The group of Pythagorean triples in number fields
type: Item
instance of: scholarly article
title: The group of Pythagorean triples in number fields
zbMATH Open document ID: 0762.11009
DOI: 10.1007/BF01766294
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1992-09-27T00:00:00Z
review text: Let \(K\) be an algebraic number field not containing \(i\). A group structure is introduced in the set of solutions of \(x^ 2+y^ 2=1\) \((x,y\in K)\) and the properties of the group so obtained (which is isomorphic to the group of elements with relative norm 1 in \(K(i))\) are studied. The authors deal actually with equivalence classes of solutions of the equation \(x^ 2+y^ 2=z^ 2\) in the ring of integers of \(K\).
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11E25
Mathematics Subject Classification ID: 11R99
zbMATH DE Number: 59766
zbMATH Keywords: Pythagorean equation
zbMATH Keywords: unit norm
Wikidata QID: Q114233929
author: P. Zanardo
author: Umberto Zannier
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
cites work: The Group of Primitive Pythagorean Triangles
cites work: A note on the group of units of an algebraic number field
cites work: Number fields
cites work: Q4402415
cites work: Q5801399
full work available at URL: https://doi.org/10.1007/bf01766294
OpenAlex ID: W2046024104
description: scientific article; zbMATH DE number 59766