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.