Integral points on the unit circle
type: Item
instance of: scholarly article
title: Integral points on the unit circle
zbMATH Open document ID: 1002.11033
author: Parvati Shastri
published in: Journal of Number Theory
publication date: 2002-08-25T00:00:00Z
review text: The author gives a complete solution to the following problem, posed by Dipendra Prasad: Determine all algebraic number fields \(K\) in which there are integers \(x\) and \(y\) such that \(x^2+y^2=1\). The proof is based on the observation that the numbers \(x\pm iy\) must be units in \(K\) or \(K(i).\)
reviewed by: Veikko Ennola
Mathematics Subject Classification ID: 11D57
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R04
zbMATH DE Number: 1787786
zbMATH Keywords: solution of \(x^2+y^2=1\) in algebraic integers
MaRDI profile type: Publication
full work available at URL: jnth.2000.2635
OpenAlex ID: W1975835087
cites work: Q5731856
cites work: Q5690489
DOI: 10.1006/JNTH.2000.2635
description: scientific article; zbMATH DE number 1787786