; Konya Technical University, Engineering and Natural Science Faculty, Department of Engineering Basic Science, Konya, Turkiye *

* Corresponding author.

Abstract

For n, \(k\geq 2\), the k -generalized Fibonacci sequence \(\left\lbrace F_{n}^{(k)} \right\rbrace \) is defined by each term afterwards is the sum of the k preceding terms with the initial values \(0,0,\ldots ,0,1\) k terms)\). In this paper, we prove that the system \(\begin{eqnarray*}
ab+1 &=&F_{x}^{\left( k\right) } \\
ac+1 &=&F_{y}^{\left( k\right) } \\
bc+1 &=&F_{z}^{\left( k\right) }\end{eqnarray*}%\)
has no solution for 1

Keywords

Diophantine triples; k-generalized Fibonacci number

Hrčak ID:

321248

URI

https://hrcak.srce.hr/321248

Publication date:

7.10.2024.

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