关于平方补数的一个注记

A note on square complements

首先指出对于平方补数函数S2（n）可乘性的研究需限制在完全平方数集合或其子集上才能进行.接着,将正整数集N＊按照某等价关系＂～＂进行分类得到商集N＊-,将S2自然诱导至N＊-上得到S2～,最后证明了S2～具有完全乘性.

First,it is pointed out that the research on multiplicative of square complements must be restricted in the set of square numbers or its subset. Then quotient set N＊-is obtained by classifying positive integer set by an equivalence relation ～ and S2～is got by inducing S2 to N＊-. Finally,it follows that S2～is completely multiplicative function.