Prove that ring $\mathbb Z[\sqrt{-5}]=\{a+b\sqrt{-5}:a,b\in\mathbb Z[\sqrt{-5}]\}$ is not factorial.
I know that two representations of an irreducible element should be found that are not associated. Could you please help?
2026-03-30 05:28:55.1774848535
Prove that ring $\mathbb Z[\sqrt{-5}]$ is not factorial.
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Hint: Consider $ 3^2 = 9 = (2+\sqrt{-5})(2-\sqrt{-5}) $