Explicit Form of Fundamental Units of Certain Real Quadratic Fields

Gül Karadeniz Gözeri, Ayten Pekin

Abstract

In this paper, for all real quadratic fields K = Q(pd) such that d is a positive square free integer congruent to 2 or 3 modulo 4 and the period kd of the continued fraction expansion of the quadratic irrational number !d =pd is equal to 7, we describe Td , Ud explicitly in the fundamental unit "d = (Td+Udpd2 )(> 1) of Q(pd) and d itself by using five parameters appearing in the continued fraction expansion of !d .

Keywords

Continued Fraction, Quadratic Extensions, Fundamental Unit

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