MERSENNE NUMBERS IN GENERALIZED LUCAS SEQUENCES

Altassan A., ALAN M.

Comptes Rendus de L'Academie Bulgare des Sciences, cilt.77, sa.1, ss.3-10, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 77 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.7546/crabs.2024.01.01
  • Dergi Adı: Comptes Rendus de L'Academie Bulgare des Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, zbMATH
  • Sayfa Sayıları: ss.3-10
  • Anahtar Kelimeler: k-generalized Lucas sequences, k-Lucas numbers, linear forms in logarithms, Lucas numbers, Mersenne numbers
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.