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DOI:http://dx.doi.org/10.26855/jamc.2021.09.008

On Some Algebraic Properties of the Chinese Remainder Theorem with Applications to Real Life

Date: September 18,2021 |Hits: 325 Download PDF How to cite this paper

Elvis Adam Alhassan1,2,*, Kaiyu Tian1, Olivier Joseph Abban1, Israel Enema Ohiemi4,5, Michael Adjabui2, Gabriel Armah3, Simon Agyemang2

1School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu, China.

2Faculty of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Upper East Region, Ghana.

3School of Computing and Information Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Upper East Region, Ghana.

4National Research Centre of Pumps, Jiangsu University, Zhenjiang, Jiangsu, China.

5Department of Mechanical Engineering, University of Nigeria, Nsukka, Nigeria.

*Corresponding author: Elvis Adam Alhassan

Abstract

The study sought to establish some algebraic properties of the Chinese Remainder Theorem.  The Chinese Remainder Theorem is an ancient but important mathematical theorem that enables one to solve simultaneous equations with respect to different modulo and makes it possible to reconstruct integers in a certain range from their residues modulo to the pairwise relatively prime modulo and also construct libraries for manipulations on very  large integers.  The study seeks to find out some real life applications of the Chinese Remainder Theorem in our everyday life activities especially in trading and in information security and retrieval avoiding any leakages to invaders or intruders.  The study presented proofs of some theorems vital in the real life applications of the Chinese Remainder Theorem.  In the study, we identified that in the statement of the Principal Ideal Domain and that of Rings can be classified as some algebraic properties of the Chinese Remainder Theorem.

References

[1] Crisan, V. and Pollack, P. (2020).  The smallest root of a polynomial congruence, Math.  Res. Lett. , 27(1). 

[2] Dartyge, C. and Martin, G. (2019).  Exponential sums with reducible polynomials.  Discrete Anal https://doi.org/10.19086/da.10793. 

[3] Saurabh, S. and Gaurav, A. (2010).  Use of Chinese Remainder Theorem to generate random numbers for Cryptography.  International Journal of Applied Engineering Research.  Volume 1, No. 2, pp. 168-174. 

[4] Alhassan, E. A., Simon, K. N., Bunyan, J. M., and Gregory, A. (2014).  On some algebraic properties of the Euclidean algorithm with applications to real life.  Research Journal of Mathematics and Statistics, 6(4): 49-55. 

[5] Stallings, W. (1999).  Cryptography and Network Security: Principles and Practice.  (2nd ed.).  New Jersey: Prentice-Hall.

How to cite this paper

On Some Algebraic Properties of the Chinese Remainder Theorem with Applications to Real Life

How to cite this paper: Elvis Adam Alhassan, Kaiyu Tian, Olivier Joseph Abban, Israel Enema Ohiemi, Michael Adjabui, Gabriel Armah, Simon Agyemang. (2021) On Some Algebraic Properties of the Chinese Remainder Theorem with Applications to Real LifeJournal of Applied Mathematics and Computation5(3), 219-224.

DOI: http://dx.doi.org/10.26855/jamc.2021.09.008

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