Proof for primitive pythagorean triples I was wondering if there was a proof that any integer pythagorean triple can be represented as a positive integer multiple of a primitive pythagorean triple. This seems quite related to the fundamental theorem of arithmetic, so I was wondering if the proof would be similar.
Hint: If you have a pythgorean triple $(a,b,c)$ divide each number by $gcd(a,b,c)$ and remember if $p$ divides any two of the new numbers it must divide the third.
A multiple of a Pythagorean triple is also a Pythagorean triple, 
$$a^2+b^2=c^2\iff(na)^2+(nb)^2=(nc)^2.$$

There is nothing more to say.