The question is:- does 12 divide the product of the pythagorean triangle?

My answer is that yes,

since $\displaystyle a=2mn$

$\displaystyle 12=2mn$

$\displaystyle 6=mn$

$\displaystyle since (3,2)=1$

I don't know if this is correct, but how can I prove this.

2)

if $\displaystyle (a,b)=1$ and $\displaystyle a b=c^n$, show that a and b are nth powers