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.
In part 1, we find 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).