Theorem 11 Let $m=m_{1} m_{2}, x_{i}^{(1)}\left(1 \leqslant i \leqslant m_{1}\right)$ be a complete residue system modulo $m_{1}$, and $x_{j}^{(2)}\left(1 \leqslant j \leqslant m_{2}\right)$ be a complete residue system modulo $m_{2}$. Then $x_{i j}=x_{i}^{(1)}+m_{1} x_{j}^{(2)}$ is a complete residue system modulo $m$. That is, when $x^{(1)}, x^{(2)}$ run through the complete residue systems modulo $m_{1}$, modulo $m_{2}$ respectively, $x=x^{(1)}+m_{1} x^{(2)}$ runs through the complete residue system modulo $m=m_{1} m_{2}$.