On Tribonacci numbers written as a product of three Fibonacci numbers

Zeynep Demirkol Ozkaya

doi:10.2478/auom-2026-0006

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On Tribonacci numbers written as a product of three Fibonacci numbers

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 34 (2026): Issue 1 (May 2026)

By: Zeynep Demirkol Ozkaya

Open Access

|May 2026

Abstract

The present paper examines the following Diophantine equation: T_n = F_k · F_l · F_m where T_n is the n-th Tribonacci number and likewise F_k is the k-th Fibonacci number and so on as variables. As an application of the Baker’s method, we show that the equation has only one solution apart from the trivial one, namely (n, k, l, m) = (12, 4, 6, 8). This paper can be considered as a continuation work of the paper by Luca et al, 2023.

References

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2026-0006 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 117 - 128

Submitted on: Jun 16, 2025

Accepted on: Nov 1, 2025

Published on: May 15, 2026

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Fibonacci numbers,

Tribonacci numbers,

linear forms in logarithms,

Diophantine equations,

applications of the Baker’s method

Related subjects:

Mathematics,

General mathematics

© 2026 Zeynep Demirkol Ozkaya, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 34 (2026): Issue 1 (May 2026)