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 Get one half by squaring (Posted on 2004-09-20)
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.

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

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 Can it be done? | Comment 1 of 31

Since no one else has posted yet, I will:

The only obvious thing is that 1/2² must be included otherwise the rest of the possible tems add to less than .4

I can't find a good place to go from here.

One thing I tried was to keep adding the larget possible term which keeps the sum under .5

1/2² + 1/3² + 1/4² + 1/5² + 1/6² + 1/11² + 1/54² + 1/519² + 1/59429² + 1/19026245²

This is very close, but surely closer can be accomplished with smaller denominators.  Does an exact solution exist?

My guess is no, but I sure can't prove that.

-Jer

 Posted by Jer on 2004-09-20 13:33:25

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