Vol. 9, No. 3, 2016

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ISSN: 1944-4184 (e-only)
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A combinatorial proof of a decomposition property of reduced residue systems

Yotsanan Meemark and Thanakorn Prinyasart

Vol. 9 (2016), No. 3, 361–366
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.

Keywords
Chinese remainder theorem, reduced residue system
Mathematical Subject Classification 2010
Primary: 11A07
Milestones
Received: 16 October 2011
Revised: 21 December 2014
Accepted: 23 June 2015
Published: 3 June 2016

Communicated by Filip Saidak
Authors
Yotsanan Meemark
Department of Mathematics and Computer Science
Faculty of Science
Chulalongkorn University
Bangkok 10330
Thailand
Thanakorn Prinyasart
Department of Mathematics and Computer Science
Faculty of Science
Chulalongkorn University
Bangkok 10330
Thailand