Gaussian Integer
A Complex Number 
where 
and 
are Integers. The Gaussian integers are members of theQuadratic Field 
. The sum, difference, and product of two Gaussian integers are Gaussianintegers, but 
only if there is an 
such that
Gaussian Integers can be uniquely factored in terms of other Gaussian Integers up toPowers of
and rearrangements.The norm of a Gaussian integer is defined by
Gaussian Primes are Gaussian integers
for which 
is Prime and is aPrime Integer satisfying 
.- 1. If
, then 
and 
. These factors are equivalent since 
. For example,
is not a Gaussian Prime. - 2. If
, then 
. - 3. If
, then or 
. If both do, then .
Every Gaussian integer is within 
of a multiple of a Gaussian integer 
.
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.
- Tangent Indicatrix
- Tangent Line
- Tangent Map
- Tangent Number
- Tangent Plane
- Tangents Law
- Tangent Space
- Tangent Vector
- Tangle
- Tanglecube
- Tangled Hierarchy
- Tangram
- Tanh
- Taniyama Conjecture
- Taniyama-Shimura Conjecture
- Tank
- Tantrix
- Tapering Function
- Tarry-Escott Problem
- Tarry Point
- Tarski's Theorem
- Tauberian Theorem
- Tau Conjecture
- Tau-Dirichlet Series
- Tau Function