Submitted:
27 June 2019
Posted:
29 June 2019
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Abstract
In this paper, we generalize Fibonacci quaternion, octonion, sedenion, trigintaduonion, etc. and define Horadam 2^{k}-ions and investigate their properties. Each Horadam (such as Fibonacci, Lucas, Pell) quaternions, octonions and sedenions are Horadam 2^{k}-ions. We also present connection to some earlier works.
Keywords:
quaternions
; octonions
; sedenions
; Horadam numbers
; Fibonacci quaternion
; Cayley-Dickson algebra
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