et $R = \ZZ[\sqrt{-n}]$ where $n$ is a squarefree integer $> 3$. Prove that $2$, $\sqrt{-n}$, and $1 + \sqrt{-n}$ are all irreducible in $R$. \item Prove that $R$ is not a UFD. [Hint: Show that either - QAmmunity.org

et $R = \ZZ[\sqrt{-n}]$ where $n$ is a squarefree integer $> 3$. Prove that $2$, $\sqrt{-n}$, and $1 + \sqrt{-n}$ are all irreducible in $R$. \item Prove that $R$ is not a UFD. [Hint: Show that either

asked Aug 5, 2020 116k views

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