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