I have read right from school that prime factorization is unique, but have never found proof for this. Can someone show me the proof?
How can we prove that among positive integers any number can have only one prime factorization?
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prime-numbers
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6http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic – 2012-02-27
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0@gigahari: The result is not difficult, but it takes a fair while to build the required machinery. You could work your way to it by following Wikipedia links. But best would be to go through the beginnings of a book on Elementary Number Theory. I think there are some freely available, but best would be to find such a book at your local library. – 2012-02-27
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11I am honestly baffled that some people (with internet access!) seem to be so unable to find the answers to their questions on the internet. The OP says that s/he has "never found proof for this". As an experiment, I cut and pasted the title of the question into google. The first hit was (surprise!) this very page. The second hit is http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic.... – 2012-02-27
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8To adjust the ancient proverb: if there is a magical web that will do much of your fishing for you automatically, then surely we help someone out more by telling him about this magical web and showing him how easy it is to use then catching individual fish for him (and maybe using the magic web to do it). No? – 2012-02-27
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1@PeteL.Clark I did search, but somehow assumed the answer to my question would not be at this link. But I now concede it was a mistake. Having never seen the fish I was looking for, I threw it back into the waters, when the magical web presented it to me! – 2012-02-27
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1I think this may be relevant: prime factorization is not unique for certain representations. For example, if you include all complex numbers of the form $a+ib\sqrt{5}$ where $a,b$ are integers. But presumably you are referring to the case of only integers, which does have unique factorization. – 2012-12-13