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.

On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

“…The set of hybrid numbers forms a non-commutative ring under addition and multiplication (please see [8]). After Özdemir's paper, hybrid numbers, whose components are defined by the homogeneous recurrence relation with constant coefficients, have been studied by a large number of researchers since 2018 (please see [9][10][11][12][13][14][15]). In [16], Kızılateş and Kone introduced Fibonacci divisor hybrid numbers that generalize the Fibonacci hybrid numbers defined by Szynal-Liana and Wloch [9].…”

Algebraic, Analytic, and Computational Number Theory and Its Applications

“…Some important properties of associative algebra can be studied by employing the standard tools of algebraic number theory, elementary number theory, computational number theory, and combinatorics (see [15][16][17][18][19][20]). Three papers of this Special Issue deal with sequences of special numbers and special quaternions [21][22][23].…”