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Use Exercise 38 to show that if m is a positive integer of

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 39E Chapter 4.1

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 39E

Problem 39E

Use Exercise 38 to show that if m is a positive integer of the form 4k + 3 for some nonnegative integer k, then m is not the sum of the squares of two integers.

Step-by-Step Solution:

Solution

In this question we have to show that if  is a positive integer in the form 4k + 3 for some nonnegative integer , then  is not the sum of the squares of two integers.

Step 1  

It is given that

=>

Let the two positive integers be  and  

So that,  

As we know that,

Or, =>

Similarly,

Or,  =>

Thus,

Or,

Or,

Now this is contradiction with , therefore  is not the sum of the squares of two integers.

Hence shown.

Step 2 of 1

Chapter 4.1, Problem 39E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Use Exercise 38 to show that if m is a positive integer of