Theorem 2 Under the notation of Theorem 1, let
$$\begin{aligned} \widetilde{g}_{l}= & M_{0} M_{0}^{-1}(-1)^{h_{h}^{(-1)}} 5^{h_{l}^{(0)}}+M_{1} M_{1}^{-1} g_{1}^{h_{1}^{(1)}} \\ & +\cdots+M_{r} M_{r}^{-1} g_{r}^{h_{r}^{(r)}}, \quad-1 \leqslant l \leqslant r, \end{aligned}$$

where we take
$$h_{l}^{(D)}=1, \quad h_{l}^{(j)}=0, \quad j \neq l,-1 \leqslant j \leqslant r$$

Then
$$\begin{array}{c} \tilde{g}_{-1} \equiv-1\left(\bmod 2^{\alpha_{0}}\right), \quad \widetilde{g}_{0} \equiv 5\left(\bmod 2^{a_{0}}\right) \\ \widetilde{g}_{j} \equiv g_{j}\left(\bmod p_{j}^{\alpha_{j}}\right), \quad 1 \leqslant j \leqslant r, \end{array}$$

and the following $\varphi(m)$ numbers form a complete set of reduced residues modulo $m$:
$$\left\{\begin{array}{l} x=\widetilde{g}_{-1}^{r_{-1}^{(1)}} \widetilde{\mathrm{g}}_{0}^{(0)} \widetilde{\mathrm{g}}_{1}^{(1)} \cdots \widetilde{\mathrm{g}}_{r}^{(r)} \\ 0 \leqslant \gamma^{(j)}<c_{j},-1 \leqslant j<r \end{array}\right.$$