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Favorable Numbers (Posted on 2006-11-02) Difficulty: 2 of 5
Call a positive integer n "favorable" if there is a set of n distinct positive integers whose reciprocals' sum adds to 1.

How many unfavorable numbers are there?

See The Solution Submitted by Gamer    
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Solution Inductive answer | Comment 3 of 4 |
If 1/a+1/b+...+1/y+1/z=1, and 1<a<b<...<y<z, then 1/a+1/b+...+1/y+1/(z+1)+1/z(z+1)=1, and 1<a<b<....<y<z+1<z(z+1), so if N is favorable, it follows that N+1 is also favorable.

Since 1/2+1/3+1/6=1, all numbers from 3 onwards are favorable. Add that N=1 is favorable, and N=2 isn't, and you get the complete answer.

  Posted by Federico Kereki on 2006-11-02 12:43:16
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