  In this paper, we will investigate the solvability of the equation $x_1^k +
x_2^k + \ldots + x_s^k = n$, $n\in \mathbb{Z}_{p^k}$, $x_1,...,x_s\in
\mathcal{A}$, $\mathcal{A}\subseteq \mathbb{Z}_{p^k}$. We will give a upper
bound of the number of solutions for $s=2$.
