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Get one half by squaring (Posted on 2004-09-20) Difficulty: 4 of 5
Can you solve the following equation?

= 1/x + 1/y +...+ 1/z

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

See The Solution Submitted by Federico Kereki    
Rating: 4.2500 (12 votes)

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No Subject | Comment 4 of 31 |
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
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