Unique pythogorean primitive for each pythagorean triplet? I am not sure if there corresponds a unique pythogorean primitive for each pythogorean triplet that is not a primitive. Whatever might be the case, a proof would be great (since I failed to prove or disprove either of the cases). For instance: $(9,12,15)$ is a pythagorean triplet. Its primitive pythogorean triplet is $(3,4,5)$.

Well, just divide all three numbers by their greatest common divisor, and you'll get another triplet. It is easy to check that (1) it is still pythagorean and (2) it is primitive, that is, has GCD=1.