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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

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

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:

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, =>...

Step 2 of 3

Chapter 4.1, Problem 39E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7th
Author: Kenneth Rosen
ISBN: 9780073383095

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