Gaussian integer

mathematics

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June 29, 2026

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A Gaussian integer is a complex number of the form a + bi, where a and b are integers, and i is the square root of -1. These numbers are significant in mathematics, particularly in number theory and algebra.1

Carl Friedrich Gauss investigated these numbers in relation to prime factorization. He proved that Gaussian integers satisfy a generalized version of the unique prime factorization theorem, where primes are specifically defined within this domain. This work opened the door for studying special subsets of complex numbers and contributed to the development of modern algebra.2

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67
More Than Just Slang: Gaussian integers
…imaginary unit, they form the Gaussian integers. These are numbers of the form a + b i ,where a and b are integers. Ordinary integers fit naturally into this system; for example, 67 can be written as 67 + 0i.
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…imaginary unit, they form the Gaussian integers. These are numbers of the form a + b i ,where a and b are integers. Ordinary integers fit naturally into this system; for example, 67 can be written as 67 + 0i.
Read More

algebra
Prime factorization
…i = Square root of√−1), sometimes called Gaussian integers. In doing so, Gauss not only used complex numbers to solve a problem involving ordinary integers, a fact remarkable in itself, but he also opened the way to the detailed investigation of special subdomains of the complex numbers.
Read More
…i = Square root of√−1), sometimes called Gaussian integers. In doing so, Gauss not only used complex numbers to solve a problem involving ordinary integers, a fact remarkable in itself, but he also opened the way to the detailed investigation of special subdomains of the complex numbers.
Read More