An Algorithm for Explicit Form of Fundamental Units of Certain Real Quadratic Fields and Period Eight

Abstract

In this paper, we have given an explicit formulation to determine the form of the fundamental units of certain real quadratic number fields. This new algorithm for such quadratic fields is first in the literature and it gives us a more practical way to calculate the fundamental unit. Where, the period in the continued fraction expansion of the quadratic irrational number of the certain real quadratic fields is equal to 8.