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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Can it be done? | Comment 1 of 31

Since no one else has posted yet, I will:

 

The only obvious thing is that 1/2 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

1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/11 + 1/54 + 1/519 + 1/59429 + 1/19026245

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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