FACTORS OF SUMS AND ALTERNATING SUMS INVOLVING BINOMIAL COEFFICIENTS AND POWERS OF INTEGERS

DOI10.1142/S1793042111004812zbMath1235.05009arXiv1008.3316MaRDI QIDQ3101590

Victor J. W. Guo, Zeng, Jiang

Publication date: 29 November 2011

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

Full work available at URL: https://arxiv.org/abs/1008.3316

zbMATH Keywords

binomial coefficientsdivisibility propertiesLucas theoremChu-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 (4)

Factors of sums and alternating sums of products of \(q\)-binomial coefficients and powers of \(q\)-integers ⋮ Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients ⋮ Sums of powers of Catalan triangle numbers ⋮ Proofs of two conjectures on Catalan triangle numbers

Cites Work

• Unnamed Item
• A \(q\)-rious positivity
• Moments on Catalan numbers
• Moments of combinatorial and Catalan numbers
• Factors of binomial sums from the Catalan triangle
• Super ballot numbers
• New identities in the Catalan triangle
• The number of convex polyominoes and the generating function of Jacobi polynomials
• Binomial coefficients and the ring of $p$-adic integers
• Congruences for the second-order Catalan numbers
• Factors of alternating sums of products of binomial and q-binomial coefficients

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