Proof of two conjectures of Sun on congruences for Franel numbers

DOI10.1080/10652469.2012.715160zbMath1360.11006arXiv1201.0617OpenAlexW3104900536WikidataQ60692379 ScholiaQ60692379MaRDI QIDQ2854300

Victor J. W. Guo

Publication date: 18 October 2013

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.0617

zbMATH Keywords

congruencesmultinomial coefficientsbinomial coefficientsFranel numbers

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)

Related Items (10)

Congruences involving \(g_n(x)=\sum\limits_{k=0}^n\dbinom{n}{k}^2\dbinom{2k}{k}x^k\) ⋮ Telescoping method and congruences for double sums ⋮ Proof of some congruence conjectures of Z.-H. Sun involving Apéry-like numbers ⋮ Polynomial reduction for holonomic sequences and applications in \(\pi\)-series and congruences ⋮ On two congruences involving Franel numbers ⋮ On two congruences involving Apéry and Franel numbers ⋮ Divisibility results on Franel numbers and related polynomials ⋮ Proof of three divisibilities of Franel numbers and binomial coefficients ⋮ Supercongruences for sums involving Domb numbers ⋮ Some congruences on \(q\)-Franel numbers and \(q\)-Catalan numbers

Uses Software

• OEIS
• SumTools

Cites Work

• Supercongruences for Apéry-like numbers
• Binomial identities -- combinatorial and algorithmic aspects
• Supercongruences for the Catalan-Larcombe-French numbers
• Unnamed Item
• Unnamed Item

This page was built for publication: Proof of two conjectures of Sun on congruences for Franel numbers