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fundamental theorem of arithmetic

The Fundamental Theorem of Arithmetic

Idea

The so-called Fundamental Theorem of Arithmetic (sometimes FTA, although this can also mean the Fundamental Theorem of Algebra) is the statement that the ring of integers is a unique factorization domain (UFD). The theorem is much older than the abstract concepts of ring theory, and indeed the concept of UFD is an abstraction of this theorem. Inasumuch as ‘arithmetic’ can refer to number theory, this is a pretty basic theorem in that field.

Statements

Theorem

For every positive natural number nn, there is a unique multiset of prime numbers whose product is nn.

Created on August 30, 2018 at 12:19:30. See the history of this page for a list of all contributions to it.