Can you solve the following equation?

½ = 1/x² + 1/y² +...+ 1/z²

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

Will it always be true that the sum of a finite number of distinct terms of the form 1/x² (x an integer) will have a denominator that is divisible by p² for some p>1?

I have a fairly strong suspicion the answer is yes. A proof, if someone finds it, would solve the puzzle.

*Edited on ***September 20, 2004, 11:40 pm**