In some circumstances, it is useful to choose, once for all, a generator for each ideal. There are two classical ways for doing that, both considering first the ideals of odd norm. If the has an odd norm , then one of and is odd, and the other is even. Thus has exactly one associate with a real part that is odd and positive. In his original paper, Gauss made another choice, by choosing the unique associate such that the remainder of its division by is one. In fact, as , the norm of the remainder is not greater than 4. As this norm is odd, and 3 is not the norm of a Gaussian integer, the norm of the remainder is one, that is, the remainder is a unit. Multiplying by the inverse of this unit, one finds an associate that has one as a remainder, when divided by .