Chinese Remainder Theorem (CRT) and the Efficient Remainder Rule (ERR)

In this seminar, I will present a comparative analysis of two approaches to solving integer congruence problems: the classical Chinese Remainder Theorem (CRT), grounded in the principles of modular arithmetic, and the Efficient Remainder Rule (ERR), a calculator-based computational technique. The CRT provides a rigorous theoretical framework rooted in number theory, enabling the determination of a set of solutions to systems of modular congruence through algebraic reasoning and the use of modular inverses. In contrast, the ERR offers a practical, step-by-step method that utilizes calculator technology to compute remainders efficiently, making it particularly suitable for students with a foundational understanding of algebra. This study explores the conceptual distinctions, algorithmic efficiency, and pedagogical implications of both methods. Through illustrative examples and comparative performance analysis, it demonstrates that while the CRT offers profound theoretical insight and mathematical generality, the ERR delivers a streamlined and accessible approach to numerical problem-solving. The findings highlight how traditional theoretical frameworks and technology-assisted methods can complement one another in enhancing both comprehension and efficiency in modular arithmetic.