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Egyptian fractions

I found this on Quora. What would the standard algorithm be, I wonder.
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David JoyceDavid Joyce, Professor of Mathematics at Clark Uni… (more)

Suppose you have five loaves of bread and you want to divide them evenly among seven people.  You could cut the five loaves in thirds, then you’d have 15 thirds.  Give two of them to each of the seven people.  You’ll have one third of a loaf left.  Cut it into seven equal slices and give one to each person.

\frac57=\frac13+\frac13+\frac1{21}
There may be other solutions.   a = b = 3, c = 21.   (Egyptian Fractions)

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