NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS

DOI10.1142/S1793042112501138zbMath1268.11028arXiv1008.2894OpenAlexW2963823779MaRDI QIDQ3165313

Zeng, Jiang, Victor J. W. Guo

Publication date: 26 October 2012

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.2894

zbMATH Keywords

Apéry numbersWolstenholme's theorem\(q\)-binomial coefficientscentral Delannoy numbers\(q\)-Lucas theorem\(q\)-Chu--Vandermonde formula

Mathematics Subject Classification ID

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

Related Items (17)

Proof of a conjecture of Sun and its extension by Guo ⋮ Some parametric congruences involving generalized central trinomial coefficients ⋮ Telescoping method and congruences for double sums ⋮ Congruences involving squares of generalized central trinomial coefficients ⋮ Proof of some conjectures of Z.-W. Sun on congruences for Apéry polynomials ⋮ $q$-analogues of two supercongruences of Z.-W. Sun ⋮ Unnamed Item ⋮ A supercongruence relation among Ap ⋮ Proof of three divisibilities of Franel numbers and binomial coefficients ⋮ Factors of alternating sums of powers of \(q\)-Narayana numbers ⋮ On divisibility of sums of Apéry polynomials ⋮ Congruences on truncated double summation series ⋮ Two congruences concerning Apéry numbers conjectured by Z.-W. Sun ⋮ Some congruences on \(q\)-Franel numbers and \(q\)-Catalan numbers ⋮ On the divisibility of sums involving powers of multi-variable Schmidt polynomials ⋮ ON THE DIVISIBILITY OF SUMS INVOLVING APÉRY-LIKE POLYNOMIALS ⋮ On the divisibility of sums of even powers of \(q\)-binomial coefficients

Uses Software

• Maple

Cites Work

• Unnamed Item
• Unnamed Item
• On sums of Apéry polynomials and related congruences
• Congruence properties of Apéry numbers
• Some congruences for Apery numbers
• An analogue of Kummer congruences for \(q\)-Euler numbers
• Another congruence for the Apéry numbers
• A note on lattice chains and Delannoy numbers
• Divisibility properties of a class of binomial sums
• Some arithmetic properties of the \(q\)-Euler numbers and \(q\)-Salié numbers
• Generalized Powers

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