If $(a,b,c)$ is a primitive Pythagorean triplet, explain why only one of $a$,$b$ and $c$ can be even-and that $c$ cannot be the one that is even.
What I Know:
A Primitive Pythagorean Triple is a Pythagorean triple $a$,$b$,$c$ with the constraint that $\gcd(a,b)=1$, which implies $\gcd(a,c)=1$ and $\gcd(b,c)=1$. Example: $a=3$,$b=4$,$c=5$ where, $9+16=25$
At least one leg of a primitive Pythagorean triple is odd since if $a$,$b$ are both even then $\gcd(a,b)>1$