Intro:

Above is a unit circle, .

- First (trivial) solution is .
- For second (non-trivial) solution, QR has a rational slope and we plug this .

This gives (non-trivial) solution of .

Simple enough. Now the exercise.

I'm having problem with a minus in part:The parameter in the pair runs through all rational numbers if and run through all pairs of integers.

Deduce that if is any Pythagorean triple then

for some integers and .

How would I use the previous exercise to prove that Euclid's generatesUse previous exercise to prove Euclid's formula for Pythagorean triples.alltriples?