## Integral bases for quadratic fields

Hi,

I was wondering if you could just clarify how you determine $O_K.$ In most quadratic examples it seems to be $Z(\sqrt{n})$, however in some it is $Z((1+\sqrt{n}/2))$. I think it must have something to do with the integral basis?

Thanks for your help.

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I refer you to lecture 11 in the online notes. You should review this material thoroughly.