
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 29th, 2007, 08:17 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, 03:05 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,281 Thanks: 1965  
October 30th, 2007, 05:28 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, 10:06 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, 11:21 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,281 Thanks: 1965 
Gauss's dissertation related to the fundamental theorem of algebra, whereas his book Disquisitiones Arithmeticae contained the fundamental theorem of arithmetic.

October 31st, 2007, 05:52 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:
 

Tags 
arithmetic, fundamental, theorem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fundamental theorem problem!  vandecm  Calculus  1  November 25th, 2013 07:03 AM 
Is this proof of the fundamental theorem of arithmetic ok?  king.oslo  Algebra  2  September 19th, 2013 11:48 PM 
the fundamental theorem  ray  Algebra  6  April 22nd, 2012 04:50 AM 
Fundamental theorem of calculus  layd33foxx  Calculus  3  December 12th, 2011 08:32 PM 
Fundamental Theorem of Calculus  mrguitar  Calculus  3  December 9th, 2007 02:22 PM 