(a) Find the smallest residue $x$ which equals $28 ! 13^{28}(\bmod 31)$.

[You may use any standard theorems provided you state them correctly.]

(b) Find all integers $x$ which satisfy the system of congruences

$$\begin{aligned} x & \equiv 1(\bmod 2) \\ 2 x & \equiv 1(\bmod 3) \\ 2 x & \equiv 4(\bmod 10) \\ x & \equiv 10(\bmod 67) \end{aligned}$$