Mersenne Numbers in Generalized Lucas Sequences

Authors

  • Alaa Altassan Department of Mathematics, King Abdulaziz University, Saudi Arabia
  • Murat Alan Department of Mathematics, Yildiz Technical University, Turkey

DOI:

https://doi.org/10.7546/CRABS.2024.01.01

Keywords:

$$k$$-generalized Lucas sequences, $$k$$-Lucas numbers, Mersenne numbers, linear forms in logarithms, Lucas numbers

Abstract

Let $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer. The aim of this paper is to determine all Mersenne numbers which lie inside $$k$$-Lucas sequences.

Author Biographies

Alaa Altassan, Department of Mathematics, King Abdulaziz University, Saudi Arabia

Mailing Address:
Department of Mathematics,
King Abdulaziz University,
21589, Jeddah, Saudi Arabia

E-mail: aaltassan@kau.edu.sa

Murat Alan, Department of Mathematics, Yildiz Technical University, Turkey

Mailing Address:
Department of Mathematics,
Yildiz Technical University,
34210, Istanbul, Turkey

E-mail: alan@yildiz.edu.tr

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Published

29-01-2024

How to Cite

[1]
A. Altassan and M. Alan, “Mersenne Numbers in Generalized Lucas Sequences”, C. R. Acad. Bulg. Sci. , vol. 77, no. 1, pp. 3–10, Jan. 2024.

Issue

Section

Mathematics