```Date: Mar 22, 2000 5:13 AM
Author: Milo Gardner
Subject: unitary (Egyptian) fractions

Dear David, Joe, and others:I can agree that with the first partitions 1/2, 1/3, 1/7 that fouradditional partitions are needed to solve the 732/733 problem. Thealgebraic identities needed to solve this problem include onlu366/733 = 1/2 - 1/1466245/733 = 1/3 + 2/2199which leaves,121/733 to be paritioned by two terms,as well as one other term smaller than 1/733.That is, I will now go onto the 1/2, 1/4, 1/8 first terms and getback with you all, especially David that listed an 'optimal' solution for 1/2, 1/4. If these fail, I will search a littlelonger using highly composite first partitions that allow theHultsch-Bruins:n/p - 1/A = (nA -p)/Apor,n/p = 1/A + (nA -p)/Apmethod to work, as Fibonacci himself understood in 1202 AD.Yes, it takes a little time to directly solve this problemeven using Fibonacci's indeterminate equation method - thatI do not think that I have seen listed among Eppstein's < 40methods. Regards to all,Milo Gardner
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