Many theorems (and their proofs) for moduli of integers can be directly transferred to moduli of Gaussian integers, if one replaces the absolute value of the modulus by the norm. This holds especially for the "primitive residue class group" (also called multiplicative group of integers modulo ) and Euler's totient function. The primitive residue class group of a modulus is defined as the subset of its residue classes, which contains all residue classes that are coprime to , i.e. . Obviously, this system builds a multiplicative group. The number of its elements shall be denoted by (analogously to Euler's totient function for integers ).