Paper 1, Section I, H

Number Theory
Part II, 2020

What does it mean to say that a positive definite binary quadratic form is reduced?

Find all reduced binary quadratic forms of discriminant 20-20.

Prove that if a prime p5p \neq 5 is represented by x2+5y2x^{2}+5 y^{2}, then p1,3,7p \equiv 1,3,7 or 9mod209 \bmod 20.