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. . Multiply both sides of this equation by 8 and then simplify the right-hand side to find values of q Because b mod 12 = 7, there is an integer m such that b = 12m + 7 and r such that 8b = 12q + r with 0 ≤r< 12. The result is q= and r= Now 0 ≤r< 12, and q is an integer becaus remainder obtained when 8b is divided by 1 ---Select--- ***** products and differences of integers are integers EX products and sums of integers are integers products of integers are integers So the uniqueness part of the quotient remainder theorem guarantees that the
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. . Multiply both sides of this equation by 8 and then simplify the right-hand side to find values of q Because b mod 12 = 7, there is an integer m such that b = 12m + 7 and r such that 8b = 12q + r with 0 ≤r< 12. The result is q= and r= Now 0 ≤r< 12, and q is an integer becaus remainder obtained when 8b is divided by 1 ---Select--- ***** products and differences of integers are integers EX products and sums of integers are integers products of integers are integers So the uniqueness part of the quotient remainder theorem guarantees that the
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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.
. Multiply both sides of this equation by 8 and then simplify the right-hand side to find values of q
Because b mod 12 = 7, there is an integer m such that b = 12m + 7
and r such that 8b = 12q + r with 0 ≤r< 12. The result is
q=
and r =
Now 0 ≤r < 12, and q is an integer because products and differences of integers are integersex
remainder obtained when 8b is divided by 12 is 62
x.
So the uniqueness part of the quotient remainder theorem guarantees that the
Transcribed Image Text: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.
Multiply both sides of this equation by 8 and then simplify the right-hand side to find values of q
Because b mod 12 = 7, there is an integer m such that b = 12m + 7
and r such that 8b = 12q + r with 0 ≤r < 12. The result is
q=
and r=
Now 0 ≤r< 12, and q is an integer becaus
remainder obtained when 8b is divided by 1
---Select---
*****
✓ products and differences of integers are integers 3X
products and sums of integers are integers
products of integers are integers
So the uniqueness part of the quotient remainder theorem guarantees that the
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