Hatcher-Topology-of-Numbers · Problem 7

The Class Group for Quadratic Forms

Mathematics — Algebraic Topology · class-group-quadratic-forms

Problem

Show that if a form

Q

of discriminant

\Delta

represents a prime

p

coprime to

\Delta

then

p^k

is represented by

Q

if and only if the order of

Q

in the class group divides

k - 1

k + 1