Ramification in relative quadratic extensions and fundamental units of real quadratic fields

Let F=Q(d) be a real quadratic field and ε=x+yd the fundamental unit of F satisfying NF/Q(ε)=1. Some connections between the ramification properties for dyadic prime ideals in quadratic extension F(ε)/F and congruence properties of x, y were established. As a corollary, some congruence properties about x, y were given when d=p1…pr or 2p1…pr with p1≡…≡pr≡1 mod 4 being distinct prime numbers.