The Rhind papyrus is an ancient Egyptian mathematical text copied by the scribe Ahmes around 1550 BC from a now-lost earlier source. It was purchased in Luxor by Alexander Henry Rhind in 1858, and most of it was acquired by the British Museum in London in 1865, where the two main sections are now cataloged as EA10057 and EA10058. Smaller fragments are held by the Brooklyn Museum in New York (British Museum; History of Mathematics Project).
The papyrus has three parts. The first contains reference tables, including the 
table, together with arithmetic
and algebra problems. The
second contains geometry problems,
and the third is a miscellany of problems.
A bootleg copy that listed the initial table of Egyptian fraction representations for fractions of the form
and 84 practical problems
and solutions was published in Germany in 1873. Hot debates between British scholars,
only seeing additive contents, and German scholars, sometimes seeing higher forms
of math, continued until the 1920s, when the debates simmered, nearly dying out during
the 1930s and World War II.
The 
table shows 50 
and 
rational numbers being
converted to exact and concise Egyptian fractions,
starting at 2/3 and progressing to 2/101. The most difficult cases were the 
conversions. They were first decoded
by Hultsch in 1895, independently confirmed by Bruins in 1950, showing that a form
of subtle number theory was present. Evidence suggests
that early Egyptians used a form of number theory
for these conversions. Egyptians used two algebraic
identities to find unit fraction series.
To the ancient scribe, there was a straightforward method of finding Egyptian fractions for numbers of the form 
. One basic rule was first published in 2002, and states
that
 |
(1)
|
where 
.
For example, to find 
,
let 
,
and 
,
so
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
as listed in the 
table.
There were only three fractions appearing that cannot be decomposed using this rule: 2/35, 2/91 and 2/95.
Taken together, the 
table and the Egyptian mathematical
leather roll show that Middle Kingdom students studied ways to convert any rational number to exact and optimal unit
fraction series. Practical applications of this early number
theory are explained by five Akhmim wooden
tablet divisions, the Moscow
Mathematical Papyrus, Kahun, the Rhind papyrus's 84 problems,
and several other Middle Kingdom mathematical texts.
Table."