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<p>In this paper, we establish two families of <i>q</i>-supercongruences modulo the fourth power of a cyclotomic polynomial, which integrate new <i>q</i>-supercongruences and generalize several existed congruences, including Van Hamme’s conjectures (C.2) and (G.2). The proofs are mainly built upon the truncated hypergeometric series transformation formulae, the creative microscoping method introduced by Guo and Zudilin in 2019, and the Chinese remainder theorem for coprime polynomials.</p>

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Two Families of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Chun Wang,
  • Jiaqi Yang,
  • Quan Zhao

摘要

In this paper, we establish two families of q-supercongruences modulo the fourth power of a cyclotomic polynomial, which integrate new q-supercongruences and generalize several existed congruences, including Van Hamme’s conjectures (C.2) and (G.2). The proofs are mainly built upon the truncated hypergeometric series transformation formulae, the creative microscoping method introduced by Guo and Zudilin in 2019, and the Chinese remainder theorem for coprime polynomials.