On the divisibility of sums of even powers of \(q\)-binomial coefficients
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Publication:2116790
DOI10.1007/s13398-022-01220-wOpenAlexW3205617491MaRDI QIDQ2116790
Publication date: 18 March 2022
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2110.09906
(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)
Related Items (11)
\(q\)-supercongruences from gasper and Rahman's summation formula ⋮ A new \(q\)-supercongruence modulo the fourth power of a cyclotomic polynomial ⋮ Some \(q\)-supercongruences from the Gasper and Rahman quadratic summation ⋮ Three families of \(q\)-supercongruences from a quadratic transformation of Rahman ⋮ Three families of \(q\)-supercongruences modulo the square and cube of a cyclotomic polynomial ⋮ Further generalizations of four supercongruences of Rodriguez-Villegas ⋮ A new extension of a “divergent” Ramanujan-type supercongruence ⋮ Unnamed Item ⋮ \(q\)-supercongruences from transformation formulas ⋮ Further \(q\)-supercongruences from the \(q\)-Pfaff-Saalschütz identity ⋮ A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula
Cites Work
- On a congruence involving \(q\)-Catalan numbers
- On supercongruences for truncated sums of squares of basic hypergeometric series
- A generalization of Wolstenholme's harmonic series congruence
- A \(q\)-microscope for supercongruences
- Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser
- Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
- Some \(q\)-supercongruences modulo the square and cube of a cyclotomic polynomial
- A \(q\)-analogue of the (A.2) supercongruence of Van Hamme for primes \(p\equiv 1\pmod{4} \)
- Some new \(q\)-congruences on double sums
- Proof of a generalization of the (C.2) supercongruence of Van Hamme
- Congruences on sums of \(q\)-binomial coefficients
- NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS
- q-Analogues of two Ramanujan-type formulas for 1/π
- $q$-analogues of two supercongruences of Z.-W. Sun
- A TRUNCATED IDENTITY OF EULER AND RELATED -CONGRUENCES
- q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
- A q-Analogue of Wolstenholme's Harmonic Series Congruence
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