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<p>An elementary proof is given of the Andrews-Krammer-Crandall formula for the number <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1217_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(r_3(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of representations of a positive integer <i>n</i> as the sum of three squares.</p>

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A classical proof of the Andrews-Krammer-Crandall formula for \(r_3(n)\)

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Zafer Selcuk Aygin,
  • Kenneth S. Williams

摘要

An elementary proof is given of the Andrews-Krammer-Crandall formula for the number \(r_3(n)\) r 3 ( n ) of representations of a positive integer n as the sum of three squares.