NOTES ON ESPECIAL CONTINUED FRACTION EXPANSIONS AND REAL QUADRATIC NUMBER FIELDS

Abstract

The primary purpose of this paper is to classify real quadratic fields Q(?d) whichinclude the form of specific continued fraction expansion of integral basis element ???? forarbitrary period length ? = ?(??) where d ? 2,3(mod4) is a square free positive integers.Furthermore, the present paper deals with determining new certain parametricformulas of fundamental unit............ and Yokoi’s d-invariants nd , md forsuch real quadratic fields. All results are also supported by several numerical tabular forms.