(a) Find the possible values of the integer $a$ such that $a \mid 0$.
(b) Find the possible values of the integer $a$ such that $a \mid 2$.
(a)
$a \mid b$ means there exists an integer $k$ such that $b = ak$.
So $a \mid 0$ means there exists an integer $k$ such that $0 = ak$.
In this case $a$ can be any integer, because $k=0$ satisfies $0=ak$.
(b)
$a \mid 2$ means there exists an integer $k$ such that $2 = ak$.
In this case, there are only four options for $a$
- $a=1$, where $k=2$
- $a=-1$, where $k=-2$
- $a=2$, where $k=1$
- $a=-2$, where $k=-1$