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how i can find a integral basis $\mathbb{Z}_K$, if $K=\mathbb{Q}(\sqrt{2},\sqrt{3})$?

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Dear P.M.O., Have you tried imitating the usual computation for the integral basis of $\mathbb Q(\sqrt{D})$, namely: write an integer of $K$ in the form $x + y \sqrt{3},$ where $x,y \in \mathbb Q(\sqrt{2})$, and then determine conditions on $x$ and $y$. Regards, – Matt E Oct 15 '12 at 3:00

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