Topology of Numbers · Problem 7.6.2

Quadratic Fields — Allen Hatcher

Mathematics — Number Theory · rational-equivalence-rational-forms

Problem

Show that for each nonzero reduced discriminant

\delta

there is a unique form

x^2 + by^2

of reduced discriminant

\delta

with

b

a squarefree integer, and show that every form of reduced discriminant

\delta

is rationally equivalent to a form

a(x^2 + by^2)