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.

Say there are 'n' terms on the left, and say 'a' is the
largest integer on the left.

Then n * (1/a^2) > 1/2 or a^2 < 2n.

But n <= a, giving n^2 <= a^2 < 2n or n < 2.

Given the irrationality of 2 it's clear n = 1 is
not a solution, so there are no solutions.

Posted by xdog on 2004-09-20 18:25:08