Hatcher-Topology-of-Numbers · Problem 6.2.13

Representations by Quadratic Forms

Mathematics — Algebraic Topology · quadratic-forms-powers-of-two

Problem

Show that if the form

x^2 + ny^2

represents

2^k

with

n

odd and

k > 0

then

n \equiv 7 \bmod 8

except when

(n,k) = (1,1)

and

(3,2)