Sums of consecutive perfect powers is seldom a perfect power

Activity: Talk or presentationOral presentationResearch


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).
Period7 Jun 2017
Event titleJournées Algophantiennes Bordelaises 2017
Event typeConference
LocationBordeaux, FranceShow on map
Degree of RecognitionInternational