Date: Mar 22, 2000 8:12 PM
Author: Bill Daly
Subject: Re: unitary (Egyptian) fractions
For what it's worth, I have tested all proper fractions a/b with b prime
and less than 3000, and all of them have an Egyptian fraction
representation of length 7 or less. For some reason, the most
time-consuming fraction was 26/1249, for which I found the following
representation after a little less than 16 minutes:
No doubt this can be improved.
A couple of questions:
1) What is the smallest N for which it is not known whether 4/N has an
Egyptian fraction representation of length 3?
2) Is it known whether the length of the minimal representation for a/b
is O(log(b)), or something similar?
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