Simple arguments on consecutive power residues

By some extremely simple arguments, we point out the following: (i) If n is the least positive k-th power non-residue modulo a positive integer m, then the greatest number of consecutive k-th power residues mod m is smaller than m/n. (ii) Let O_K be the ring of algebraic integers in a quadratic field $K=Q(\sqrt d)$withdin-1,-2,-3,-7,-11\mathrm{.}Then,foranyirreducible$\pi\in O_K$ and positive integer k not relatively prime to $\pi \bar{\pi }-1$, there exists a k-th power non-residue $\omega \in O_K$ modulo $\pi$ such that $\mathrm{\mid }\omega \mathrm{\mid }<\sqrt{\mathrm{\mid }\pi \mathrm{\mid }}+0.65$.