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CONGRUENCES FOR TRUNCATED HYPERGEOMETRIC SERIES $_{2}F_{1}$

Part of: Elementary number theory

Published online by Cambridge University Press:  06 March 2017

JI-CAI LIU
JI-CAI LIU*
Affiliation:
College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, PR China email [email protected]
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Abstract

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Rodriguez-Villegas conjectured four supercongruences associated to certain elliptic curves, which were first confirmed by Mortenson by using the Gross–Koblitz formula. In this paper we prove four supercongruences between two truncated hypergeometric series $_{2}F_{1}$. The results generalise the four Rodriguez-Villegas supercongruences.

Keywords

supercongruencehypergeometric seriesFermat quotient

MSC classification

Primary: 11A07: Congruences; primitive roots; residue systems
Secondary: 33C05: Classical hypergeometric functions, $_2F_1$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 1 , August 2017 , pp. 14 - 23
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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