Perfect Powers that are Sums of Consecutive like Powers

Activity: Talk or presentationInvited talkResearch

Description

In this talk, we present some of the techniques used to tackle subfamilies of the Diophantine equation $(x+1)^k + (x+2)^k + ... + (x+d)^k = y^n$. We compare two very different approaches which naturally arise when considering the parity of k. We present all integer solutions, (x,y,n) to the equation in the case $k=3, 1<d<51$ (joint work with Mike Bennett - UBC and Samir Siksek - Warwick), and a (natural) density result when k is a positive even integer, showing that for almost all d at least 2, the equation has no integer solutions, (x,y,n) with n at least 2(joint work with Samir Siksek - Warwick).
Period10 May 2017
Held atMax Planck Institute for Mathematics, Germany
Degree of RecognitionInternational