Explicit Form of Fundamental Units of Certain Real Quadratic Fields

Authors

  • Gul Karadeniz Gozeri Istanbul University, Faculty of Science, Department of Mathematics, Vezneciler/Istanbul
  • Ayten Pekin Istanbul University, Faculty of Science, Department of Mathematics, Vezneciler/Istanbul

Keywords:

Continued Fraction, Quadratic Extensions, Fundamental Unit

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 .

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Published

2014-01-29

Issue

Vol. 7 No. 1: (January 2014)

Section

Number Theory

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How to Cite

Explicit Form of Fundamental Units of Certain Real Quadratic Fields. (2014). European Journal of Pure and Applied Mathematics, 7(1), 55-64. https://www.ejpam.com/index.php/ejpam/article/view/2029