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PROOF OF TWO CONJECTURES ON SUPERCONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS

Published online by Cambridge University Press:  13 February 2020

CHENG-YANG GU
Affiliation:
School of Mathematics and Statistics, Huaiyin Normal University, Huai’an 223300, Jiangsu, PR China email 525290408@qq.com
VICTOR J. W. GUO*
Affiliation:
School of Mathematics and Statistics, Huaiyin Normal University, Huai’an223300, Jiangsu, PR China email jwguo@hytc.edu.cn

Abstract

In this note we use some $q$-congruences proved by the method of ‘creative microscoping’ to prove two conjectures on supercongruences involving central binomial coefficients. In particular, we confirm the $m=5$ case of Conjecture 1.1 of Guo [‘Some generalizations of a supercongruence of Van Hamme’, Integral Transforms Spec. Funct.28 (2017), 888–899].

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The second author was partially supported by the National Natural Science Foundation of China (Grant No. 11771175).

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