Abstract

In this paper, we study the Pell polynomials according to modulo mwhere $X^2=2x+1$ and various properties of these sequences are obtained. Also, Pell polynomials to the ring of complex numbers was defined. We define the Pell Polynomial-type orbits $P_（α,β){^R}(x)={X_i}$ where R be a 2-generator ring and (α,β) is a generating pair of the ring. Furthermore, we obtain the periods of the Pell Polynomial-type orbits P_（α,β){^R}(x) in finite 2-generator rings of order P{^2}.

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