## Proof That The Difference of The Square of Two Odd Numbers is Divisible By 4

Any odd number can be written in the form
$2n+1$
where
$n$
is any number, so let two odd numbers be
$2n+1$
and
$2m+1$
.
Then
\begin{aligned} (2n+1)^2-(2m+1)^2 &= = (4n^2+4n+1) \\ &-(4m^1+4m+1) \\ &= 4n^2 +4n-4m^2-4m \\ &= 4(n^2+n-m^2-m)\end{aligned}

Proved.