NOTES ON ESPECIAL CONTINUED FRACTION EXPANSIONS AND REAL QUADRATIC NUMBER FIELDS

Özet

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 𝑤𝑑 forarbitrary period length ℓ = ℓ(𝑑) 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.