A Galois property of even degree Bernoulli polynomials

Activity: Talk or presentationInvited talk


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).
8 Dec 2019

Event (Conference)

Title2019 Canadian Mathematical Society Winter Meeting
Abbrev. Title2019CMS
Web address (URL)
Degree of recognitionInternational event