0. For each of the following statements, determine if it is true or false. If true, then provide a proof; if false, explain why (for instance, by giving an example in which the statement does not hold).
(a) (17 \cdot 13) = 5 \mod 18.
(b) In $\mathbb{Z}/24\mathbb{Z}$ the only squares (= classes of the form $\bar{a}\bar{a}$) are $\bar{0}$, $\bar{1}$, $\bar{4}$, $\bar{9}$, $\bar{16}$.
(c) Suppose $a, b, n \in \mathbb{Z}$ and $a \neq \pm b$. If $\bar{a}\cdot\bar{a} = \bar{b}\cdot\bar{b}$ in $\mathbb{Z}/n\mathbb{Z}$, then either $gcd(a + b, n) \neq 1$ or $gcd(a - b, n) \neq 1$.