Let $a,b$ be elements of an integral domain $R$. Let $N$ denote the norm. Let $x,y$ be other elements of the same integral domain $R$. I know that $\gcd(x,y)=\gcd(x,x-y)$ iff $N(x)>N(y)>0$. However if $N(a)=N(b)$ how do I compute $\gcd(a,b)$ ?
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