Some q-congruences involving central q-binomial coefficients

2021/10/20 by He-Xia Ni, Ni, He-Xia
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.10361

openalex publication_date 2021/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that p is an odd prime and m is an integer not divisible by p. Sun and Tauraso [Adv. in Appl. Math., 45(2010), 125--148] gave ∑_k=0^n-1\binom2kk+d/m^k and ∑_k=0^n-1\binom2kk+d/(km^k) modulo p for all d=0,1, … n and n= p^a, where a is a positive integer. In this paper, we present some q-analogues of these congruences in the cases m=2, 4 for any positive integer n.

Citations

• A q-microscope for supercongruences

Related

• Congruences involving the reciprocals of central binomial coefficients
• A congruence involving products of q-binomial coefficients
• Various congruences involving binomial coefficients and higher-order Catalan numbers
• Congruences involving binomial coefficients and Lucas sequences
• Note on super congruences modulo p²