On Iterative Relations in Pell Subscripts
Dişkaya, Orhan
In this study, we define iterative relations in Pell subscripts using Pell numbers, and examine the divisibility properties of these iterative relations. Furthermore, despite the computational difficulty of determining the divisibility of very large Pell numbers, the study possible to obtain results through theoretical methods. Thus, we have successfully generalized Desmond's work on the Fibonacci sequence by using Pell numbers to develop a dissimilar approach
On the Quaternion Padovan Numbers
Dişkaya, Orhan | Menken, Hamza
In the present work, we explore the concept of quaternion Padovan sequences, extending the classical Padovan sequence into the realm of quaternions. Quaternions, introduced by Hamilton in 1843, are a number system that generalizes complex numbers into four dimensions, with applications in various fields such as quantum physics, computer graphics, and three-dimensional rotations. The study begins by reviewing the definition and properties of quaternions, including their non- commutative multiplication rules and the formulation of quaternion numbers. The Padovan sequence is defined by the recurrence relation Pn+3 = Pn+1 + Pn with initial conditions P0 = P1 = P2 =1. This sequence is generalized to quaternions by defining quaternion Padovan numbers, denoted QP (a,b, c, d) , wh...