7. Let $m=2^{\alpha_{0}} p_{1}^{\alpha_{1}} \cdots p_{r}^{\alpha_{r}}, p_{j}$ be different odd primes, $\alpha_{j} \geqslant 1(1 \leqslant j \leqslant r)$, $\alpha_{0} \geqslant 0$. Prove: The number of solutions to the congruence equation $x^{2} \equiv 1(\bmod m)$ is
$$T=\left\{\begin{array}{ll} 2^{r}, & \alpha_{0}=0,1 \\ 2^{r+1}, & \alpha_{0}=2 \\ 2^{r+2}, & \alpha_{0} \geqslant 3 \end{array}\right.$$