Question

Use a direct proof to show that every odd integer is the difference of two squares.  

Answer 1

Let $a\in Z$ . Let's consider $M=(a+1)^2-a^2=a^2+2a+1-a^2=2a+1$ . Formula $2a+1$ is the general formula for an odd number, so every odd number can be written as the difference of two squares. Thus, the statement has been proved.