If x is an odd integer and y is an odd integer then xy is an odd integer. Use direct proof to prove the following.

I am stumped on where to go from here. All I know is that the definition of an odd integer is n=2k+1 where n is the integer.

So I assume that I need x=2n+1 and y=2m+1 but I really don't know where to go from here. This seems really simple but where to start is stubborn to me.