More congruences from Apery-like formulae

2011/10/18 by Roberto Tauraso, Tauraso, Roberto
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1110.4013

openalex publication_date 2011/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present some congruences modulo p^6-d for sums of the type ∑_k=0^(p-3)/2x^k2k\choose k/(2k+1)^d, for d=1,2,3 where p>5 is a prime.

Related

• New conjectures involving binomial coefficients and Apéry-like numbers
• Congruences for the Apéry numbers modulo p³
• New congruences for sums involving Apery numbers or central Delannoy numbers
• Congruences for partial sums of the generating series for \binom3kk
• Congruences involving the reciprocals of central binomial coefficients