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let $m$ be an integer with $m\equiv 1 \pmod4$ and $m<-3$.

$U\left(\mathbb{Z}+\mathbb{Z}(\frac{1+\sqrt{m}}{2})\right)=\{\pm1\}$ How can I prove that?

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    Hint: If you already have proved some of the properties of **norm**, this should not be difficult.2012-04-03
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    To expand on Andre's comment. If $X = (1+\sqrt{m})/2$, then define $N(a+bX)=(a+bX)(a-bX)$. Notice that $N(AB)=N(A)N(B)$ (the norm is multiplicative). Also, $N(1)=1$. If $AB=1$, what can you say about $N(A),N(B)$?2012-04-03
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    @BillCook $(a+bX)(a-bX)$ is not the norm. $(a+bX)(a+b\bar X)$ is the norm.2012-04-03
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    @ThomasAndrews Oops! Thanks for catching that!2012-04-03

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