NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS-Reference-Cited by-同舟云学术

NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS

Published:2012-09-19 Issue:08 Volume:08 Page:2003-2016
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

GUO VICTOR J. W.¹,ZENG JIANG²

Affiliation:

1. Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

2. Institut Camille Jordan, Université de Lyon, Université Lyon 1, UMR 5208 du CNRS, 43, boulevard du 11 novembre 1918, F-69622, Villeurbanne Cedex, France

Abstract

The Apéry numbers An and central Delannoy numbers Dn are defined by [Formula: see text] Motivated by some recent work of Z.-W. Sun, we prove the following congruences: [Formula: see text] where n ≥ 1, r ≥ 0, and ε = ± 1. For r = 1, we further show that [Formula: see text] where p > 3 is a prime. The following congruence [Formula: see text] plays an important role in our proof.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042112501138

Reference14 articles.

1. Another congruence for the Apéry numbers

2. Factors of sums of powers of binomial coefficients

3. A note on lattice chains and Delannoy numbers

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