Bivariate Factorizations via Galois Theory, with Application to Exceptional Polynomials

We present a method for factoring polynomials of the shapef(X) − f(Y), wherefis a univariate polynomial over a fieldk. We then apply this method in the case whenfis a member of the infinite family of exceptional polynomials we discovered jointly with H. Lenstra in 1995; factoringf(X) − f(Y) in this case was posed as a problem by S. Cohen shortly after the discovery of these polynomials.