On members of Lucas sequences with bounded prime gaps
In this paper, we look at terms of Lucas sequences whose prime factors have indices with bounded gaps in the sequence of all prime numbers. Some of our results depend on certain widely believed conjectures. In our proofs we combine various tools, including Baker's method, the subspace theorem, and results of Stewart, and Murty and Wong.
Authors
- Florian Luca (ORCID: https://orcid.org/0000-0003-1321-4422)
- István Pink (ORCID: https://orcid.org/0000-0003-2098-1830)
- Lajos Hajdu
- Attila Bérczes
Institutions
- University of Debrecen (HU)
- Stellenbosch University (ZA)
- University of Oxford (GB)
- Max Planck Institute for Software Systems (DE)
- Applications Research (United States) (US)
Publication Details
- Journal
- Journal of Number Theory
- Published
- 2025-10-02
- DOI
- https://doi.org/10.1016/j.jnt.2025.09.005
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00