Pythagorean Triangle/Examples/1380-19,019-19,069

Example of Primitive Pythagorean Triangle
The triangle whose sides are of length $1380$, $19 \, 019$ and $19 \, 069$ is a primitive Pythagorean triangle.


 * 1380-19,019-19,069.png

It has generator $\left({138, 5}\right)$.

Proof
We have:

It follows by Pythagoras's Theorem that $1380$, $19 \, 019$ and $19 \, 069$ form a Pythagorean triple.

We have that:

It is seen that $1380$ and $19 \, 019$ share no prime factors.

That is, $1380$ and $19 \, 019$ are coprime.

Hence, by definition, $1380$, $19 \, 019$ and $19 \, 069$ form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.