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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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Some Thoughts A Conjecture | Comment 10 of 31 |

Will it always be true that the sum of a finite number of distinct terms of the form 1/x (x an integer) will have a denominator that is divisible by p for some p>1?

I have a fairly strong suspicion the answer is yes.  A proof, if someone finds it, would solve the puzzle.

Edited on September 20, 2004, 11:40 pm
  Posted by David Shin on 2004-09-20 23:40:38

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