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