A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields

Abstract

In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study special Leonardo quaternions over finite fields. In particular, we determine the Leonardo quaternions that are zero divisors or invertible elements in the quaternion algebra over the finite field Zp for special values of prime integer p.

Keywords

• hybrid numbers
• quaternions
• Fibonacci numbers
• Leonardo numbers
• quantum integer
• zero divisor