Perfect Powers that are Sums of Consecutive like Powers

Activity: Talk or presentationInvited talkResearch

Description

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).
Period12 Jun 2017
Held atThe University of Warwick, United Kingdom
Degree of RecognitionNational