On the k-Mersenne and k-Mersenne-Lucas octonions

Abstract

This paper aims to introduce the k-Mersenne and k-Mersenne-Lucas octonions. We investigate the algebraic properties of these octonions in closed form and give some well-known identities like Catalan identity, d’Ocagne identity, Simson identity, etc. Moreover, we present various generating functions and partial sum formulae for these octonions. Lastly, we study the combined identities and matrix representation for these octonions.