![To show $\mathbb{Z}[\sqrt{-5}]$ is not a Euclidean domain, why suffices to show only the field norm $N(a+b\sqrt{-5})=a^2+5b^2$ doesn't work? - Mathematics Stack Exchange To show $\mathbb{Z}[\sqrt{-5}]$ is not a Euclidean domain, why suffices to show only the field norm $N(a+b\sqrt{-5})=a^2+5b^2$ doesn't work? - Mathematics Stack Exchange](https://i.stack.imgur.com/KpOko.png)
To show $\mathbb{Z}[\sqrt{-5}]$ is not a Euclidean domain, why suffices to show only the field norm $N(a+b\sqrt{-5})=a^2+5b^2$ doesn't work? - Mathematics Stack Exchange
![Euclidean Rings - Fletcher - 1971 - Journal of the London Mathematical Society - Wiley Online Library Euclidean Rings - Fletcher - 1971 - Journal of the London Mathematical Society - Wiley Online Library](https://londmathsoc.onlinelibrary.wiley.com/cms/asset/d88adc52-c5b2-4ac5-b387-6de880b96197/jlms_s2-4.1.79.fp.png)
Euclidean Rings - Fletcher - 1971 - Journal of the London Mathematical Society - Wiley Online Library
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