Definition:Generator for Primitive Pythagorean Triple
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Definition
The generator for a primitive Pythagorean triple is an ordered pair:
- $G = \left({m, n}\right)$
where $m, n \in \Z$ such that:
- $m, n \in \Z_{>0}$ are (strictly) positive integers
- $m \perp n$, that is, $m$ and $n$ are coprime
- $m$ and $n$ are of opposite parity
- $m > n$.
The primitive Pythagorean triple which has been generated by $G$ is:
- $\left({2 m n, m^2 - n^2, m^2 + n^2}\right)$
Also see
Sources
- Weisstein, Eric W. "Pythagorean Triple." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PythagoreanTriple.html