Topology of Numbers · Problem 7.2.3

The Class Group for Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · numbers-represented-sum-of-squares

Problem

Show that the numbers represented by

x^2 + 4y^2

are the numbers

2^m p_1 \cdots p_k

where

m

0

2

, or

3

and each

p_i

is a prime congruent to

1 \bmod 4