Theorem 5 For modulo $2^{l}(l \geqslant 3)$, the following $2^{l-1}$ numbers form a complete set of reduced residues: $\square$
$$(-1)^{j_{0}} 5^{j_{1}}, \quad 0 \leqslant j_{0}<2,0 \leqslant j_{1}<2^{l-2}$$

In fact, for any $m=2^{l}, 2 \nmid g_{0}, l \geqslant 3\left(l=3\right.$ when, $\left.g_{0} \neq 8 k-1\right)$, if $\delta_{m}\left(g_{0}\right)=2^{l-2}$, then the following $2^{l-1}$ numbers form a complete set of reduced residues modulo $2^{l}$:
$$(-1)^{j_{0}} g_{0}^{j_{1}}, \quad 0 \leqslant j_{0}<2,0 \leqslant j_{1}<2^{l-2}$$