Proof of three divisibilities of Franel numbers and binomial coefficients

DOI10.1142/S1793042120500797zbMath1472.11028WikidataQ114071948 ScholiaQ114071948MaRDI QIDQ3303485

Peisen Yuan, Yong Zhang

Publication date: 11 August 2020

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

zbMATH Keywords

congruencesbinomial coefficientsChinese remainder theoremFranel numbers

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Other combinatorial number theory (11B75) Congruences; primitive roots; residue systems (11A07) Special sequences and polynomials (11B83)

Cites Work

• Congruences for Franel numbers
• Factors of sums and alternating sums of products of \(q\)-binomial coefficients and powers of \(q\)-integers
• Proof of two conjectures of Sun on congruences for Franel numbers
• NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS
• Two new kinds of numbers and related divisibility results
• Telescoping method and congruences for double sums
• Divisibility results on Franel numbers and related polynomials
• Supercongruences for the Catalan-Larcombe-French numbers
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