Simple arguments on consecutive power residues Original Research Article

By some extremely simple arguments, we point out the following: (i) If n is the least positive kth power non-residue modulo a positive integer m, then the greatest number of consecutive kth power residues mod m is smaller than m/n. (ii) Let OK be the ring of algebraic integers in a quadratic field image with dset membership, variant{−1,−2,−3,−7,−11}. Then, for any irreducible πset membership, variantOK and positive integer k not relatively prime to image, there exists a kth power non-residue ωset membership, variantOK modulo π such that image.