On the real quadratic elds with certain continued fraction expansions and fundamental units

The purpose of this paper is to investigate the real quadratic number fields Q(√d) which contain the specific form of the continued fractions expansions of integral basis element where d ≡ 2,3(mod4) is a square free positive integer. Besides, the present paper deals with determining the fundamental unit
d =td ud√d/2i1
and nd and md Yokoi’s d-invariants by reference to continued fraction expansion of integral basis element where `(d) is a period length. Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.