On a Diophantine Equation with Jacobsthal and Fibonacci Numbers
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.
Authors
- Daeyeoul Kim (ORCID: https://orcid.org/0000-0002-2970-1666)
- İlker İnam (ORCID: https://orcid.org/0000-0001-5765-1718)
- Zeynep Demirkol Özkaya
- Zekiye Pinar Cihan (ORCID: https://orcid.org/0000-0003-4486-1593)
Institutions
- Van Yüzüncü Yıl Üniversitesi (TR)
- Bilecik Şeyh Edebali Üniversitesi (TR)
- Jeonbuk National University (KR)
Publication Details
- Journal
- Hacettepe Journal of Mathematics and Statistics
- Published
- 2026-05-18
- DOI
- https://doi.org/10.15672/hujms.1823402
- Primary Topic
- Advanced Mathematical Theories and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00