There are no k-Pell numbers expressible as products of two Fermat numbers
Let k 2. A generalization of the well-known Pell sequence is the k-Pell sequence.The first k terms of the sequence are 0, . . ., 0, 1 and each term afterwards is given by the linear recurrenceIn this paper, we use Baker's method to determine all the solutions of the Diophnatine equationwhere a and b are positive integers.Then, we deduce that there are no k-Pell numbers expressible as products of two Fermat numbers.
Authors
- Salah Eddine Rihane (ORCID: https://orcid.org/0000-0002-4145-7942)
- Alain Togbé (ORCID: https://orcid.org/0000-0002-5882-936X)
- Alioune Badara Guèye (ORCID: https://orcid.org/0000-0003-3428-8092)
Publication Details
- Journal
- Az Eszterházy Károly Tanárképző Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Az Eszterházy Károly Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Annales mathematicae et informaticae
- Published
- 2025-01-01
- DOI
- https://doi.org/10.33039/ami.2025.05.001
- Primary Topic
- Advanced Mathematical Theories and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Purdue University