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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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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 as binary operation from Z { 0 } × Z to Z + .

To determine

Whether the statement, “The greatest common divisor is a binary operation from {0}× to + ” is true or false.

Explanation

Consider the statement, “The greatest common divisor is a binary operation from {0}× to +.”

By using 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=am+bn for integers m and n, and d is the smallest positive integer that can be written in this form

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