Ankeny–Artin–Chowla Conjecture and Continued Fraction Expansion Original Research Article

For any prime p congruent to 1 modulo 4, let (t+u image)/2 be the fundamental unit of Q(image). Then Ankeny, Artin, and Chowla conjectured that u is not divisible by p. In this paper, we investigate a certain relation between the conjecture and the continued fraction expansion of (1+image)/2. Consequently, we prove that the conjecture is true if p is not “small” in some sense.