ON THE HYPERBOLIC k-MERSENNE AND k-MERSENNE-LUCAS OCTONIONS


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Uysal M., Kumarı M., Kuloğlu B., Prasad K., Özkan E.

KRAGUJEVAC JOURNAL OF MATHEMATICS, vol.49, no.5, pp.765-779, 2025 (ESCI)

  • Publication Type: Article / Article
  • Volume: 49 Issue: 5
  • Publication Date: 2025
  • Journal Name: KRAGUJEVAC JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.765-779
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

In this paper, we introduce the hyperbolic k-Mersenne and k-MersenneLucas octonions and investigate their algebraic properties. We give Binet’s formula and present several interrelations and some well-known identities such as Catalan identity, d’Ocagne identity, Vajda identity, generating functions, etc. of these octonions in closed form. Furthermore, we investigate the relations between hyperbolic k-Mersenne octonions and hyperbolic k-Mersenne-Lucas octonions.