
Re: unitary (Egyptian) fractions
Posted:
Mar 22, 2000 8:12 PM


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 timeconsuming fraction was 26/1249, for which I found the following representation after a little less than 16 minutes:
26/1249 = 1/49 + 1/2449 + 1/6245053 + 1/40696362770053 + 1/1731475485562249549506926522 + 1/1558019571407872739990323772114944573152396986805272178 + 1/98934242784399918989385559529298980395177208662134783303
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?
Regards,
Bill
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