Gaussian integer factorizations

Factorization:  

A Gaussian integer is either the zero, one of the four units (± 1, ± i). For the rational prime 5, Gaussian integer factorizations of 5 = (-i) (2 + i) (1 + 2i).

For example, Gaussian integer factorizations of 10 = (-1) (1 + i) (1 + i) (2 + i) (1 + 2i)

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