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AN EXTENSION OF SURY’S IDENTITY AND RELATED CONGRUENCES

Part of: Sequences and sets Combinatorics Elementary number theory

Published online by Cambridge University Press:  04 October 2011

ROMEO MEŠTROVIĆ
ROMEO MEŠTROVIĆ*
Affiliation:
Maritime Faculty, University of Montenegro, Dobrota 36, 85330 Kotor, Montenegro (email: [email protected])
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Abstract

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In this paper we give an extension of a curious combinatorial identity due to B. Sury. Our proof is very simple and elementary. As an application, we obtain two congruences for Fermat quotients modulo p3. Moreover, we prove an extension of a result by H. Pan that generalizes Carlitz’s congruence.

Keywords

Sury’s combinatorial identityharmonic numberFermat quotientCarlitz’s congruence

MSC classification

Secondary: 11A07: Congruences; primitive roots; residue systems 05A10: Factorials, binomial coefficients, combinatorial functions 11B65: Binomial coefficients; factorials; $q$-identities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 482 - 496
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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