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Let$C$_{$k$}$(p)$denote the group of the$k$-th powers (mod$p$)$p$a prime with ($k, p$−1)>1. A new elementary result for the least$k$-th power non-residue is given and the result is applied to finding a new elementary bound for the maximum number of consecutuve integers in any coset of$C$_{$k$}$(p)$.

Let$Z$be the zero set of a holomorphic section$f$of a Hermitian vector bundle. It is proved that the current of integration over the irreducible components of$Z$of top degree, counted with multiplicities, is a product of a residue factor$R$^{$f$}and a “Jacobian factor”. There is also a relation to the Monge-Ampère expressions ($dd$^{$c$}log|$f$|)^{$k$}, which we define for all positive powers$k$.