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Technical Report: UTEP-CS-20-119

Published in Applied Mathematical Sciences, 2020, Vol. 14, No. 19, pp. 919-924.


Ancient Egyptians represented fractions as sums of inverses of natural numbers, and they made sure that all these natural numbers are different. The representation as a sum of inverses makes some sense: it is known to lead to an optimal solution to the problem of dividing bread between workers, a problem often described in the Egyptian papyri. However, this does not explain why the corresponding natural numbers should be all different: some representations with the same natural number repeated several times lead to the same smallest number of cuts as the representations that the ancient Egyptians actually used. In this paper, we provide yet another possible explanation of Egyptian fractions -- based on fairness; this idea explains also why all the natural numbers should be different.

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