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

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Özkan E.

KRAGUJEVAC JOURNAL OF MATHEMATICS, cilt.49, sa.5, ss.765-779, 2025 (ESCI, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 49 Sayı: 5
• Basım Tarihi: 2025
• Doi Numarası: 10.46793/kgjmat2505.765u
• Dergi Adı: KRAGUJEVAC JOURNAL OF MATHEMATICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
• Sayfa Sayıları: ss.765-779
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Marmara Üniversitesi Adresli: Evet

Özet

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.