TITLE: Prove that square of even integer is even.
QUESTION [9 upvotes]: Is my proof correct?
Suppose $n=2m$
  is an even integer. Since $n=2m$
 , then $n^{2}=(2m)^{2}$
$n^{2}$   =   $(2m)^{2}$
=   $4m^{2}$
=$2(2m^{2)}$
Since $(2m^{2})$
  is an integer and $2(2m^{2})$
  is in the form $2m$
 , we have proven that the square of an even integer is even.

REPLY [5 votes]: Yes, that is pretty much it. Good job.