Factoring Gaussian Integers

10i+18(7-2i)(-i)

3

(i+1)

Every nonzero Gaussian integer

a+bi

, where

a

and

b

are ordinary integers and

i=

-1

,

can be expressed uniquely as the product of a unit and powers of special Gaussian primes. Units are 1,

i

, -1,

-i

. Special Gaussian primes are

1+i

and primes

z

with

Re(z)>0

and

Re(z)>|Im(z)|

.

J. H. Conway and R. K. Guy, The Book of Numbers, New York: Copernicus Books/Springer, 2006 pp. 217–220.

Izidor Hafner