Congruences involving binomial coefficients and Apery-like numbers

DOI10.5486/PMD.2020.8577zbMath1474.11002arXiv1803.10051OpenAlexW3023071828MaRDI QIDQ5126093

Zhi-Hong Sun

Publication date: 2 October 2020

Published in: Publicationes Mathematicae Debrecen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10051

zbMATH Keywords

binary quadratic formBernoulli numberLegendre polynomialcongruencebinomial coefficientsApéry-like numbers

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Sums of squares and representations by other particular quadratic forms (11E25) Congruences; primitive roots; residue systems (11A07)

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On some congruences involving Apéry-like numbers S_n ⋮ Proof of some conjectural congruences involving Domb numbers and binary quadratic forms ⋮ Supercongruences involving Domb numbers and binary quadratic forms ⋮ Supercongruences involving products of three binomial coefficients ⋮ Proof of some congruence conjectures of Z.-H. Sun involving Apéry-like numbers ⋮ On three conjectural congruences of Z.-H. Sun involving Apéry and Apéry-like numbers ⋮ Supercongruences and binary quadratic forms ⋮ An algorithm to prove holonomic differential equations for modular forms ⋮ Congruences for certain families of Apéry-like sequences

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