Period four and real quadratic fields of class number one
R. A. Mollin, H. C. Williams · Proceedings of the Japan Academy Series A Mathematical Sciences · 1989
The purpose of this note is to provide criteria, in terms of prime- producing quadratic polynomials, for a real quadratic field Q(/-) to have class number h(d)=l, when the continued fraction expansion of w is 4 (where =(1+/d)/2 if d--1 (mod 4) and =/d if d--2,3 (mod 4)).This continues the work of the first author in [4]-[11] and that of both authors in [12]-[18] in the quest or a general "Rabinowitsch-like" result for real quadratic field.Rabinowitch [19]-[20], proved that if p--3 (mod 4) is prime then h (--p) 1 i and only i xx / (p + 1)/4 is prime or all integers x with 1_ x_ (p--7) 4, p 7. In [4] the first author found such (1) b (fb c) + l is prime.