An annoying algebra probelm

[Guest AkaMan]

consider the set :

A = {(x,y) ε (N × N) | x <y , 2x^2 - 5xy + 2y^2 - x - y - 1 = 11}

 

The problem is to determine number of A's members. I have found x=2, y=6 as an answer. But I haven't been able to prove it's uniqueness and I'm not even sure about that. Because my solution is not complete, I don't bring it here. Can anyone help me on this?

[matt grime]

You recognize that that is an ellipse in R^3 right? So there are only a finite number of things to check.

[Guest AkaMan]

Ahhhhhhhhhhh, goddamit...

Now I got it!!

Thanks alot. This was gonna make me mad. I hadn't thought on it in this way!!