Table of Gaussian integer factorizations
Encyclopedia
Gaussian integer
s may be categorized as zero, the four units, Gaussian primes and composites. This is a list of Gaussian Integers in the first quadrant followed either by an explicit factorization or followed by a label (p) for primes. The factorizations take the form of an optional unit
multiplied by integer powers of Gaussian primes. They are usually not unique in the sense that the unit could be absorbed into any other factor with exponent equal to one.
The table might have been further reduced to the integers that reside in the first octant of the
complex plane using the symmetry
.
The entries are sorted according to increasing norm . Primes occur only for a restricted subset of norms, detailed in sequence . This here
is a human-readable version of sequences and .
Gaussian integer
In number theory, a Gaussian integer is a complex number whose real and imaginary part are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. The Gaussian integers are a special case of the quadratic...
s may be categorized as zero, the four units, Gaussian primes and composites. This is a list of Gaussian Integers in the first quadrant followed either by an explicit factorization or followed by a label (p) for primes. The factorizations take the form of an optional unit
Unit (ring theory)
In mathematics, an invertible element or a unit in a ring R refers to any element u that has an inverse element in the multiplicative monoid of R, i.e. such element v that...
multiplied by integer powers of Gaussian primes. They are usually not unique in the sense that the unit could be absorbed into any other factor with exponent equal to one.
The table might have been further reduced to the integers that reside in the first octant of the
complex plane using the symmetry
.
The entries are sorted according to increasing norm . Primes occur only for a restricted subset of norms, detailed in sequence . This here
is a human-readable version of sequences and .