Trouble with a proof.

[nauticaricky]

Hey all.

I am asked to prove that for integers M,

M is even if and only if M^2 is even.

Any advice? I know I have to start with M and then get M^2, and vice versa, but I don't know where to begin.

Thanks

[pseudonym]

What does it mean for a number to be even and what does m^2 represent?

It should be easy to see that if m is even then m^2 must be even too. For the other direction suppose that m is not even and prove that in this case m^2 will not be even either. You could start by noting that if m is not even it must be equal to n+1 for some even number n. You can then work out (n+1)^2 and see if this helps you.

[jason.spade]

I shall show something of the same vein.

If I multiply an even number and an odd number, I will get an even number.