PythagoreanTriples

A Pythagorean Triples is set of positive integers $(a,b,c)$ such that $a^2+b^2 = c^2$ . For example $\begin{aligned} & 3^2 +4^2 =5^2 \\& 5^2+12^2 = 13^2 \\& 7^2 +24^2 = 25^2 \end{aligned}$

If $a$ and $b$ and are of distinct parity. Is it true that $a$ , $b$ and $c$ are always co-prime integers?