Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 3 (2016), 361-366.

A combinatorial proof of a decomposition property of reduced residue systems

Yotsanan Meemark and Thanakorn Prinyasart

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Abstract

In this paper, we look at three common theorems in number theory: the Chinese remainder theorem, the multiplicative property of the Euler totient function, and a decomposition property of reduced residue systems. We use a grid of squares to give simple transparent visual proofs.

Article information

Source
Involve, Volume 9, Number 3 (2016), 361-366.

Dates
Received: 16 October 2011
Revised: 21 December 2014
Accepted: 23 June 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511371017

Digital Object Identifier
doi:10.2140/involve.2016.9.361

Mathematical Reviews number (MathSciNet)
MR3509330

Zentralblatt MATH identifier
1342.11005

Subjects
Primary: 11A07: Congruences; primitive roots; residue systems

Keywords
Chinese remainder theorem reduced residue system

Citation

Meemark, Yotsanan; Prinyasart, Thanakorn. A combinatorial proof of a decomposition property of reduced residue systems. Involve 9 (2016), no. 3, 361--366. doi:10.2140/involve.2016.9.361. https://projecteuclid.org/euclid.involve/1511371017


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References

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  • A. Ledet, “Faro shuffles and the Chinese remainder theorem”, Math. Mag. 80:4 (2007), 283–289.
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