  In this article, we present streamlined proofs of results of Ankeny, Artin,
and Chowla concerning the fundamental unit of the real quadratic field
$\mathbb{Q}(\sqrt{p})$ for primes $p\equiv 1 \bmod{4}$ while providing a
generalization of their conjecture. Using our generalization, we relate Fermat
quotients of quadratic non-residues $\bmod{p}$ to sums of harmonic numbers.
