Question 706285
n is any natural or whole number.
Even Integer: 2n
Odd Integer: 2n+1

Let m be any whole number.
(2(n)+1)(2(n+m)+1)
4n(n+m)+2(n+m)+2n+1
=2(2n(n+m)+(n+m)+n)+1


Notice very carefully that the expression inside the outermost parentheses,
2n(n+m)+(n+m)+n, is a whole number, we may call N, so that
we have 2N+1.  This is an odd number.  Proved!