Determine all positive integer solutions of x

^{2y}+(x+1)

^{2y}=(x+2)

^{2y}
Of course, for y>1 you could use Fermat's theorem, but that would be unsporting!

For y=1, x=1 gives the only answer: 3^2+4^2=5^2, since it's easy to show that x^2+(x+1) ^2 is always greater than (x+2) ^2 for x>3, so that's the only answer for y=1.

And I'm tempted to cheat, and apply the not-so-long-ago-proved Fermatīs theorem to show there is no answer for y greater than 1...