Question

Resolve this equation into fundamental units.

Answer 1

Answer:

Find the fundamental solution of Pell's equation x2−13y2=1. For (a), let ϵ=r+s√13,r,s∈Q,r,s>0 be the fundamental unit of OQ(√13). x2−2rx+r2−13s2=(x−r−s√13)(x−r+s√13). Hence, [Q(ϵ):Q]=2.