10 Facts About Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.

In other words, a Gaussian integer is a complex number such that its real and imaginary parts are both integers.

Norm of a Gaussian integer is thus the square of its absolute value as a complex number.

The norm of a Gaussian integer is a nonnegative integer, which is a sum of two squares.

An associate of a Gaussian integer prime is a Gaussian integer prime.

The conjugate of a Gaussian integer prime is a Gaussian integer prime .

Positive integer is a Gaussian prime if and only if it is a prime number that is congruent to 3 modulo 4 .

Gaussian integer is a Gaussian prime if and only if either:.

In other words, a Gaussian integer is a Gaussian prime if and only if either its norm is a prime number, or it is the product of a unit and a prime number of the form.

Residue class ring modulo a Gaussian integer is a field if and only if is a Gaussian prime.