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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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Chapter
Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem

Label each of the following statement as either true or false.

The greatest common divisor is unique, when it exists.

To determine

Whether the statement, “The greatest common divisor is unique, when it exists” is true or false.

Explanation

Consider the statement, “The greatest common divisor is unique, when it exists.”

By using the theorem on Greatest Common Divisors, let a and b be the integers, at least one of them is non-zero. Then, there exists a unique greatest common divisor d of a and b. Moreover, d can be written as d=a

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