Integer Divisor Results/One Divides all Integers

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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.

$\blacksquare$


Sources