On the number of points on one class of curves in a ring of residues

The number of points on a curve $x^m\equiv y^k\pmod n$ is calculated. The concept of $m/k$-power residue (rational power residue) is introduced. Let n be a natural number. The number of rational power residues modulo n is calculated. As a corollary the classic result on the number of quadratic residues is obtained.