# Integer Divisor Results/One Divides all Integers

(Redirected from One Divides all Integers)

## Theorem

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

Then:

 $\displaystyle 1$ $\divides$ $\displaystyle n$ $\displaystyle -1$ $\divides$ $\displaystyle n$

where $\divides$ denotes divisibility.

## Proof

From Integers form Integral Domain, the concept divisibility is fully applicable to the integers.

Therefore this result follows directly from Unity Divides All Elements.

$\blacksquare$