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 September 14th, 2013, 04:26 PM #1 Senior Member   Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2 Is this proof of the fundamental theorem of arithmetic ok? Hello there, I am a university student, and I was just trying to prove the fundamental theorem of arithmetic. I proved that there are an infinite number of primes. Now I have to prove that numbers can only be expressed uniquely. is the smallest product of primes which could be expressed in more than one way. It would be impossible to construct this with fewer than two primes: and This is my contradiction: and is a smaller number than , and it is possible to express this number in more than one way. But was the smallest number possible to construct from primes. This is the contradiction. What do you think? Criticism is most welcome. Thank you for your time. Kind regards, Marius September 19th, 2013, 11:17 AM #2 Senior Member   Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2 Re: Is this proof of the fundamental theorem of arithmetic o Anyone? M September 19th, 2013, 10:48 PM   #3
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Re: Is this proof of the fundamental theorem of arithmetic o

You proof is not right. Here are some problems with it:

Quote:
 Originally Posted by king.oslo is the smallest product of primes which could be expressed in more than one way. It would be impossible to construct this with fewer than two primes: and
n could be the product of more than 2 primes and a different number of primes in each case. E.g.:

and

Quote:
 Originally Posted by king.oslo This is my contradiction: and is a smaller number than , and it is possible to express this number in more than one way. But was the smallest number possible to construct from primes. This is the contradiction.
You haven't shown that is prime. It's simply a number less than n. It could even be 0. Tags arithmetic, fundamental, proof, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post vandecm Calculus 1 November 25th, 2013 06:03 AM ray Algebra 6 April 22nd, 2012 03:50 AM Aurica Calculus 1 June 14th, 2009 08:04 AM johnny Algebra 11 December 21st, 2007 09:51 PM johnny Number Theory 5 October 31st, 2007 04:52 AM

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