I am not sure how the following statement makes sense. I understand that any common prime divisor of $x$ and $x^{2}+z^{4}$ would divide $z^{4} $because if $p|x $ => $p|x^{2}$ and $ p|(x^{2}+z^{4}-x^{2}) $ => $p|z^{4}$. But I don't understand why this means there are no common prime divisors?
Any help would be much appreciated!
