Proof: $a = x^2 - y^2, x - y > 1 \implies a$ is not a prime number I am having trouble doing a proof on the subject:
$a = x^2 - y^2, x - y > 1 \implies a$ is not a prime number.
$a, x, y \in Z$
The book has not yet introduced the theory of congruences, so it should be a 'fairly' simple proof i guess ?
Thanks for your time

$x^2-y^2 = (x-y)(x+y)$ 
if $x-y$ is not zero and $x+y$ is not zero and $(x-y)>1$ so is $(x+y)$ 
then $x^2-y^2$ is divisible by both $(x-y)$ and $(x+y)$ so it is not prime number
my concern is he doesn't mention if both $x$ and $y$ are natural numbers if they are not then this claim would be not correct
