Some new \(q\)-supercongruences involving one free parameter

DOI10.1216/rmj.2023.53.1285zbMath1528.33020OpenAlexW4386273612MaRDI QIDQ6184977

Menglin Yu, Xiaoxia Wang

Publication date: 5 January 2024

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-53/issue-4/SOME-NEW-q-SUPERCONGRUENCES-INVOLVING-ONE-FREE-PARAMETER/10.1216/rmj.2023.53.1285.full

zbMATH Keywords

\(q\)-congruencecyclotomic polynomial\(q\)-supercongruencecombinatorial congruence

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)

Cites Work

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• Binomial coefficients, Catalan numbers and Lucas quotients
• Two \(q\)-congruences from Carlitz's formula
• New congruences for central binomial coefficients
• Some congruences involving central \(q\)-binomial coefficients
• A \(q\)-microscope for supercongruences
• Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser
• Some \(q\)-supercongruences from a quadratic transformation by Rahman
• Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme
• \(q\)-supercongruences on triple and quadruple sums
• Proof of two conjectures of Guo and Schlosser
• Some \(q\)-congruences arising from certain identities
• Congruences on sums of \(q\)-binomial coefficients
• Some generalizations of a congruence by Sun and Tauraso
• Some q-analogs of congruences for central binomial sums
• Proof of a q-congruence conjectured by Tauraso
• A FAMILY OF -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL
• Some congruences that extend Van Hamme's (D.2) supercongruence
• A GENERALISATION OF A SUPERCONGRUENCE ON THE TRUNCATED APPELL SERIES

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