Topology of Numbers · Problem 7.2.4

The Class Group for Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · class-group-product-represents-product

Problem

Show that if two forms

Q_1

and

Q_2

in the class group

CG(\Delta)

represent coprime numbers

n_1

and

n_2

then their product

Q_1 Q_2

represents

n_1 n_2

. Give an example where this fails without the coprimeness assumption, even if

n_1

and

n_2

are coprime to

\Delta