Bivariate factorizations via Galois theory, with application to exceptional polynomials (Q1279932)

A method for factoring polynomials of the shape \(f(X)-f(Y)\) where \(f\) is a univariate polynomial over a field is presented. The problem is connected with Galois theory. The method is applied to the family of exceptional polynomials \(f\) discovered by \textit{H. W. Lenstra} jun. and \textit{M. Zieve} in 1995 [Finite Fields and Applications, Glasgow 1995, Lond. Math. Soc. Lect. Note Ser. 233, 209-218 (1996; Zbl 0871.11087)]. The exceptional polynomials are connected with permutation polynomials.