기본 정의

 

정의1

Let $a, b \in \mathbb{Z}$ and $a \neq 0$

$a$ divides $b$ if $b = ak$  for some $k \in \mathbb{Z}$, we write $a|b$

($a \!\!\! \not | b$ if $a$ doesn't divide $b$)

 

 

 

정의2

Let $a, b \in \mathbb{Z} \setminus \left\{\mathbf{0} \right\}$ 

The greatest common divisor of $a$ and $b$ is the positive integer $d$ s.t.

$\mathrm{i})$ $d|a$ and $d|b$

$\mathrm{ii})$ $d'|a$ and $d'|b$ $\Rightarrow$ $d' \leq d$

we write $d = gcd(a,b)$

 

 

 

정의3

We say that $a$ and $b$ are relatively prime (mutually prime / coprime) if $gcd(a, b)=1$