Egyptian number theory Might there be a good historical reference on Egyptian number theory ($ \sim 2000$ B.C.)? The following online reference by a professor at the UCLA indicates that they were aware of the Pythagorean theorem [1]. This makes me wonder whether Egyptian scientists and engineers might have done fundamental work in number theory as well.
In particular, I'd like to know whether they were aware of Euclid's theorem of the infinitude of primes.
References:

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*Allen Klinger. Right Triangles - Pythagorean Theorem
. http://web.cs.ucla.edu/~klinger/dorene/math1.htm


*Thomas Eric Peet. Mathematics in Ancient Egypt. 1931.
 A: Besides the Pythagorean theorem, it appears that the Egyptians had general algorithms for computing the volume of a pyramid [1]. As for number theory, it appears that the theory of Egyptian numbers(i.e. integers which are the sum of Egyptian fractions(circa 3500 BC)) has motivated non-trivial developments in combinatorial number theory:

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*There is a theorem due to Erdős which shows that it is not possible for a Harmonic progression to form an Egyptian number [3].


*In an analysis of integer partitions, Ronald Graham found that if $n$ is an integer exceeding 77 there are positive integers $\{a_i\}_{i=1}^k$ such that $n = \sum_{i=1}^k a_i$ and $\sum_{i=1}^k \frac{1}{a_i} = 1$ [2].


*More recently, Steve Butler, Erdős, and Graham found that any integer may be expressed as a sum of Egyptian fractions with denominators $a_i < a_{i+1}$ and where $a_i$ is the product of three distinct primes [4].
While it is not clear why the Egyptians developed Egyptian fractions [3], the methods used to compute Egyptian numbers in the Rhind papyrus suggest that they had a partial understanding of the difference between prime and composite numbers [5]. Moreover, from my analysis of the available papyri it appears that Egyptian mathematicians focused strictly on algorithmic/constructive methods which did not include a notion of infinity.
This precludes methods such as Archimedes' method of exhaustion or Euclid's existence proof that there are infinitely many primes.
References:

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*Struve, Vasilij Vasil'evič, and Boris Turaev. 1930. Mathematischer Papyrus des Staatlichen Museums der Schönen Künste in Moskau. Quellen und Studien zur Geschichte der Mathematik; Abteilung A: Quellen 1. Berlin: J. Springer


*R. L. Graham. A theorem on partitions. 1963.


*Graham, Ronald L. (2013), "Paul Erdős and Egyptian fractions" (PDF), Erdös centennial, Bolyai Soc. Math. Stud., 25, János Bolyai Math. Soc., Budapest, pp. 289–309


*Steve Butler, Paul Erdős, and R.L. Graham. Egyptian fractions with each denominator having three distinct prime divisors. 2015.


*Abdulrahman A. Abdulaziz. On the Egyptian method of decomposing 2/n into unit fractions. Elsevier. 2007.
A: According to the chapter on Egyptian mathematics and astronomy in the book by O. Neugebauer, The Exact Sciences in Antiquity (1951, 1957), Egyptian mathematics only involved basic arithmetic with positive integers and a restricted class of fractions.  So the answer to your question appears to be "no".
