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Tang, On the addition of squares of units and nonunits modulo $n$, J. Number Theory., 155 (2015) 1--12] gave a formula for the number of solutions of the equation $x_1^2+x_2^2=c$ with $x_{1},x_{2}\\in \\mathbb{Z}_n^{\\ast}$. In this paper, we generalize this result. 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