On the Diophantine equation $(x+1{)}^k+(x+2{)}^k+...+(lx{)}^k=y^n$

Gökhan Soydan

Let $k,l\ge 2$ be fixed integers. In this paper, firstly, we prove that all solutions of the equation $(x+1{)}^k+(x+2{)}^k+...+(lx{)}^k=y^n$ in integers $x,y,n$ with $x,y\geq1, n…