Divisibility of some binomial sums
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Publication:3298869
DOI10.4064/aa181114-24-7zbMath1464.11029arXiv1808.03213OpenAlexW3014672235MaRDI QIDQ3298869
Publication date: 16 July 2020
Published in: Acta Arithmetica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.03213
Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)
Related Items (14)
q-Analogues of some supercongruences related to Euler numbers ⋮ Proof of two conjectures of Guo and Schlosser ⋮ A \(q\)-Dwork-type generalization of Rodriguez-Villegas' supercongruences ⋮ On a generalization of a congruence related to \(q\)-Narayana numbers ⋮ Some \(q\)-congruences arising from certain identities ⋮ Some \(q\)-analogues of supercongruences for truncated \({}_3 F_2\) hypergeometric series ⋮ Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series ⋮ New \(q\)-supercongruences from the Bailey transformation ⋮ Two \(q\)-supercongruences from Watson's transformation ⋮ Some \(q\)-supercongruences modulo the square and cube of a cyclotomic polynomial ⋮ Factors of certain sums involving central \(q\)-binomial coefficients ⋮ Some variations of a ‘divergent’ Ramanujan-type q-supercongruence ⋮ Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\)
Cites Work
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- A \(q\)-microscope for supercongruences
- Super congruences and Euler numbers
- Products and sums divisible by central binomial coefficients
- Some new \(q\)-congruences for truncated basic hypergeometric series
- Factors of the Gaussian coefficients
- Mosaic Supercongruences of Ramanujan Type
- Supercongruences for polynomial analogs of the Apéry numbers
- q-Analogues of two Ramanujan-type formulas for 1/π
- Some congruences involving fourth powers of central q-binomial coefficients
- q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
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