On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions
Mi̇ne Uysal, Munesh Kumari, Bahar Kuloğlu, Kalika Prasad, Engi̇n Özkan
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.
Topics & Concepts
Mersenne primeMathematicsIdentity (music)Algebraic numberPure mathematicsAlgebra over a fieldCombinatoricsMathematical analysisArtAestheticsAdvanced Mathematical Theories and ApplicationsAdvanced Mathematical TheoriesMathematics and Applications