Proof of some supercongruences via the Wilf–Zeilberger method

DOI10.1080/10236198.2020.1854239zbMath1461.11008arXiv1909.13173OpenAlexW2975295329MaRDI QIDQ4963881

Guo-Shuai Mao

Publication date: 24 February 2021

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.13173

zbMATH Keywords

binomial coefficientsFermat quotientsupercongruencesWilf-Zeilberger method

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Cites Work

• On the supercongruence conjectures of van Hamme
• Proof of three conjectures on congruences
• Hypergeometric evaluation identities and supercongruences
• On congruences related to central binomial coefficients
• On sums of binomial coefficients involving Catalan and delannoy numbers modulo \(p^2\)
• Ramanujan-type supercongruences
• Hypergeometric series acceleration via the WZ method
• A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients
• A \(q\)-microscope for supercongruences
• \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
• A refinement of a congruence result by van Hamme and Mortenson
• Congruences involving Bernoulli and Euler numbers
• “Divergent” Ramanujan-type supercongruences
• Some congruences on truncated hypergeometric series
• Some congruences related to a congruence of Van Hamme
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