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arXiv · 2304.02789

Fermat quotients and the Ankeny-Artin-Chowla conjecture

Nic Fellini·M. Ram Murty
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Abstract

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.

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Nic Fellini, M. Ram Murty. 2023-04-05. Fermat quotients and the Ankeny-Artin-Chowla conjecture. https://arxiv.org/abs/2304.02789

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