Proof of Sun's conjecture on the divisibility of certain binomial sums

zbMath1295.11021arXiv1301.4877MaRDI QIDQ396941

Victor J. W. Guo

Publication date: 14 August 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4877

zbMATH Keywords

congruencesStirling's formulabinomial coefficientssuper Catalan numbers

Mathematics Subject Classification ID

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

Related Items

Some divisibility properties of binomial and \(q\)-binomial coefficients, Proof of two divisibility properties of binomial coefficients conjectured by Z.-W. Sun, Towards characterising polynomiality of \(\frac{1-q^b}{1-q^a}{n\brack m}\) and applications, On the divisibility properties of certain binomial sums, Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients, Unnamed Item, Some congruences on harmonic numbers and binomial sums, Proof of Sun's conjectures on super congruences and the divisibility of certain binomial sums

Cites Work

• Unnamed Item
• A \(q\)-rious positivity
• Super ballot numbers
• Products and sums divisible by central binomial coefficients
• Factorial ratios, hypergeometric series, and a family of step functions
• ON DIVISIBILITY OF BINOMIAL COEFFICIENTS