Geodesic
On The Hyperbolic $k$-Mersenne And $k$-Mersenne-Lucas Octonions
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 5, p. 765

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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.
Classification : 11B39, 11R52, 11B37
Keywords: hyperbolic k-Mersenne octonions, hyperbolic k-Mersenne-Lucas octonions, Binet formula, Catalan identity, generating function. 
Mine Uysal; Munesh Kumari; Bahar Kuloğlu; Kalika Prasad; Engin Özkan. On The Hyperbolic $k$-Mersenne And $k$-Mersenne-Lucas Octonions. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 5, p. 765 . http://geodesic.mathdoc.fr/item/KJM_2025_49_5_a8/
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     title = {On {The} {Hyperbolic} $k${-Mersenne} {And} $k${-Mersenne-Lucas} {Octonions}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {765 },
     year = {2025},
     volume = {49},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2025_49_5_a8/}
}
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