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Every nonzero Gaussian integer

, where

and

are ordinary integers and

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

, -1,

. Special Gaussian primes are

and primes

with

and

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

Contributed by: Izidor Hafner

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Factoring Gaussian Integers