Abstract
Let [Formula: see text] be a positive square-free integer and [Formula: see text] be the fundamental unit of the real quadratic field [Formula: see text]. The Ankeny–Artin–Chowla (AAC) conjecture asserts that [Formula: see text] (mod [Formula: see text]) for primes [Formula: see text] (mod 4), which still remains unsolved. In this paper, sufficient conditions for [Formula: see text] have been given in terms of Yokoi’s invariants [Formula: see text] and [Formula: see text], and it has been shown that the AAC conjecture is true in some special cases.
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