Egyptian fractions

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An Egyptian fraction is the sum of distinct unit fractions, such as $\scriptstyle {\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{16}}\,$. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number $\scriptstyle {\frac {n}{d}}\,$; for instance the Egyptian fraction above sums to 43/48.

Every positive rational number can be represented by an Egyptian fraction.

External links

• Dr Ron Knott, Egyptian Fractions, © 1996-2008.