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