Table of Contents
ISRN Combinatorics
Volume 2013 (2013), Article ID 363724, 7 pages
http://dx.doi.org/10.1155/2013/363724
Research Article

An Extension of a Congruence by Tauraso

Department of Mathematics, Maritime Faculty, University of Montenegro, Do-Brota 36, 85330 Kotor, Montenegro

Received 23 September 2012; Accepted 10 October 2012

Academic Editors: C. da Fonseca and B. Wu

Copyright © 2013 Romeo Meštrović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For a positive integer let be the th harmonic number. In this paper we prove that, for any prime ,   . Notice that the first part of this congruence is proposed in 2008 by Tauraso. In our elementary proof of the second part of the above congruence we use certain classical congruences modulo a prime and the square of a prime, some congruences involving harmonic numbers, and a combinatorial identity due to Hernández. Our auxiliary results contain many interesting combinatorial congruences involving harmonic numbers.