I've came across this problem some hours ago and, although it looks (and possibly is) just some algebra calculus, I can't get on the right track.

> 
> Find $x$, $y$ integers such that
>  $$ (x+1)^2 + (y+1)^2 + xy(x+y+3)=2 $$
> 
> 
> 

Some basic algebra will lead to:

$$
(x+y)^2 + x(xy+2) + y(xy+2) + xy = 0$$
 $$(x+y)(xy+x+y+2)=-xy$$
Now, some divisibility properties should end the problem.
Well, maybe my approach isn't the right one, but I'm just stuck at this point.

A piece of advice or a hint would be apreciated.