Hatcher-Topology-of-Numbers · Problem 7.2.3

The Class Group for Quadratic Forms

Mathematics — Algebraic Topology · numbers-represented-by-x-squared-plus-4y-squared

Problem

Show that the numbers represented by

x^2 + 4y^2

are the numbers

2^m p_1 \cdots p_k

where

m

is 0, 2, or 3 and each

p_i

is a prime congruent to 1 mod 4.