Efficient remainder rule

ABSTRACT

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.

KEYWORDS:

• Dividend
• divisor
• quotient
• remainder
• even numbers
• odd numbers
• coprime (relatively prime) numbers
• least common multiple (LCM) for integers and fractions
• linear equation and arithmetic progression

Acknowledgments

The authors would like to express their thanks to the referee who kindly provided suggestions to improve this note. The authors also acknowledge the excellent research facilities at Arizona State University, USA.

Disclosure statement

No potential conflict of interest was reported by the authors.