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- A '''Gaussian integer''' is any [[complex number]] of the form <math>a + bi</math> where196 bytes (34 words) - 20:05, 23 January 2017
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- === 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 ri6 KB (1,036 words) - 18:26, 2 September 2024
- ...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 e6 KB (994 words) - 06:16, 8 April 2015
- ...primitive <math>q</math>th root of unity in <math>K</math>. We define the Gaussian sum7 KB (1,182 words) - 16:46, 28 April 2016
- ...l and physics terms named after him including the [[Gaussian integer]]s, [[Gaussian distribution]]s, and [[Gauss's Law]].816 bytes (118 words) - 11:17, 27 September 2024
- === Gaussian Elimination ===5 KB (784 words) - 23:27, 30 July 2020
- * The ring of [[Gaussian integers]] <math>\mathbb Z[i]</math> with norm given by <math>N(a+bi) = a^22 KB (357 words) - 15:28, 22 August 2009
- The main idea is to take a gaussian prime <math>a+bi</math> and multiply it by a "twice as small" <math>c+di</m5 KB (1,002 words) - 01:09, 19 November 2023
- 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]]. Hence4 KB (612 words) - 12:10, 30 May 2019
- A '''Gaussian integer''' is any [[complex number]] of the form <math>a + bi</math> where196 bytes (34 words) - 20:05, 23 January 2017
- * The [[Gaussian integer]]s, <math>\mathbb Z[i]</math>6 KB (1,217 words) - 23:05, 23 August 2009
- ...<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 ar8 KB (1,377 words) - 13:20, 2 August 2024
- ...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 prop3 KB (464 words) - 11:02, 27 May 2012
- ...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 prop1 KB (224 words) - 08:43, 28 May 2012
- ...math>, in particular, leads to [[factorization]] in the [[Gaussian integer|Gaussian integers]].10 KB (1,646 words) - 15:04, 28 May 2020
- ==== Gaussian Elimination ==== ==== Gaussian Primes ====35 KB (5,886 words) - 09:20, 28 September 2024
- ...<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 ...ent values are all <math>i</math>-multiples of each other, so they are all Gaussian integers, and none of them lie in the same quadrant. Furthermore, because,2 KB (440 words) - 12:06, 2 August 2024