   Chapter 2.4, Problem 9TFE

Chapter
Section
Textbook Problem

Label each of the following statement as either true or false.Let a and b be integers, not both zero. Then ( a ,   b ) = ( − a ,   b ) .

To determine

Whether the statement, “Let a and b be integers, not both zero. Then, (a,b)=(a,b) ” is true or false.

Explanation

Consider the statement, “Let a and b be integers, not both zero. Then, (a,b)=(a,b).”

Let d=(a,b), then d satisfies the following conditions

1. d is a positive integer.

2. d|a and d|b.

3. c|a and c|b imply c|d.

d|a imply a=dk1,k1

Multiply both sides by negative sign,

a=dk1

a=d(

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