Integer Combination of Coprime Integers/Sufficient Condition

Theorem
Let $a, b \in \Z$ be integers, not both zero.

Let $a$ and $b$ be coprime to each other.

Then there exists an integer combination of them equal to $1$:
 * $\forall a, b \in \Z: a \perp b \implies \exists m, n \in \Z: m a + n b = 1$