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Suppose b is any integer., If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b 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 + values of g and r such that 4b = 12g +r with 0 sr< 12. The result is Multiply both sides of this equation by 4 and then simplify the right-hand side to find q = and r= Now 0 sr< 12, and g is an integer because -Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is

Suppose b is any integer., If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b 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 + values of g and r such that 4b = 12g +r with 0 sr< 12. The result is Multiply both sides of this equation by 4 and then simplify the right-hand side to find q = and r= Now 0 sr< 12, and g is an integer because -Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is

Elements Of Modern Algebra
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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Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b 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 + Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12g + r with 0 sr< 12. The result is q = and r= Now 0 sr< 12, and g is an integer because ---Select--- v . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is
Transcribed Image Text:Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b 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 + Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12g + r with 0 sr< 12. The result is q = and r= Now 0 sr< 12, and g is an integer because ---Select--- v . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is
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