Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 8b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + 7 8b = 129 + r with 0 sr< 12. The result is Multiply both sides of this equation by 8 and then simplify the right-hand side to find values of q and r such that q = 7m + 2 and r= 4 Now 0 sr< 12, and q is an integer because products and sums of integers are integers So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 8b is divided by 12 is 4

Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 8b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + 7 8b = 129 + r with 0 sr< 12. The result is Multiply both sides of this equation by 8 and then simplify the right-hand side to find values of q and r such that q = 7m + 2 and r= 4 Now 0 sr< 12, and q is an integer because products and sums of integers are integers So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 8b is divided by 12 is 4

Name: Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In othe
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Description: Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 8b is divided by 12? Fill in the blanks to show that thesame answer will be obtained no matter wh

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 18E

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