Real quadratic field

Fundamental unit of a real quadratic field

Let be a Real quadratic field and let be a reduced element1 of discriminant with simple continued fraction

with period . Then the fundamental unit of is #m/thm/num/alg

which is to say by Dirichlet's unit theorem

Proof

#missing/proof

Monogenic case

If then one simple has

#state/tidy | #lang/en | #SemBr

Footnotes

  1. i.e. such that the simple continued fraction is purely periodic, or equivalently, . ↩