On The Hyperbolic $k$-Mersenne And $k$-Mersenne-Lucas Octonions


Mine Uysal, Munesh Kumari, Bahar Kuloğlu, Kalika Prasad, Engin Özkan




In this paper, we introduce the hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas 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.