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- In [[mathematics]], the '''unique factorization theorem''', also known as the '''fundamental theorem of arithmetic''' state ...om which all other whole numbers can be assembled through multiplication. Unique factorization is the foundation for most of the structure of whole numbers as described b3 KB (479 words) - 12:12, 9 April 2008
- ...which whole numbers. Actually, Euclid didn't show that these numbers have unique factorization, but only that if a whole number is a product of distinct primes p_1 p_2 p_ ...ue factorization". However, there are other mathematical objects for which unique factorization is an important concept: polynomial rings and rings of integers in number f7 KB (1,092 words) - 12:14, 9 April 2008
- #Redirect [[Unique factorization]]34 bytes (3 words) - 15:56, 20 May 2008
- | pagename = Unique factorization | abc = Unique factorization685 bytes (60 words) - 09:26, 15 March 2024
- 12 bytes (1 word) - 08:03, 15 November 2007
- ...r theorem]]) would either be nonsensical, or at least more complicated, if unique factorization did not hold. == A number system where unique factorization fails ==9 KB (1,496 words) - 06:25, 23 April 2008
- 134 bytes (20 words) - 15:55, 20 May 2008
- Auto-populated based on [[Special:WhatLinksHere/Unique factorization]]. Needs checking by a human.574 bytes (75 words) - 21:21, 11 January 2010
Page text matches
- #Redirect [[Unique factorization]]34 bytes (3 words) - 15:59, 20 May 2008
- #REDIRECT [[Unique factorization]]34 bytes (3 words) - 14:07, 12 May 2007
- #Redirect [[Unique factorization]]34 bytes (3 words) - 22:53, 3 April 2008
- #REDIRECT [[Unique factorization]]34 bytes (3 words) - 14:08, 12 May 2007
- #Redirect [[Unique factorization]]34 bytes (3 words) - 22:54, 3 April 2008
- #Redirect [[Unique factorization]]34 bytes (3 words) - 15:56, 20 May 2008
- #Redirect [[Unique factorization]]34 bytes (3 words) - 15:57, 20 May 2008
- #Redirect [[Unique factorization]]34 bytes (3 words) - 15:57, 20 May 2008
- #Redirect [[Unique factorization]]34 bytes (3 words) - 15:58, 20 May 2008
- | pagename = Unique factorization | abc = Unique factorization685 bytes (60 words) - 09:26, 15 March 2024
- {{r|unique factorization}} {{r|unique factorization domain}}356 bytes (46 words) - 13:02, 29 November 2008
- In [[mathematics]], the '''unique factorization theorem''', also known as the '''fundamental theorem of arithmetic''' state ...om which all other whole numbers can be assembled through multiplication. Unique factorization is the foundation for most of the structure of whole numbers as described b3 KB (479 words) - 12:12, 9 April 2008
- ...d domain <math>A</math> is a principal ideal domain if and only if it is a unique factorization domain.2 KB (306 words) - 15:51, 10 December 2008
- One method of finding the greatest common divisor of two integers involves [[Unique factorization|factoring]] both into [[prime number]]s:4 KB (570 words) - 18:05, 1 July 2009
- {{r|Unique factorization}}225 bytes (28 words) - 13:16, 14 June 2008
- ...r theorem]]) would either be nonsensical, or at least more complicated, if unique factorization did not hold. == A number system where unique factorization fails ==9 KB (1,496 words) - 06:25, 23 April 2008
- {{r|Unique factorization}}454 bytes (55 words) - 03:14, 21 October 2010
- ...or polynomials]] may be expressed as stating that for polynomials over a [[unique factorization domain]], the content of the product of two polynomials is the product of t971 bytes (132 words) - 15:00, 29 October 2008
- ...which whole numbers. Actually, Euclid didn't show that these numbers have unique factorization, but only that if a whole number is a product of distinct primes p_1 p_2 p_ ...ue factorization". However, there are other mathematical objects for which unique factorization is an important concept: polynomial rings and rings of integers in number f7 KB (1,092 words) - 12:14, 9 April 2008
- {{r|Unique factorization}}556 bytes (69 words) - 11:49, 11 January 2010
- {{r|Unique factorization}}498 bytes (64 words) - 16:23, 11 January 2010
