Egyptian fraction

Finite sum of distinct unit fractions

An Egyptian fraction is a finite sum of distinct unit fractions, such as 1 2 + 1 3 + 1 16 . {\displaystyle {\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 a b {\displaystyle {\tfrac {a}{b}}} ; for instance the Egyptian fraction above sums to 43 48 {\displaystyle {\tfrac {43}{48}}} .

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