Original scientific paper

Solving index form equations in two parametric families of biquadratic fields

Borka Jadrijević orcid.org/0000-0002-5913-3719 ; Department of Mathematics, University of Split, Split, Croatia

Abstract

In this paper we find a minimal index and determine all integral elements with the minimal index in two families of totally real bicyclic biquadratic fields
\[K_{c}=\mathbb{Q}\left( \sqrt{\left( c-2\right) c},\sqrt{\left(
c+2\right) c}\right) \,\,\mbox{and}\,\, L_{c}=\mathbb{Q}\left( \sqrt{\left(c-2\right) c},\sqrt{\left( c+4\right) c}\right).\]

Keywords

index form equations; minimal index; totally real bicyclic biquadratic fields; simultaneous Pellian equations

Hrčak ID:

44028

URI

https://hrcak.srce.hr/44028

Publication date:

9.12.2009.

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