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

Abstract

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.