Can the perimeter of a rectangle be any integer value

Let's just say it can. then let w=width and l=length. then the perimeter would be 2w+2l
which we can write as 2(w+l). but w+l it's an integer because integers are closed under addition. then the perimeter is even because it has 2 as a factor. if the perimeter had to be even it cannot be an odd integer. and obviously it cannot be any negative integer either. also it cannot be 0. that leaves only even integers as possibilities among the integers