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.
A 9 term solution would be
2, 3, 4, 5, 7, 8, 56, 168, 840
Kind of a pain, but after picking first 6 numbers, you know what the smallest possible value for the next would be (in my case it was 54). Make an Exel grid with 54300 on the top (300 is just a big number) and 55300 along the left.
Given the 7th (top) and 8th (left) numbers, you calculate the 9th (bc + ac + bc = abcx =>
c = ab/(abxab) where x is whats left of the .5 after the first 6 variables and a,b,c are the squares of the 7th, 8th, and 9th).
Filling the grid in with the proper equation (sum1/a^21/b^21/c^2 and conditional formatting (for 0) turns up the answer.
Rajal
(p.s. after all this work I sure hope the answer is right! Any independent verification?)

Posted by Rajal
on 20040922 19:21:04 