Theorem 1
(1) The following equivalence relations hold:
$$a|b \Leftrightarrow(-a)| b \Leftrightarrow a \mid(-b)$$

Therefore, the theory of divisibility always discusses the divisibility relationship between positive integers.
(2) If $a|b, b| c$, then $a \mid c$.
(3) If $a|b, a| c$, then for any $x, y \in \mathbf{Z}$, we have $a \mid(b x+c y)$, i.e., $a$ divides any integer linear combination of $b$ and $c$.
(4) If $a \mid b, b \neq 0$, then $|a| \leqslant|b|$. From this, we know that if $a, b$ are both positive integers, $a \mid b$ and $b \mid a$, then $a=b$, which provides a common method for proving the equality of two positive integers.

These basic properties can all be easily derived from the definition of divisibility, they may seem trivial, but they are very useful.