Integer Combination of Coprime Integers

Theorem
Two integers are coprime iff there exists an integer combination of them equal to $1$:
 * $\forall a, b \in \Z: a \perp b \iff \exists m, n \in \Z: m a + n b = 1$

Proof
Note that in the integer combination $m a + n b = 1$, the integers $m$ and $n$ are also coprime.

Also known as
This result is sometimes known as Bézout's Identity, as is the more general Bézout's Lemma.