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CONGRUENCES FOR THE $(p-1)$TH APÉRY NUMBER

Part of: Elementary number theory Combinatorics Sequences and sets

Published online by Cambridge University Press:  28 November 2018

JI-CAI LIU Open the ORCID record for JI-CAI LIU [Opens in a new window]  and
CHEN WANG
JI-CAI LIU*
Affiliation:
Department of Mathematics, Wenzhou University, Wenzhou 325035, PR China email jcliu2016@gmail.com
CHEN WANG
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China email chenwjsnu@163.com
*
✉jcliu2016@gmail.com
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Abstract

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We prove two conjectural congruences on the $(p-1)$th Apéry number, which were recently proposed by Z.-H. Sun.

Keywords

Apéry numberscongruencesBernoulli numbers

MSC classification

Primary: 11A07: Congruences; primitive roots; residue systems
Secondary: 05A19: Combinatorial identities, bijective combinatorics 11B68: Bernoulli and Euler numbers and polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 3 , June 2019 , pp. 362 - 368
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author was supported by the National Natural Science Foundation of China (grant 11801417).

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