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In this paper, we study the dynamics of the Potts-Bethe mapping associated with the p-adic q-state Potts model over the Cayley tree of order three. Namely, we establish the regularity of the Potts-Bethe mapping for the case p = 2 (mod 3) with p > 5.This content has been downloaded from IOPscience. Please scroll down to see the full text. Downlo