The Diophantine Equation $(x+1{)}^k+(x+2{)}^k+\cdots +(\ell x{)}^k=y^n$ Revisited

Daniele Bartoli, Gökhan Soydan

Let $k,\ell \ge 2$ be fixed integers and $C$ be an effectively computable constant depending only on $k$ and $\ell$. In this paper, we prove that all solutions of the equation $(x+1…