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Question: Egyptian Fractions

Question:Egyptian Fractions

Matt C Anderson 165 Maple 13
rational number-theory
November 22 2020
0

Hello Maple community and others,

It has been proven that every positive
rational number can be represented in 
Egyptian Fraction form

See wikipedia on Egyptian Fractions

We have the fact that the harmonic series diverges
Let Hn = 1 + 1/2 + 1/3 + ... + 1/n.

Then the limit as n goes to infinity of Hn is unbounded.

It seems these two facts go hand in hand.

Is there a procedure in Maple that will give
Egyptian Fraction representation of an arbitrary
rational number?

I made a worksheet with some examples.

egyptian_fractions.mw

egyptian_fractions.pdf

 

Regards,
Matt
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