• On Continued Fractions of Period Five and Real Quadratic Fields of Class Number Even

Abstract

In this paper, by using the methods of T. Azuhata in and K. Tomita in , in the case of for where that is not investigated in the papers of R.A. Mollin in and K. Tomita in , the general forms of the continued fraction expansions of and explicitly in the fundamental unit of are determined.Furthermore, the necessary and sufficent conditions are given for Yokoi’s invariant value of which is defined in terms of coefficent of fundamental unit. Also, it is denoted that the class number is always even.Finally, the real quadratic fields with and are given in the Table 3.1.