[math-fun] A cute number theory problem

I came across the following problem: Show that there are an infinite number of pairs (x,y) of positive integers such that 2^(x^2) + 2^(y^2) + 1 is a square. I would suspect that the answer that you'll come up with is the same as what I came up with, but I wondered if it's possible to characterize all (or all but a finite number) of the pairs which work. By this I mean to show that all (x,y) are in one of a finite set of specific sequences, with a possible finite set of exceptions. Victor