Translation and analysis of words by ChatGPT artificial intelligence
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What (who) is Gaussian primes - definition
![The [[discrete Gaussian kernel]] (solid), compared with the [[sampled Gaussian kernel]] (dashed) for scales <math>t = 0.5,1,2,4.</math>](https://commons.wikimedia.org/wiki/Special:FilePath/Discrete Gaussian kernel.svg?width=200 "The [[discrete Gaussian kernel]] (solid), compared with the [[sampled Gaussian kernel]] (dashed) for scales <math>t = 0.5,1,2,4.</math>")
![A [[halftone]] print rendered smooth through Gaussian blur](https://commons.wikimedia.org/wiki/Special:FilePath/Halftone, Gaussian Blur.jpg?width=200 "A [[halftone]] print rendered smooth through Gaussian blur")
Wikipedia
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as or
Gaussian integers share many properties with integers: they form a Euclidean domain, and have thus a Euclidean division and a Euclidean algorithm; this implies unique factorization and many related properties. However, Gaussian integers do not have a total ordering that respects arithmetic.
Gaussian integers are algebraic integers and form the simplest ring of quadratic integers.
Gaussian integers are named after the German mathematician Carl Friedrich Gauss.
