On Some Algebraic Properties of the Euclidean Algorithm with Applications to Real Life

Alhassan, Erwin; Simon, K.N.; Bunyan, J.M.; Gregory, Adam

doi:10.19026/rjms.6.5271

Cited by 1 publication

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“…The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. According to Alhassan et al [4], one of the most useful results of number theory is the Chinese Remainder Theorem. In essence, the CRT says it is possible to reconstruct integers in a certain range from their residues modulo a set of pairwise relatively prime moduli.…”

Section: Introductionmentioning

confidence: 99%

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

Alhassan¹,

Tian²,

Abban³

et al. 2021

JAMC

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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.

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Section: Introductionmentioning

confidence: 99%