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Interesting problem on Egyptian Numbers

Source:

9/1/2010
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 11. For example, 32=2+3+9+1832 = 2 + 3 + 9 + 18 is Egyptian because 12+13+19+118=1\frac 12 +\frac 13 +\frac 19 +\frac{1}{18}=1 . Prove that all integers greater than 2323 are Egyptian.
number theoryegyptian fractionsIMO ShortlistIMO LonglistAdditive Number Theory