Proof of Sun's conjectures on super congruences and the divisibility of certain binomial sums

DOI10.1007/s11139-019-00138-zzbMath1428.11040arXiv1511.05553OpenAlexW3098178741WikidataQ123184161 ScholiaQ123184161MaRDI QIDQ2337341

Tao Zhang, Guo-Shuai Mao

Publication date: 19 November 2019

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.05553

zbMATH Keywords

congruencescentral binomial coefficientsdivisibility problem

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)

Related Items (7)

Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series ⋮ Proof of a Dwork-type supercongruence by induction ⋮ Proof of some supercongruences concerning truncated hypergeometric series ⋮ Proof of a supercongruence via the Wilf-Zeilberger method ⋮ Factors of certain sums involving central \(q\)-binomial coefficients ⋮ Symbolic summation methods and hypergeometric supercongruences ⋮ Some variations of a ‘divergent’ Ramanujan-type q-supercongruence

Cites Work

• Proof of Sun's conjecture on the divisibility of certain binomial sums
• On an extension of a Van Hamme supercongruence
• \(q\)-analogues of two ``divergent Ramanujan-type supercongruences
• Super congruences and Euler numbers
• Products and sums divisible by central binomial coefficients
• Two congruences involving harmonic numbers with applications
• “Divergent” Ramanujan-type supercongruences
• Unnamed Item

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