Table of Gaussian integer factorizations
 |
Gaussian integers may be categorized as zero, the four units, Gaussian primes and composites. This is a list of Gaussian Integers x + iy 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 y + ix =i (x - iy).
The entries are sorted according to increasing norm x2 + y2 (sequence A001481 in the OEIS). Primes occur only for a restricted subset of norms, detailed in sequence OEIS: A055025. This here is a human-readable version of sequences OEIS: A103431 and OEIS: A103432.
Factorizations
class="wikitable " class="wikitable " class="wikitable " class="wikitable "
See also
References
Dresden, Greg; Dymacek, Wayne (2005). "Finding factors of factor rings over the Gaussian integers". American Mathematical Monthly,. 112 (7): 602–611. MR2158894.{{cite journal}}: CS1 maint: extra punctuation (link) JSTOR 30037545