Hatcher-Topology-of-Numbers · Problem 6.2.10

Representations by Quadratic Forms

Mathematics — Algebraic Topology · quadratic-forms-odd-coefficients

Problem

Consider forms

Q = ax^2+bxy+cy^2

of discriminant

\Delta

. Show that the following three conditions are equivalent: ((1)) The coefficients

a

b

, and

c

Q

are all odd. ((2))

Q

represents only odd numbers. ((3))

\Delta \equiv 5 \bmod 8