RU-ALLRUSSIAN 1970 Problem 14

S is the set of all positive integers with n decimal digits or less and with an even digit sum. T is the set of all positive integers with n decimal digits or less and an odd digit sum. Show that the sum of the kth powers of the members of S equals the sum for T if $1 \leq \mathrm{k} < \mathrm{n}$ .