The Fibonacci Polynomials in Rings

In this paper, we study the Fibonacci polynomials modulo m such that chi(2) = x + 1 and then we obtain miscellaneous properties of these sequences. Also, we extend the Fibonacci polynomials to the ring of complex numbers. We define the Fibonacci Polynomial-type orbits F-(a,b)(R)(x) = {x(i)} where R be a 2-generator ring and (a, b) is a generating pair of the ring R. Furthermore, we obtain the periods of the Fibonacci Polynomial-type orbits F(a,b)Rw(x) in finite 2-generator rings of order p(2).