Fundamental Discriminant - Factorization

Factorization

Fundamental discriminants may also be characterized by their factorization into positive and negative prime powers. Define the set

where the prime numbers ≡ 1 (mod 4) are positive and those ≡ 3 (mod 4) are negative. Then, a number D₀ ≠ 1 is a fundamental discriminant if, and only if, it is the product of pairwise relatively prime members of S.