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Abstract <p> The Pell equation with right-hand side <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3068_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\pm2\)</EquationSource> </InlineEquation> is considered and a connection is established between its solutions and the convergents of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3068_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sqrt D\)</EquationSource> </InlineEquation>, which is similar to the well-known statements about the solutions of the Pell equation with right-hand side <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3068_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\pm1\)</EquationSource> </InlineEquation>. </p>

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On Solving the Pell Equation with Right-Hand Side \(\pm2\) Using Continued Fractions

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • M. E. Changa

摘要

Abstract

The Pell equation with right-hand side \(\pm2\) is considered and a connection is established between its solutions and the convergents of \(\sqrt D\) , which is similar to the well-known statements about the solutions of the Pell equation with right-hand side \(\pm1\) .