Show that if a is an integer and d is an integer greater than 1, then the quotient and remainder obtained when a is divided by d are [a/d] and a - d[a/d], respectively.
Step 1 :
In the theorem (2) of the division algorithm states that “let be an integer a positive integer then there are unique integer q and r with such that ”.
Step 2 :
Dividing equation by d .
Textbook: Discrete Mathematics and Its Applications
Author: Kenneth Rosen
Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: Integer, quotient, Divided, obtained, Greater. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Show that if a is an integer and d is an integer greater than 1, then the quotient and remainder obtained when a is divided by d are [a/d] and a - d[a/d], respectively.” is broken down into a number of easy to follow steps, and 34 words. Since the solution to 18E from 4.1 chapter was answered, more than 267 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 18E from chapter: 4.1 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7.