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Find all units in $\mathbb{Z}[\sqrt n] = \{a + b\sqrt n \mid a, b \in \mathbb Z \}$ and $n \in\mathbb N$, $n\ge 2$.

First let $c +d\sqrt n$ be a unit so $$(a +b\sqrt n)(c +d\sqrt n) = 1,$$ $$ac + bdn +(bc + ad)\sqrt n = 1.$$

What next?

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    next you need $ac + bdn = 1$ and $bc + ad = 0$.2012-03-26
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    Duplicate of [infinitely many units in $\mathbb{Z}\[\sqrt{d}\]$ for any $d>1$.](http://math.stackexchange.com/questions/118315/infinitely-many-units-in-mathbbz-sqrtd-for-any-d1)2012-03-26
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    @lhf I don't think this is a duplicate. This question is asking for finding all the units (which is a difficult task), not only to show that there are infinitely many.2013-02-14

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