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.
- Random Walk--1-D
- Random Walk--2-D
- Random Walk--3-D
- Range (Image)
- Range (Line Segment)
- Range (Statistics)
- Rank
- Rank (Group)
- Rank (Quadratic Form)
- Rank (Sequence)
- Rank (Statistics)
- Rank (Tensor)
- Ranunculoid
- RAT-Free Set
- Ratio
- Ratio Distribution
- Rational Approximation
- Rational Canonical Form
- Rational Cuboid
- Rational Distances
- Rational Domain
- Rational Double Point
- Rational Function
- Rational Integer
- Rational Number