\begin{definition}[Definition:Primitive Triple]
Let $x, y, z \in \Z_{>0}$ be (strictly) positive integers.
Let $A, B, C \in \Z_{>0}$ be (strictly) positive integers that satisfy:
:$A^x + B^y = C^z$
Let $\left({A, B, C}\right)$ be pairwise coprime.
Then $\left({A, B, C}\right)$ is a '''primitive triple'''.
\end{definition}