Little extension of Euler's criterion for quadratic residue
type: Item
instance of: scholarly article
title: Little extension of Euler's criterion for quadratic residue
zbMATH Open document ID: 1503.11002
author: Victor Pires Domingues
published in: São Paulo Journal of Mathematical Sciences
publication date: 2022-12-02T00:00:00Z
review text: The main result of this article is the criterion that an integer \(a\) is a quadratic residue modulo \(n\) if \(a^{\rho(n)} \equiv 1 \bmod n\), where \(\rho\) is a certain number theoretic function. This is, however, a special case of the observation that if \(a^m \equiv 1 \bmod n\) for some odd integer \(m = 2k+1\), then \(a\) is a quadratic residue modulo \(n\) since \(a \equiv (a^{-k})^2 \bmod n\).
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11A07
zbMATH DE Number: 7626139
zbMATH Keywords: Euler's criterion
zbMATH Keywords: quadratic residue
MaRDI profile type: Publication
full work available at URL: s40863-022-00309-9
OpenAlex ID: W4283158364
Wikidata QID: Q122160113
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DOI: 10.1007/S40863-022-00309-9
description: scientific article; zbMATH DE number 7626139