Definition 6.2.14
Given two integers ,
, we say that divides
(or that is a divisor of ) and write if and there exists an integer such that
. The number is called a proper divisor of if is not or .

For example, is a proper divisor of and has no proper divisor.

Definition 6.2.15
A prime integer or, more briefly a prime is an integer which has no proper divisor.

For example, the numbers and are primes, and the number is not a prime as
. More on primes will be seen further (v.i. section 5.

Proposition 6.2.16
The relation is a partial ordering in
.

Proof.
The proof that is an ordering goes exactly as in Chapter 4, Example 4.3.
As
, we see that this ordering is partial.

Proposition 6.2.17
Let , and be three integers. If and then for any two integers and , we have:
.