Power values of power sums: a survey (Q6611637)

The paper under review is a survey. More precisely, they give a comprehensive overview of results towards the following families of exponential Diophantine equations: \N\[ \Nx^k + (x+r)^k + \dots + (x+(d-1)r)^k=y^n \N\]\Nwhere \(d,k,r,n,x,y \in \mathbb{Z}\) with parameters \((k,d,r,n)\) and \N\[\Ns(1^k + 2^k + \dots + x^k) + r(x) = y^n \N\]\Nwhere \((k,n,x,y,s) \in \mathbb{Z}, r(x) \in \mathbb{Z}[x] \) with parameters \((k,n,s,r(x)).\) Furthermore, they give a full and efficient road map for the solutions of these Diophantine equations.\N\NFor the entire collection see [Zbl 1542.11001].