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.
This is trivial from the definition.
We say that $(a,b,c)$ is a primitive Pythagorean triple if it is a Pythagorean Triple and there do not exist $(a',b',c')$, also a Pythagorean Triple, such that $\exists k$ such that $a=ka'$ etc.
Let $(a,b,c)$ be a Pythagorean triple. If it's primative, $k=1$ and we are done. If it's not, the. $\exists k$ such that...