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Victor Klee and Stan Wagon's book is out-of-date with respect to an Egyptian Fractions chapter, citing the conversion of 5/121 by a greedy algorithm solution and an improved but un-concise solution ( published by Bleicher):
5/121 = 1/35 + 1/1225 + 1/3477 + 1/7081 + 1/11737
on page 206. In 2002, 2005, 2008 and 2010 an improved RMP 2/n table red number method was broken and published on-line in the context of the EMLR, RMP 36 and RMP 37 such that:
5/121 = 1/11*(5/11)
with 5/11 *(3/3) = 15/33 = (11 + 3 + 1)/33 = 1/3 + 1/11 + 1/33
reaching
5/121 = 1/11*(1/3 + 1/11 + 1/33) = 1/33 + 1/121 + 1/363
as Ahmes,the RMP scribe, in 1650 BCE solved
2/95 by 1/5*(2/19)*(12/12) = (19 + 3 + 2)/1140 = 1/60 + 1/380 + 1/570
Wikipedia has posted the 2/95 solution on its Rhind Mathematical Papyrus page
http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus
Stan Wagon also discussed Fibonacci's 1202 AD Liber Abaci and the conversion of 4/23 by the un-concise modern solution on page 177:
4/23 = 1/7 + 1/33 + 1/1329 + 1/23536559
rather than following Fibonacci's solution
(4/23 - 1/6) = (24 -23)/138
recorded in one of three unit fraction notations.
Ahmes' arithmetic discussed on
http://ahmespapyrus.blogspot.com/2009/01/ahmes-papyrus-new-and-old.html
would have solved 4/23 with LCM 6 finding
4/23*(6/6) = 24/138 = (24 + 1)/138 = 1/6 + 1/138
In RMP 36 and RMP 37 Ahmes used a subtraction method that would have reported
(4/23 - 1/6) = 1/138 by recording
4/23 = 1/6 + 1/138
Hence, Greeks, Arabs and medieval scribes like Fibonacci copied Egyptian number theory, dated to 2050 BCE, to record exact rational number' unit fraction mathematics.
Best Regards to the ancient scribes and modern math historians. Modern books on ancient math and modern unsolved problems need to be updated from time to time.
Milo Gardner
 

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