Perfect Powers that are Sums of Consecutive like Powers

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).