½ = 1/x² + 1/y² +...+ 1/z²

All variables must be different, positive integers, and there must be a finite number of terms.

Peruse the following for some interesting 411:

Federico (not Frederico, by the way, David) was almost certainly thinking Egyptian here. This problem may have been solved by Ron Graham, but I do not have access to Proceedings of the London Math. Society. I tend to think that the problem may be more of a Code Red, difficulty 5 rather than Code Orange, difficulty 4.