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Math / Contemporary Abstract Algebra 8 / Chapter 0 / Problem 9E

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

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Let n be a fixed positive integer greater than 1. If a mod

Chapter 0, Problem 9E

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QUESTION:

Problem 9E

Let n be a fixed positive integer greater than 1. If a mod n = a' and b mod n = b', prove that (a + b) mod n = (a' + b') mod n and (ab) mod n = (a'b') mod n. (This exercise is referred to in Chapters 6, 8, 10, and 15.)

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QUESTION:

Problem 9E

Let n be a fixed positive integer greater than 1. If a mod n = a' and b mod n = b', prove that (a + b) mod n = (a' + b') mod n and (ab) mod n = (a'b') mod n. (This exercise is referred to in Chapters 6, 8, 10, and 15.)

ANSWER:

Step 1 of 3

To find: and .

It is given that and .

From Modular Arithmetic, when where is quotient and is remainder upon dividing by , write it as .

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