On Quaternion-Gaussian Fibonacci Numbers and Their Properties

Abstract

We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients. Using the Binet form we prove fundamental relations between these numbers. Moreover, we investigate whether the quaternions newly defined provide existing some important identities such as Cassini’s identity for quaternions.

Keywords

• fibonacci number
• gaussian number
• quaternion
• recurrence relation
• 11b37
• 11b39
• 11r52