Usefulness of $\mathbb Z [\sqrt p] $

Question

So I started examining FLT for $n=3$ with my professor, using properties of the Eisenstein integers. The professor made a diversion and spent a whole lecture proving that there are exactly two types of ideals in $\mathbb Z[ \sqrt{ -5}]$, but we didn't make a connection to the FLT, and that left me wondering: Where are rings of the form $\mathbb Z[\sqrt d]$ useful? Do they help us solve some other kind of Diophantine equation?