Pythagorean Triangle/Examples/3059-8580-9109

Example of Primitive Pythagorean Triangle
The triangle whose sides are of length $3059$, $8580$ and $9109$ is a primitive Pythagorean triangle.


 * 3059-8580-9109.png

It has generator $\left({78, 55}\right)$.

Proof
We have:

It follows by Pythagoras's Theorem that $3059$, $8580$ and $9109$ form a Pythagorean triple.

We have that:

It is seen that $3059$ and $8580$ share no prime factors.

That is, $3059$ and $8580$ are coprime.

Hence, by definition, $3059$, $8580$ and $9109$ form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.