Are there coprime integer solutions to: $$\frac{x^n \pm y^n}{x \pm y}=z^m$$ with $n>5 , m>1$ and excluding $x=y=z=1$?z=0$? I suppose the abc conjecture implies finitely many solutions. 3 not x=y=z=1 Are there coprime integer solutions to: $$\frac{x^n \pm y^n}{x \pm y}=z^m$$ with$n>5 , m>1$?and excluding$x=y=z=1\$?