- {{r|Unique factorization}}535 bytes (68 words) - 18:22, 11 January 2010
- Auto-populated based on [[Special:WhatLinksHere/Unique factorization]]. Needs checking by a human.574 bytes (75 words) - 21:21, 11 January 2010
- ...nt applications to other fields. These include the [[unique factorization|unique factorization theorem]], [[algebraic number fields]], [[elliptic curves]], and [[modular2 KB (340 words) - 12:36, 22 February 2012
- {{r|Unique factorization}}927 bytes (119 words) - 16:24, 11 January 2010
- ...e theory of vector spaces, in the same way that the [[unique factorization|unique factorization theorem]] is of fundamental importance in the study of integers. For insta3 KB (464 words) - 19:45, 1 December 2008
- Euclid's lemma is used in the proof of the [[unique factorization theorem]], which states that a number cannot have more than one prime facto2 KB (322 words) - 12:51, 18 December 2007
- {{r|Unique factorization}}1 KB (174 words) - 20:03, 11 January 2010
- ...sbaum published in 1959, it was shown that every regular local ring is a [[unique factorization domain]].1 KB (191 words) - 00:03, 21 February 2010
- :: in fact, it factors completely into prime numbers, due to unique factorization8 KB (1,252 words) - 11:12, 30 October 2011
- :: in fact, it factors completely into prime numbers, due to unique factorization ...Again, the required statement and proof would have to be included on the unique factorization page. My preference, actually, is to have the complete proof of an infinit29 KB (4,820 words) - 02:18, 2 April 2008
- ...he sum and the product now follows from the fact that every number has a [[unique factorization]] into primes. This also indicates the connection between the function <mat4 KB (703 words) - 12:02, 13 November 2007
- ...property of the integers. In fact, in other number systems, the analog of unique factorization FAILS to be true, which is what Gauss realized and motivated him to prove t :::# We have an article about [[unique factorization]]. Do we need a different article about the [[Fundamental Theorem of Arithm36 KB (6,274 words) - 16:22, 27 November 2008
- The importance of prime numbers in arithmetic comes in large part from the [[unique factorization]] of numbers. The existence of a single unique factorization into prime numbers is formalized as the [[Fundamental Theorem of Arithmetic18 KB (2,917 words) - 10:27, 30 August 2014
- ...why it's impossible that no prime divides ''N'') by adding a discussion on unique factorization. ...lence of the two definitions for prime numbers is in fact quite important (unique factorization depends on it), and should perhaps be stressed more.44 KB (7,323 words) - 23:34, 30 March 2008
- The importance of prime numbers in arithmetic comes in large part from the [[unique factorization]] of numbers. ...imes 2 \times 7 \times 2 \times 3 \times 2 \times 5</math>. Because of the unique factorization of numbers into prime numbers, an analogy can be made between the role prim14 KB (2,281 words) - 12:20, 13 September 2013
- I do think it is important to alter the very misleading statement about "unique factorization" in the currently approved version. [[User:Michael Hardy|Michael Hardy]] 226 KB (905 words) - 23:27, 13 January 2008
- ...t to compute a GCD, you can first factor (which requires knowing about the Unique Factorization theorem), then use the largest of the exponents common to each number to fo13 KB (2,027 words) - 10:29, 21 April 2010
- ** [[Unique factorization domain]] (UFD)10 KB (1,667 words) - 13:47, 5 June 2011
- ...that emulated divisors of numbers, in particular in a way that allowed for unique factorization in what we now call rings of integers in number fields.)9 KB (1,551 words) - 10:52, 14 November 2007
- The next step, however, is mathematical: the cryptanalyst [[Unique factorization|factors]] the separations, and discovers the all have 5 as a prime factor.35 KB (5,600 words) - 10:40, 15 May 2024
- ...ster Volunteer Force]], [[Umberto Eco]], [[UNESCO]], [[Union Blockade]], [[Unique factorization]], [[United Auto Workers]], [[United States Army]], [[United States Federal45 KB (4,912 words) - 07:29, 24 April 2024