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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  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Fundamental theorem of Arithmetic Quote:
. . . 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  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Fundamental theorem of Arithmetic Quote:
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  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
 

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