Integer Divisor Results/Integer Divides Itself

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Theorem

Let $n \in \Z$ be an integer.

Then:

$n \divides n$

That is, $n$ divides itself.


Proof 1

From Integer Multiplication Identity is One:

$\forall n \in \Z: 1 \cdot n = n = n \cdot 1$

thus demonstrating that $n$ is a divisor of itself.

$\blacksquare$


Proof 2

As the set of integers form an integral domain, the concept divides is fully applicable to the integers.

Therefore this result follows directly from Element of Integral Domain is Divisor of Itself.

$\blacksquare$


Sources