Work

On a Diophantine Equation with Jacobsthal and Fibonacci Numbers

Year: 2026

Type: article

Abstract: In the present paper, we identify all Jacobsthal numbers that may be expressed as a product of three Fibonacci numbers. More precisely, our main result shows that the only solution to the Diophantine equationFkFlFm = Jnfor 2 < k < l < m is expressed as (k,l,m,n) = (5,7,8,12). The proof relies on techniquesinvolving linear forms in logarithms.

Source: Hacettepe Journal of Mathematics and Statistics

DOI: 10.15672/hujms.1823402

Authors: Daeyeoul Kim, Zekiye Pinar Cihan, Zeynep Demirkol Özkaya, İlker İnam

Institutions: Jeonbuk National University, Mi̇lli̇ Eği̇ti̇m Bakanliği, Van Yüzüncü Yıl Üniversitesi, Bilecik Şeyh Edebali Üniversitesi

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Jeonbuk National University

Award: G5244869610