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

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

M. Kumari, K. Prasad, H. Mahato

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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.

Keywords

k-Mersenne Octonions, Binet Formula, Catalan's Identity, Finite sum, Generating Function.