Question

Prove that the square of odd positive integers can never be of the form 7k+1.

Answer 1

Before going to the solution we must know the result:

For any natural natural number n

n^2 + n is even.

In the attachment I have proved that
square of any odd positive integer can be put in the form 8k + 1.

Hence any odd positive integer can never be of the form 7k +1

I hope this answer helps you

Answer 2

Answer:

Before going to the solution we must know the result:

For any natural natural number n

n^2 + n is even.

In the attachment I have proved that square of any odd positive integer can be put in the form 8k +1.

Hence any odd positive integer can never be of the form 7k +1

I hope this answer helps you