My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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?
johnny is offline  
 
October 30th, 2007, 02:05 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 20,484
Thanks: 2041

See http://en.wikipedia.org/wiki/Fundame..._of_arithmetic.
skipjack is offline  
October 30th, 2007, 04:28 AM   #3
Global Moderator
 
CRGreathouse's Avatar
 
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:
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.
CRGreathouse is offline  
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:
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.
cknapp is offline  
October 30th, 2007, 10:21 AM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 20,484
Thanks: 2041

Gauss's dissertation related to the fundamental theorem of algebra, whereas his book Disquisitiones Arithmeticae contained the fundamental theorem of arithmetic.
skipjack is offline  
October 31st, 2007, 04:52 AM   #6
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Quote:
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.
CRGreathouse is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

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 06:03 AM
Is this proof of the fundamental theorem of arithmetic ok? king.oslo Algebra 2 September 19th, 2013 10:48 PM
the fundamental theorem ray Algebra 6 April 22nd, 2012 03:50 AM
Fundamental theorem of calculus layd33foxx Calculus 3 December 12th, 2011 07:32 PM
Fundamental Theorem of Calculus mrguitar Calculus 3 December 9th, 2007 01:22 PM





Copyright © 2019 My Math Forum. All rights reserved.