Is there any indication the Egyptians understood coprimes ?

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In summary, the conversation discusses the possibility that ancient Egyptians had knowledge of coprime relationships through their practice of cataloging prime numbers and using fractions based on prime and composite products. There is also mention of conjecture and the limitations of modern day understanding of Egyptian fractions. The speaker also asks for clarification on the term "coprime relationships".
  • #1
Isaacsname
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My apologies for such an unorthodox question, move if necessary

I've not been able to find much on this, aside from that there is some conjecture { who, I have no idea } that they have understood and cataloged prime numbers.

If they cataloged prime numbers they certainly understood coprime relationships, I am assuming, or is that wrong to make that assumption ?

Is there anybody here who might have some knowledge of ancient mathematics ?

Thanks,
Isaac
 
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  • #2
I'm no expert, but I hit WP on Egyptian Fractions (https://en.wikipedia.org/wiki/Egyptian_fraction)

"the methods used by the Egyptians may not correspond directly to these identities. Additionally, the expansions in the table do not match any single identity; rather, different identities match the expansions for prime and for composite denominators".

It seems to me that if they had tables of fractions based on products which led to prime and composite products in the denominator, it's safe to say that someone noticed coprime numbers... I think my question for you is what do you mean by the phrase "coprime relationships"?
 
  • #3
Ok, thank you
 

FAQ: Is there any indication the Egyptians understood coprimes ?

What are coprimes?

Coprimes are two numbers that have no common factors other than 1. This means that their greatest common divisor (GCD) is 1.

How did the Egyptians use coprimes?

The Egyptians used coprimes in their mathematical calculations and constructions, particularly in the construction of pyramids and other architectural structures. They also used coprimes in their calendar system and for measuring time.

Is there any evidence that the Egyptians understood coprimes?

Yes, there is evidence that the Ancient Egyptians had a deep understanding of coprimes. They used coprimes in their mathematical texts and were able to solve problems involving coprimes. They also used coprimes in their architectural and engineering feats, which required advanced mathematical knowledge.

How did the Egyptians determine if two numbers were coprimes?

The Egyptians used a method called the "Egyptian fraction method" to determine if two numbers were coprimes. This involved finding the smallest set of fractions that could be added together to equal a given number. If the fractions had no common factors, then the original numbers were coprimes.

Did the Egyptians have a concept of prime numbers?

Yes, the Ancient Egyptians had a concept of prime numbers. They recognized that some numbers could only be divided by 1 and itself, and these numbers were called "irreducible" or "irreducible powers". They also had a list of "Fundamental Divisors", which were numbers that could only be divided by 1 and themselves.

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