×
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.1 - Problem 39e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.1 - Problem 39e

×

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

ISBN: 9780073383095 37

## Solution for problem 39E Chapter 4.1

Discrete Mathematics and Its Applications | 7th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Discrete Mathematics and Its Applications | 7th Edition

4 5 1 244 Reviews
11
5
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

#### Related chapters

Unlock Textbook Solution