On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers

Carlos A. Gómez; Jhonny C. Gómez; Florian Luca

doi:10.1007/s40840-022-01439-1

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On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers

Journal article

Peer reviewed

On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers

Carlos A. Gómez, Jhonny C. Gómez and Florian Luca

Bulletin of the Malaysian Mathematical Sciences Society, Vol.46(2)

01/03/2023

DOI: https://doi.org/10.1007/s40840-022-01439-1

Abstract

Applications of Mathematics

Article

general

Mathematics

Mathematics and Statistics

F n + 1 3 + F n 3 - F n - 1 3 = F 3 n , for all n ≥ 1 , is a well-known identity fulfilled by the Fibonacci numbers. In this paper, we study a variant of this identity, replacing the cubic powers by a general power on the left–hand side and allowing an additional unknown exponent on the right–hand side.

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Title: On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers
Creators - without role: Carlos A. Gómez - Departamento de Matemáticas, Universidad del Valle, Research Group ALTENUA–Universidad del Valle: Algebra, Teoría de Números y Aplicaciones, Colciencias code: COL0017217
Jhonny C. Gómez - Universidad Libre de Colombia
Florian Luca - King Abdulaziz University
Publication Details: Bulletin of the Malaysian Mathematical Sciences Society, Vol.46(2)
Publisher: Springer Nature Singapore
Identifiers: 9936772108331
Academic Unit: King Abdulaziz University
Language: English
Resource Type: Journal article