Integers are Coprime iff Powers are Coprime

Theorem
Let $a, b \in \Z$ be integers.

Then:
 * $a \perp b \iff \forall n \in \N: a^n \perp b^n$

That is, two integers are coprime all their positive integer powers are coprime.

Proof
The forward implication is shown in Powers of Coprime Numbers are Coprime.

The reverse implication is shown by substituting $n = 1$.