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

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  • Miomir Andjić
  • Romeo Meštrović

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.

Suggested Citation

  • Miomir Andjić & Romeo Meštrović, 2017. "An Identity in Commutative Rings with Unity with Applications to Various Sums of Powers," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-7, February.
    • Handle: RePEc:hin:jnddns:9092515
    DOI: 10.1155/2017/9092515
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