A Galois property of even degree Bernoulli polynomials

Activity: Talk or presentationInvited talkResearch


Let k be an even integer such that k is at least 2. We give a (natural) density result to show that for almost all d at least 2, the equation $(x+1)^k+(x+2)^k+...+(x+d)^k=y^n$ with n at least 2, has no integer solutions (x,y,n). The proof relies upon some Galois theory and group theory, whereby we deduce some interesting properties of the Bernoulli polynomials. This is joint work with Samir Siksek (University of Warwick).
Period18 Oct 2019
Held atUtrecht University, Netherlands
Degree of RecognitionInternational