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<p>We obtain a new family of <i>q</i>-congruences modulo the fourth power of a cyclotomic polynomial. The key ingredients of our proof are the creative microscoping method, Jackson’s <sub>6</sub><InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2369_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi _5\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϕ</mi> <mn>5</mn> </msub> </math></EquationSource> </InlineEquation> summation, and the Chinese remainder theorem for polynomials.</p>

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A New Family of q-Supercongruences from Jackson’s 6\(\phi _5\) Summation

  • 期刊论文

  • 发表日期：

    2025年2月15日

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  • Victor J. W. Guo

摘要

We obtain a new family of q-congruences modulo the fourth power of a cyclotomic polynomial. The key ingredients of our proof are the creative microscoping method, Jackson’s 6 \(\phi _5\) ϕ 5 summation, and the Chinese remainder theorem for polynomials.