On two questions of Ono.
type: Item
instance of: scholarly article
title: On two questions of Ono.
zbMATH Open document ID: 1036.11006
author: Qiang Lin
author: Takashi Ono
published in: Proceedings of the Japan Academy. Series A
publication date: 2002-01-01T00:00:00Z
review text: The authors provide an elementary proof of a well-known result: Theorem 1: If \((T,U)\) is the fundamental solution of \(x^2-py^2=1\), where \(p\) is prime, then \(T\equiv 1\pmod p\) if and only if \(p=2\) or \(p \equiv 7\pmod 8\). They also provide a variant of Lagrange's theorem on the solvability of \(x^2-py^2=\pm 1\) using continued fractions.
reviewed by: Richard A. Mollin
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 1918568
zbMATH Keywords: Pell equation
zbMATH Keywords: periods of quadratic irrationals
MaRDI profile type: Publication
full work available at URL: pjaa.78.181
OpenAlex ID: W1991821373
cites work: Legendre symbols and continued fractions
cites work: Über Pell'sche Gleichungen und Kettenbrüche. (On Pell equations and continued fractions)
cites work: On certain exact sequences for \(\Gamma_ 0(m)\).
cites work: Q4039898
cites work: Some results concerning the nearest integer continued fraction expansion of D.
cites work: Q3815389
DOI: 10.3792/PJAA.78.181
description: scientific article; zbMATH DE number 1918568