A short and simple proof of the Chinese Remainder theorem and some of its applications

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Basic Sciences, Maragheh University, Maragheh, Iran

Abstract

In this article, we prove the Chinese Remainder Theorem using a simple and concise method. The constructive nature of the proof allows us to derive an explicit formula for computing all powers of elements in certain rings, especially the ring of integers modulo $m$, denoted by  $\mathbb{Z}/m\mathbb{Z}$‎. Additionally, we obtain a new result regarding the exponentiation of powers.

Keywords

References

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Mathematics and Society
Volume 4, Issue 4 - Serial Number 4
December 2019
Pages 49-52

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History

  • Receive Date: 11 July 2020
  • Revise Date: 24 September 2020
  • Accept Date: 25 September 2020
  • Publish Date: 20 February 2020

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