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On extensions of van Hamme's conjectures

Part of: Elementary number theory Combinatorics

Published online by Cambridge University Press:  30 August 2018

Bing He
Bing He*
Affiliation:
College of Science, Northwest AandF University, Yangling 712100, Shaanxi, People's Republic of China
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Abstract

Some congruences on conjectures of van Hamme are established. These results give partial answers to some of Swisher's conjectures.

Keywords

congruencevan Hamme conjecturesSwisher conjectures

MSC classification

Primary: 11A07: Congruences; primitive roots; residue systems
Secondary: 05A10: Factorials, binomial coefficients, combinatorial functions 33C20: Generalized hypergeometric series, $_pF_q$
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 5 , October 2018 , pp. 1017 - 1027
Copyright
Copyright © Royal Society of Edinburgh 2018 

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Footnotes

*

Present address: School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, People's Republic of China (yuhe001@foxmail.com).