(a) Use Euclid's algorithm to find positive integers $m, n$ such that $79 m-100 n=1$.

(b) Determine all integer solutions of the congruence

$$237 x \equiv 21(\bmod 300)$$

(c) Find the set of all integers $x$ satisfying the simultaneous congruences

$$\begin{aligned} &x \equiv 8(\bmod 79) \\ &x \equiv 11(\bmod 100) \end{aligned}$$