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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 9092515, 7 pages
https://doi.org/10.1155/2017/9092515
Research Article

An Identity in Commutative Rings with Unity with Applications to Various Sums of Powers

1Faculty for Information Technology, University “Mediterranean”, Vaka Djurovića BB, Podgorica, Montenegro
2Maritime Faculty Kotor, University of Montenegro, Dobrota 36, 85330 Kotor, Montenegro

Correspondence should be addressed to Romeo Meštrović; em.ca@oemor

Received 19 December 2016; Accepted 8 February 2017; Published 27 February 2017

Academic Editor: Piergiulio Tempesta

Copyright © 2017 Miomir Andjić and 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

Let be a commutative ring of characteristic ( may be equal to ) with unity and zero 0. Given a positive integer and the so-called -symmetric set such that for each , define the th power sum as , for We prove that for each positive integer there holds As an application, we obtain two new Pascal-like identities for the sums of powers of the first positive integers.