Topology of Numbers · Problem 6.2.10

Representations by Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · 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 \pmod{8}