## Gaussian integer |

In **Gaussian integer** is a **Z**[*i*].^{[1]} This integral domain is a particular case of a

- basic definitions
- euclidean division
- principal ideals
- gaussian primes
- unique factorization
- gaussian rationals
- greatest common divisor
- congruences and residue classes
- primitive residue class group and euler's totient function
- historical background
- unsolved problems
- see also
- notes
- references
- external links

The Gaussian integers are the set^{[1]}

In other words, a Gaussian integer is a

When considered within the

The *conjugate* of a Gaussian integer *a* + *bi* is the Gaussian integer *a* – *bi*.

The *norm*

The norm of a Gaussian integer is thus the square of its *k* + 3, with *k* integer.

The norm is ^{[2]}

for every pair of Gaussian integers *z*,*w*. This can be shown either by a direct check, or by using the multiplicative property of the absolute value of complex numbers.

The *i* and –*i*.^{[3]}

Other Languages

العربية: عدد صحيح غاوسي

беларуская: Гаусавы цэлыя лікі

català: Enter de Gauss

čeština: Gaussovo celé číslo

Deutsch: Gaußsche Zahl

español: Entero gaussiano

Esperanto: Gaŭsa entjero

français: Entier de Gauss

한국어: 가우스 정수

हिन्दी: गाऊसी पूर्णांक

italiano: Intero di Gauss

עברית: חוג השלמים של גאוס

қазақша: Гаусс саны

magyar: Gauss-egész

Nederlands: Geheel getal van Gauss

日本語: ガウス整数

polski: Liczby całkowite Gaussa

português: Inteiro de Gauss

русский: Гауссовы целые числа

slovenščina: Gaussovo praštevilo

suomi: Gaussin kokonaisluku

svenska: Gaussiskt heltal

தமிழ்: காஸியன் முழுஎண்(முழுமை)

українська: Гаусові числа

Tiếng Việt: Số nguyên Gauss

中文: 高斯整數