A Complex Number where and are Integers. The Gaussian integers are members of the
Quadratic Field
. The sum, difference, and product of two Gaussian integers are Gaussian
integers, but only if there is an such that
The norm of a Gaussian integer is defined by
Every Gaussian integer is within of a multiple of a Gaussian integer .
See also Complex Number, Eisenstein Integer, Gaussian Prime, Integer, Octonion
References
Conway, J. H. and Guy, R. K. ``Gauss's Whole Numbers.'' In The Book of Numbers. New York: Springer-Verlag,
pp. 217-223, 1996.
Shanks, D. ``Gaussian Integers and Two Applications.'' §50 in Solved and Unsolved Problems in Number Theory, 4th ed.
New York: Chelsea, pp. 149-151, 1993.