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Suyogya
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If the euclid division lemma was not discovered by euclid himself, then why was the name "euclid lemma"? (https://en.wikipedia.org/wiki/Euclidean_division#History)
From the same article, "it seems that he did not know the existence and uniqueness theorem". My interpretation is that he (Euclid) could perform the division, but was unaware of the details of existence and uniqueness.Suyogya said:If the euclid division lemma was not discovered by euclid himself, then why was the name "euclid lemma"? (https://en.wikipedia.org/wiki/Euclidean_division#History)
Wikipedia said:The term "Euclidean division" was introduced during the 20th century as a shorthand for "division of Euclidean rings".
The Euclid Division Lemma, also known as the Euclidean Division Algorithm, is a fundamental theorem in number theory that states that given two positive integers, there exists a unique quotient and remainder when one is divided by the other.
Euclid was a Greek mathematician who lived around 300 BC and is often referred to as the "Father of Geometry." His legacy includes his famous work, "The Elements," which is a compilation of mathematical proofs and theories that have greatly influenced the development of mathematics.
The Euclid Division Lemma is significant because it provides a method for finding the greatest common divisor of two numbers, which is a crucial concept in number theory and has many applications in fields such as cryptography and computer science.
Some examples of applications of the Euclid Division Lemma include finding the simplest form of a fraction, determining whether two numbers are relatively prime, and solving problems involving modular arithmetic.
The Euclid Division Lemma is the basis for the Euclidean algorithm, which is an efficient method for finding the greatest common divisor of two numbers. The algorithm uses repeated applications of the division lemma to simplify the problem until a solution is found.