An Egyptian number is a positive integer that can be expressed as a sum of positive integers, not necessarily distinct, such that the sum of their reciprocals is 1. For example, 32 = 2 + 3 + 9 + 18 is Egyptian because 1/2+1/3+1/9+1/18=1 . Prove that all integers greater than 23 are Egyptian.
Fibonacci proved that any fraction can be represented as a sum of distinct unit fractions, and can be constructed using the identity 1/a = 1/(a+1) + 1/(a(a+1)).
This is not a proof, but might lead another to finding the proof without having to solve this problem from scratch.
Edited on February 9, 2013, 11:45 pm
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Posted by Dej Mar
on 2013-02-09 23:27:09 |
A simple answer, probably not as expected
