数论中欧拉公式的一个初等证明及欧拉函数的性质

An Elementary Proof of Euler Formula in Number Theory and the Properties of Euler's Totient Function

数论中的欧拉函数即比给定的自然数小且与之互素的自然数的个数,包括1在内,定义为φ(n)。欧拉给出了它的计算公式。文章对于该公式给出了一种初等证明,并讨论了它的一些性质。

Euler’s totient function in number theory is defined as the number of positive integers which are smaller than the given number and are mutually prime with,including defined asφ(n).Euler gives its calculation formula.This paper gives an elementary proof for this formula.Some properties of this function are discussed.