A generalization of Morley's congruence

DOI10.1186/s13662-015-0568-6zbMath1422.11049OpenAlexW1814834287WikidataQ59429793 ScholiaQ59429793MaRDI QIDQ1721886

Hao Pan, Yong Zhang, Jian-Xin Liu

Publication date: 13 February 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-015-0568-6

zbMATH Keywords

binomial sums\(q\)-analogueMorley's congruence

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Special sequences and polynomials (11B83)

Related Items (16)

Two \(q\)-congruences from Carlitz's formula ⋮ q-Analogues of some supercongruences related to Euler numbers ⋮ A \(q\)-analogue of the (L.2) supercongruence of van Hamme ⋮ A \(q\)-analogue of the (J.2) supercongruence of van Hamme ⋮ Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series ⋮ A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients ⋮ Some generalizations of a congruence by Sun and Tauraso ⋮ Two new 𝑞-supercongruences arising from Carlitz’s identity ⋮ A q-analogue of the (I.2) supercongruence of Van Hamme ⋮ Proof of a q-congruence conjectured by Tauraso ⋮ A q-analogue of a curious supercongruence of Guillera and Zudilin ⋮ Some congruences with $q-$binomial coefficients and $q-$harmonic numbers ⋮ Some congruences involving fourth powers of central q-binomial coefficients ⋮ \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme ⋮ Proof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomial ⋮ \(q\)-analogues of two ``divergent Ramanujan-type supercongruences

Cites Work

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• Some recurrences for sums of powers of binomial coefficients
• Recurrences for alternating sums of powers of binomial coefficients
• Recurrences for sums of powers of binomial coefficients
• On the residues of binomial coefficients and their products modulo prime powers
• Factors of sums of powers of binomial coefficients
• A q-analogue of Lehmer's congruence

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