½ = 1/x² + 1/y² +...+ 1/z²

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

Oops - I didn't realize that Richard had put the exact value of pi^2/6 in his previous post - I only saw the approximation 1.6449 at first glance.  This post adds no new content.  =) 

More specifically, if you've had some differential equations before, you can show that the sum 1/1+1/4+1/9+... + 1/n^2+ ... is equal to PI^2/6.

I like this problem a lot.  Hit a lot of dead ends trying to solve it - always a sign of a great problem.  Still working at it.  Kudos to Frederico. 

Edited on September 20, 2004, 11:05 pm

Posted by David Shin on 2004-09-20 22:51:37