im4110 - M. A. Korolev, On the average number of power residues modulo a composite number, Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 6, 127–156

We study the behaviour of the quantities an(q) and bn(q), that is, the number of nnth power residues in the reduced and complete residue systems modulo a composite number q, respectively, where n≥2 is an arbitrary fixed number. In particular, we prove asymptotic formulae for the sum functions An(x) and Bn(x) of these quantities.