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• Field
  There is also a unique name for <math>(k\backslash\{0\},\cdot)</math>, which most accept as the ''
  2 KB (362 words) - 23:24, 31 December 2021
• Identity
  Identities in this sense are [[unique]]. Imagine we had two identities, <math>e</math> and <math>e'</math>, for s
  1 KB (238 words) - 13:38, 14 July 2021
• Quadratic reciprocity
  ...define the function <math>a \mapsto \genfrac{(}{)}{}{}{a}{p}</math> as the unique nontrivial multiplicative [[homomorphism]] of <math>\mathbb{F}_p^\times</ma
  7 KB (1,182 words) - 16:46, 28 April 2016
• Dedekind domain
  * Dedekind domains have unique prime factorizations of [[ideal]]s (but not necessarily of elements).
  9 KB (1,648 words) - 16:36, 14 October 2017
• Operator inverse
  If the operation <math>G</math> is associative, inverses are unique.
  1 KB (275 words) - 11:40, 23 November 2007
• Mock AIME 1 2006-2007 Problems/Problem 6
  ...h>P_2</math>, we have that <math>a(y^2 + \frac{45}4) + by = c</math> has a unique [[root]] so <math>b^2 - 4\cdot a \cdot (\frac{45}4a - c) = 0</math> or equi
  3 KB (460 words) - 15:52, 3 April 2012
• Mock AIME 1 2006-2007 Problems/Problem 13
  This is a set of three linear equations. In our case, it has a unique solution <math>(p,q,r)=(-2,-1,1)</math>, hence <math>d_7 = -2d_6 - d_5 + d_
  3 KB (568 words) - 15:50, 3 April 2012
• Mock AIME 2 2006-2007 Problems/Problem 8
  ...x_3 + x_2) = 2</math>. It is clear that <math>x_3 = x_2 = 1</math> is the unique solution to this equation in positive integers. Then <math>x_1 = 8 - x_2 =
  3 KB (470 words) - 00:33, 10 August 2019
• 2006 Romanian NMO Problems
  b) For which matrix <math>A</math> is the pseudo-inverse unique?
  11 KB (1,779 words) - 14:57, 7 May 2012
• Divisor function
  ...ermore, all of those products are unique since each positive integer has a unique prime factorization.
  3 KB (511 words) - 06:58, 21 May 2009
• Stanford Mathematics Tournament
  ...milarly proof-based team round where teams prove foundational results in a unique topic, tied together by a common theme. Topics in the past have included ga
  1 KB (214 words) - 22:37, 10 November 2023
• Free group
  ...group <math>G</math> and a function <math>\theta:I\to G</math>, there is a unique group homomorphism <math>\psi:F\to G</math> so that <math>\theta=\psi\phi</
  2 KB (454 words) - 17:54, 16 March 2012
• Odd integer
  ...Every odd integer can be written in the form <math>2k + 1</math> for some unique integer <math>k</math>.
  736 bytes (127 words) - 13:08, 20 February 2024
• Even integer
  ...en. Every even integer can be written in the form <math>2k</math> for some unique integer <math>k</math>.
  796 bytes (134 words) - 16:45, 17 January 2023
• Monoid
  Often one speaks of groups acting on sets. Since elements groups must have unique inverses, for every <math>a</math> in a group <math>G</math> acting on a se
  3 KB (670 words) - 22:45, 21 May 2008
• 2004 AMC 10A Problems/Problem 4
  ...| = 2-x</math>, so we must solve <math>x - 1 = 2 - x</math>, which has the unique solution <math>x = \frac32</math>.
  2 KB (289 words) - 18:01, 16 January 2021
• Chinese Remainder Theorem
  ...to the [[intersection]] of a unique residue class mod <math>m</math> and a unique residue class mod <math>n</math>, and the intersection of each residue clas
  6 KB (1,022 words) - 14:57, 6 May 2023
• Euclid's proof of the infinitude of primes
  ...ndamental Theorem of Arithmetic]] states that all positive integers have a unique prime factorization. Therefore, <math>N</math> must have a prime factor (po
  1 KB (179 words) - 11:57, 14 August 2022
• ELMO
  ...common mistakes (often this rubric only includes the most common solution; unique ideas are determined on a case-by-case basis). The sheer amount of ideas th
  5 KB (773 words) - 19:16, 17 June 2022
• Mock AIME 4 2006-2007 Problems/Problem 8
  Note that in fact, the answer is not unique because a many numbers can be represented as a [[binomial coefficient]] in
  2 KB (293 words) - 16:20, 8 October 2007

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