Complete decomposition of Dickson-type polynomials and related Diophantine equations Original Research Article

We characterize decomposition over image of polynomials image defined by the generalized Dickson-type recursive relation (ngreater-or-equal, slanted1)image where image or image. As a direct application of the uniform decomposition result, we fully settle the finiteness problem for the Diophantine equationimage This extends and completes work of Dujella/Tichy and Dujella/Gusić concerning Dickson polynomials of the second kind. The method of the proof involves a new sufficient criterion for indecomposability of polynomials with fixed degree of the right component.