For each of the following congruence equations, either find a solution \(x \in \mathbb{Z}\) or show that no solution exists:

(a) \(99 x \equiv 18 \bmod 30\).

(b) \(91 x \equiv 84 \bmod 143\).

(c) \(x^{2} \equiv 2 \bmod 5\).

(d) \(x^{2}+x+1 \equiv 0 \bmod 5\).

(e) \(x^{2}+x+1 \equiv 0 \bmod 7\).