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Prove if $n$ is an integer, $n \geq 2$, then either $n$ is prime or else can be factored into a product of primes.

I don't quite understand (at all) how to connect this to the fundamental theorem of arithmetic, so ANY help would be appreciated!

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This IS the Fundamental Theorem of Arithmetics (minus the part on uniqueness of the factorisation). –  user39280 Mar 18 '13 at 18:14
Somehow I was brought up to believe that the fundamental theorem of arithmetic is the uniqueness assertion: A number cannot have more than one prime factorization. –  Michael Hardy Mar 18 '13 at 18:18
@ Michael Hardy: Well yes! The existence argument is (very) straightforward so the "non trivial" and important part of the theorem is uniqueness. @Jacob en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic contains the required answer. –  user39280 Mar 18 '13 at 18:23

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