Generalized Lucas numbers of the form 3 × 2m

Salah Eddine Rihane, Chefiath Awero Adegbindin and Alain Togbé
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 129–136
DOI: 10.7546/nntdm.2021.27.2.129-136
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Authors and affiliations

Salah Eddine Rihane
Department of Mathematics and Computer Science
Abdelhafid Boussouf University
Mila 43000, Algeria

Chefiath Awero Adegbindin
Institut de Mathematiques et de Sciences Physiques
Dangbo, Benin

Alain Togbé
Department of Mathematics, Statistics, and Computer Science
Purdue University Northwest
1401 S, U.S. 421, Westville IN 46391, United States

Abstract

For an integer k\geq 2, let (L_n^{(k)})_n be the k-generalized Lucas sequence which starts with 0,\ldots,0,2,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we look the k-generalized Lucas numbers of the form 3\times 2^m i.e. we study the Diophantine equation L^{(k)}_n = 3\times 2^m in positive integers n, k, m with k \geq 2.

Keywords

  • k-generalized Lucas numbers
  • Linear form in logarithms
  • Reduction method

2020 Mathematics Subject Classification

  • 11B39
  • 11J86

References

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Cite this paper

Rihane, S. E., Adegbindin, C. A., & Togbé, A. (2021). Generalized Lucas numbers of the form 3 × 2m. Notes on Number Theory and Discrete Mathematics, 27(2), 129-136, DOI: 10.7546/nntdm.2021.27.2.129-136.

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