On the cubic character of quadratic units

An elementary proof is given of the theorem: If D = ?3q or ?27q is the discriminant of a cubic field, where q ≡ 1 (mod 4) is a prime, and if p or 4p is represented by c² + ∥ D ∥ d², then the fundamental unit in the field $\text{Q(q}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ is a cubic residue of the prime p. In special cases necessary and sufficient conditions are derived.