On k-Mersenne and k-Mersenne-Lucas Octonions

2022/07/25 by Munesh Kumari, Kalika Prasad, Kumari, Munesh +3
Mathematics · Physics and Astronomy · #11B37 #11B39 #11R52 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2207.12243

openalex publication_date 2022/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper aims to introduce the k-Mersenne and k-Mersenne-Lucas octonions. We give the closed form formulae for these octonions and obtain some well-known identities like Cassini's identity, d'Ocagne's identity, Catalan identity, Vajda's identity and generating functions of them. As a consequence k=1 yields all the above properties for Mersenne and Mersenne-Lucas octonions.

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