积性函数的应用

Application of Multiplicative Function

积性函数在数论函数中有着重要的地位。积性函数由在素数幂处的取值完全决定,两个积性函数相等当且仅当它们在所有素数幂的取值均相等。本文主要利用这一特点证明了几个数论问题。

The multiplicative function, which has an important position in the arithmetic function, is completely deter- mined by the value of the prime power. Two multiplicative functions are equal if and only if they are equal in all prime powers. This paper mainly uses this feature to prove some problems in the number theory.