The Fundamental Theorem of Arithmetic

John W. Dawson

doi:10.1007/978-3-319-17368-9_6

The Fundamental Theorem of Arithmetic

John W. Dawson

https://doi.org/10.1007/978-3-319-17368-9_6

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Publication Date: Jan 1, 2015

#Fundamental Theorem Of Arithmetic #Theorem Of Arithmetic + Show 1 more

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Abstract

The Fundamental Theorem of Arithmetic (FTA) states that every integer greater than 1 has a factorization into primes that is unique up to the order of the factors. The theorem is often credited to Euclid, but was apparently first stated in that generality by Gauss. Note that the statement has two parts: First, every integer greater than 1 has a factorization into primes; second, any two factorizations of an integer greater than 1 into primes must be identical except for the order of the factors. The proofs of each of those parts will thus be considered separately.

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