Definition:Primitive Triple

Definition
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 $\tuple {A, B, C}$ be pairwise coprime.

Then $\tuple {A, B, C}$ is a primitive triple.

Also see

 * Definition:Pythagorean Triple
 * Definition:Primitive Pythagorean Triple