Efficient remainder rule

• Published in: International journal of mathematical education in science and technology Vol. 48; no. 5; pp. 756 - 762
• Main Authors: Firozzaman, Firoz, Firoz, Fahim
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 04.07.2017; Taylor & Francis Ltd
• Subjects: Algebra; Arithmetic; coprime (relatively prime) numbers; Dividend; divisor; Equations (Mathematics); even numbers; Fractions; Integers; least common multiple (LCM) for integers and fractions; linear equation and arithmetic progression; Mathematical analysis; Mathematical Concepts; Mathematics Instruction; Number Concepts; Number theory; Numbers; odd numbers; Problem Solving; quotient; remainder; Students
• ISSN: 0020-739X; 1464-5211
• DOI: 10.1080/0020739X.2016.1267807

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the given conditions, one may need to understand the concept of modulo arithmetic in number theory. The Chinese Remainder Theorem is a known method to solve these types of problems using modulo arithmetic. In this paper, an efficient remainder rule has been proposed based on basic mathematical concepts. These core concepts are as follows: basic remainder rules of divisions, linear equation in slope intercept form, arithmetic progression and the use of a graphing calculator. These are easily understood by students who have taken prealgebra or intermediate algebra.