Divisibility results on Franel numbers and related polynomials

DOI10.1142/S1793042119500222zbMath1435.11041OpenAlexW2890797854WikidataQ114071977 ScholiaQ114071977MaRDI QIDQ4628670

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Publication date: 15 March 2019

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

Full work available at URL: https://doi.org/10.1142/s1793042119500222

zbMATH Keywords

integer sequencesdivisibilityFranel numberscombinatorial congruences

Mathematics Subject Classification ID

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

Related Items (4)

Polynomial reduction for holonomic sequences and applications in \(\pi\)-series and congruences ⋮ Proof of three divisibilities of Franel numbers and binomial coefficients ⋮ Congruences and telescopings of P-recursive sequences ⋮ On a supercongruence conjecture of Z.-W. Sun

Uses Software

• OEIS

Cites Work

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• Congruences involving \(g_n(x)=\sum\limits_{k=0}^n\dbinom{n}{k}^2\dbinom{2k}{k}x^k\)
• Congruences for Franel numbers
• Connections between \(p=x^2+3y^2\) and Franel numbers
• Binomial identities -- combinatorial and algorithmic aspects
• Supercongruences involving Lucas sequences
• A telescoping method for double summations
• Proof of some conjectures of Z.-W. Sun on the divisibility of certain double sums
• Proof of two conjectures of Sun on congruences for Franel numbers
• Telescoping method and congruences for double sums
• Proof of a conjecture involving Sun polynomials

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