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Definition 2024

Egyptian fraction ‎(plural Egyptian fractions)

(number theory) A representation of a rational number as a sum of distinct unit fractions.

The fraction ${\frac {7}{10}}$ can be written as the Egyptian fraction ${\frac {1}{2}}+{\frac {1}{5}}$

The calculation of $M^{N}$ where both M and N are real numbers can be done by expressing N as the sum of an integer h and an Egyptian fraction $1/g_{1}+1/g_{2}+1/g_{3}+...$ . Then $M^{N}=M^{h}{\sqrt[{g_{1}}]{M}}{\sqrt[{g_{2}}]{M}}{\sqrt[{g_{3}}]{M}}...$ where each of the roots can be calculated by means of the Newton–Raphson method.
(number theory, rare) A unit fraction.