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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

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# 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

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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

##### ISBN: 9780073383095

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