Page "Fundamental theorem of arithmetic" Paragraph 41

The first generalization of the theorem is found in Gauss's second monograph ( 1832 ) on biquadratic reciprocity.

This paper introduced what is now called the ring of Gaussian integers, the set of all complex numbers a + bi where a and b are integers.

It is now denoted by He showed that this ring has the four units ± 1 and ± i, that the non-zero, non-unit numbers fall into two classes, primes and composites, and that ( except for order ), the composites have unique factorization as a product of primes.