Some results on a special type of real quadratic fields

Abstract

determining fundamental units and Yokoi’s d-invariants nd and md in the relation to continued fraction expansion of wd where ` (d) is a period length of wd for the such type of real quadratic number fields Q( √ d). The present paper improve the theory of fundamental unit which generates the unit group of real quadratic fields and also determine the special form of continued fraction expansion of integral basis element in real quadratic fields.