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<p>In 2021, the first author and Kalita obtained two general hypergeometric formulas for sums involving certain rising factorials to prove some supercongruence conjectures of Guo related to (B.2) and (C.2) supercongruences of VanHamme. In this paper, we further generalize these formulas using the WZ-method and the Zeilberger algorithm, respectively. Consequently, we deduce some new supercongruence results related to (B.2) and (C.2).</p>

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Generalization of some supercongruences related to (B.2) and (C.2) supercongruences of VanHamme

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Arijit Jana,
  • Liton Karmakar

摘要

In 2021, the first author and Kalita obtained two general hypergeometric formulas for sums involving certain rising factorials to prove some supercongruence conjectures of Guo related to (B.2) and (C.2) supercongruences of VanHamme. In this paper, we further generalize these formulas using the WZ-method and the Zeilberger algorithm, respectively. Consequently, we deduce some new supercongruence results related to (B.2) and (C.2).