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 October 29th, 2007, 07:17 PM #1 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Fundamental theorem of Arithmetic I think the FTOA is in number theory section. Can anyone tell me the basic definition of FTOA? Does it has to do anything with prime numbers? October 30th, 2007, 02:05 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 October 30th, 2007, 04:28 AM   #3
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Re: Fundamental theorem of Arithmetic

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 Originally Posted by johnny Can anyone tell me the basic definition of FTOA? Does it has to do anything with prime numbers?
Yes, and yes.

. . .

Oh, you wanted a statement of it. It says that every positive integer has a unique (up to order of factors) decomposition into primes. 12 = 2 * 2 * 3 = 2 * 3 * 2 = 3 * 2 * 2, but these are just reorderings.

Essentially, the natural numbers can be thought of just as well as a multiset of prime factors (2 * 2 * 3) as an additive collection (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1). If you have two prime factorizations, and they don't match, then they represent different numbers. This isn't true in all number systems, and it's an important fact about whole numbers.

The greatest mathematician did his dissertation (at the age of 21 or 22) on the fundamental theorem of arithmetic. October 30th, 2007, 09:06 AM   #4
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Re: Fundamental theorem of Arithmetic

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 Originally Posted by CRGreathouse The greatest mathematician did his dissertation (at the age of 21 or 22) on the fundamental theorem of arithmetic.
No bias, there Although Gauss is, well... Gauss. October 30th, 2007, 10:21 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 Gauss's dissertation related to the fundamental theorem of algebra, whereas his book Disquisitiones Arithmeticae contained the fundamental theorem of arithmetic. October 31st, 2007, 04:52 AM   #6
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 Originally Posted by skipjack Gauss's dissertation related to the fundamental theorem of algebra, whereas his book Disquisitiones Arithmeticae contained the fundamental theorem of arithmetic.
Sorry, I flipped those. Wasn't Disquisitiones Arithmeticae even earlier, though? Gauss sure was something else. Tags arithmetic, fundamental, 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 king.oslo Algebra 2 September 19th, 2013 10:48 PM ray Algebra 6 April 22nd, 2012 03:50 AM layd33foxx Calculus 3 December 12th, 2011 07:32 PM mrguitar Calculus 3 December 9th, 2007 01:22 PM

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