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?
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?