9. Show that although there are no primitive roots modulo $2^{k}$ where $k$ is an integer, $k \geqslant 3$, every odd integer is congruent to exactly one of the integers $(-1)^{\alpha} 5^{\beta}$, where $\alpha=0$ or 1 and $\beta$ is an integer satisfying $0 \leqslant \beta \leqslant 2^{k-2}-1$.