Good night.

I have a proof question here that I needs validating. I was also wondering if I could receive alternative solutions for the question.

Thanks in advance for the help

Question

Prove that the square of an odd integer is always of the form where is an integer

Answer

We wish to prove that , where is an odd integer

Let be an odd integer of the form:

As is an integer, it can either be odd or even

Case 1: is odd, i.e. it is of the form:

Let

Case 2: is even, i.e. it is of the form

Let

Proven in both cases, hence the statement is true.

End of solution. Q.E.D

I welcome your critiques and say thanks in advance,