Noun
(number theory) A representation of a rational number as a sum of distinct unit fractions.
The fraction
7
10
{\displaystyle {\frac {7}{10}}}
can be written as the Egyptian fraction
1
2
+
1
5
{\displaystyle {\frac {1}{2}}+{\frac {1}{5}}}
.
The calculation of
M
N
{\displaystyle 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
+
.
.
.
{\displaystyle 1/g_{1}+1/g_{2}+1/g_{3}+...}
. Then
M
N
=
M
h
M
g
1
M
g
2
M
g
3
.
.
.
{\displaystyle 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.
Source: en.wiktionary.org