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.

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, =>...