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• Gaussian integer
  A '''Gaussian integer''' is any [[complex number]] of the form <math>a + bi</math> where
  196 bytes (34 words) - 20:05, 23 January 2017

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• Prime number
  === Gaussian Primes === ...e that extends the idea of the traditional prime to the [[Gaussian integer|Gaussian integers]]. One can define this term for any [[ring]], especially number ri
  6 KB (985 words) - 12:38, 25 February 2024
• Ring
  ...ger]]s (<math>\mathbb{Z}[i]</math>). Note that of these, the integers and Gaussian integers do not have inverses; the rest do, and therefore also constitute e
  6 KB (994 words) - 06:16, 8 April 2015
• Quadratic reciprocity
  ...primitive <math>q</math>th root of unity in <math>K</math>. We define the Gaussian sum
  7 KB (1,182 words) - 16:46, 28 April 2016
• Carl Friedrich Gauss
  ...l and physics terms named after him including the [[Gaussian integer]]s, [[Gaussian distribution]]s, and [[Gauss's Law]].
  642 bytes (94 words) - 08:40, 21 August 2009
• System of equations
  === Gaussian Elimination ===
  5 KB (784 words) - 23:27, 30 July 2020
• Euclidean domain
  * The ring of [[Gaussian integers]] <math>\mathbb Z[i]</math> with norm given by <math>N(a+bi) = a^2
  2 KB (357 words) - 15:28, 22 August 2009
• 2008 IMO Problems/Problem 3
  The main idea is to take a gaussian prime <math>a+bi</math> and multiply it by a "twice as small" <math>c+di</m
  5 KB (1,002 words) - 01:09, 19 November 2023
• Fermat's Two Squares Theorem
  The theorem, with some study of the Gaussian integers <math>\mathbb{Z}[i]</math>, resolves these questions for the form We use the fact that the set of [[Gaussian integer]]s <math>\mathbb{Z}[i]</math> has a [[Euclidean algorithm]]. Hence
  4 KB (612 words) - 12:10, 30 May 2019
• Gaussian integer
  A '''Gaussian integer''' is any [[complex number]] of the form <math>a + bi</math> where
  196 bytes (34 words) - 20:05, 23 January 2017
• Unique factorization domain
  * The [[Gaussian integer]]s, <math>\mathbb Z[i]</math>
  6 KB (1,217 words) - 23:05, 23 August 2009
• Mock AIME 1 2010 Problems
  ...<math>b</math> are reals, is defined to be <math>\sqrt{a^2+b^2}</math>. A Gaussian integer is defined to be a complex number whose real and imaginary parts ar
  7 KB (1,297 words) - 01:29, 25 November 2016
• 2006 SMT/Algebra Problems
  ...nteger factors of smaller absolute value. Factor <math> -4+7i </math> into Gaussian primes with positive real parts. <math> i </math> is a symbol with the prop
  3 KB (464 words) - 11:02, 27 May 2012
• 2006 SMT/Algebra Problems/Problem 3
  ...nteger factors of smaller absolute value. Factor <math> -4+7i </math> into Gaussian primes with positive real parts. <math> i </math> is a symbol with the prop
  1 KB (224 words) - 08:43, 28 May 2012
• Algebraic number theory
  ...math>, in particular, leads to [[factorization]] in the [[Gaussian integer|Gaussian integers]].
  10 KB (1,646 words) - 15:04, 28 May 2020
• What is the definition of Pure Mathematics?
  ==== Gaussian Elimination ==== ==== Gaussian Primes ====
  35 KB (5,882 words) - 18:08, 28 June 2021