MERSENNE NUMBERS IN GENERALIZED LUCAS SEQUENCES

Altassan A., ALAN M.

Comptes Rendus de L'Academie Bulgare des Sciences, vol.77, no.1, pp.3-10, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.7546/crabs.2024.01.01
  • Journal Name: Comptes Rendus de L'Academie Bulgare des Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, zbMATH
  • Page Numbers: pp.3-10
  • Keywords: k-generalized Lucas sequences, k-Lucas numbers, linear forms in logarithms, Lucas numbers, Mersenne numbers
  • Yıldız Technical University Affiliated: Yes

Abstract

Let k ≥ 2 be an integer and let (L(nk))n≥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 2a−1, where a is any positive integer. The aim of this paper is to determine all Mersenne numbers which lie inside k-Lucas sequences.