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- ...arithmetic]] holds. More precisely an integral domain <math>R</math> is a unique factorization domain if for any nonzero element <math>r\in R</math> which i * This representation is unique up to units and reordering, that is if <math>r = p_1p_2\cdots p_n = q_1q_2\6 KB (1,217 words) - 22:05, 23 August 2009
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- The accomplishments of every student are unique, and there is no way to measure that success. However, we try to record an5 KB (642 words) - 17:48, 22 December 2024
- ...math>a</math> or <math>b-c</math>—a contradiction.) This inverse is unique, and each number is the inverse of its inverse. If one integer <math>a</ma4 KB (639 words) - 00:53, 2 February 2023
- ...n the coefficients of the polynomial. We can solve this system and find a unique solution when we have as many equations as we do coefficients. Thus, given6 KB (1,100 words) - 14:57, 30 August 2024
- ...uct of cyclic groups of prime order where the set of prime power orders is unique. We can do this because if any two prime powers are not coprime then <math16 KB (2,660 words) - 22:42, 28 August 2024
- Orthic triangles are not unique to their mother triangle; one acute and one to three obtuse triangles are g8 KB (1,408 words) - 08:39, 10 July 2024
- ...a product of primes ([[permutation|permutations]] not withstanding). This unique [[prime factorization]] plays an important role in solving many kinds of [[6 KB (1,036 words) - 17:26, 2 September 2024
- ...tal Theorem of Arithmetic]] tells us that every [[positive integer]] has a unique prime factorization, up to changing the order of the terms.3 KB (496 words) - 21:14, 5 January 2024
- ...League''' ('''NOML'''), formerly known as the '''Cody Bowl''', is a highly unique and challenging [[mathematics competition]] for high school and college stu3 KB (452 words) - 10:21, 25 June 2006
- ...at <math>{x}</math>.") If such a matrix <math>M</math> exists, then it is unique, and it is called <math>F'(x)</math>. Intuitively, the fact that <math>\fr12 KB (2,377 words) - 10:48, 22 July 2009
- ...e this video link for detailed explanation of the proof and the concept of unique factorization: https://youtu.be/jfDbnz-Bp_g3 KB (453 words) - 10:13, 9 June 2023
- ...ation in an improper fractional base. (Note that this means there is not a unique representation for each number in an improper fractional base.)787 bytes (118 words) - 18:20, 23 October 2010
- ...\mathcal{Y}</math> in the ordered pair <math>(x,y)</math>, there exists a unique <math>x \in \mathcal{X}</math>.4 KB (743 words) - 23:28, 17 November 2024
- ...is the center of the [[incircle]]. Every [[nondegenerate]] triangle has a unique incenter.2 KB (381 words) - 18:38, 24 November 2011
- <math>\mathbb{Z}</math>: the [[integer]]s (a [[unique factorization domain]]).8 KB (1,401 words) - 12:11, 17 June 2008
- of a unique combination of [[prime number]]s, the zeta function can be9 KB (1,547 words) - 02:04, 13 January 2021
- ...adratic equation that have <math>3</math> terms and contain <math>1</math> unique root.954 bytes (155 words) - 00:14, 29 November 2023
- ...e unique. Fortunately, it is always the case that if a limit exists, it is unique. a contradiction. Therefore limits are unique, as we wanted.7 KB (1,327 words) - 17:39, 28 September 2024
- The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The l12 KB (1,792 words) - 12:06, 19 February 2020
- ...f(x)</math> where the coefficient of <math>x^k</math> equals the number of unique terms in <math>(x+y+z)^k + (x-y-z)^k</math>. ...ome constant. Therefore, the generating function for the MAXIMUM number of unique terms possible in the simplified expression of <math>(x+y+z)^k + (x-y-z)^k<8 KB (1,332 words) - 16:37, 17 September 2023
- '''OpenCourseWare''' is a unique resource offered by [[MIT]]. There are course decriptions, sample syllabi,289 bytes (40 words) - 11:20, 3 July 2006