Gauss’s class number one problem for real quadratic fields

Establish the existence of infinitely many real quadratic number fields Q(√d) whose class number equals 1.

Background

The paper contrasts the well-understood case of imaginary quadratic fields—where only nine fields have class number one—with the real quadratic case, where Gauss conjectured infinitely many examples but no proof is known. This classical problem underscores the difficulty of understanding class numbers of real quadratic fields and motivates broader investigations into their divisibility properties.