关于Andrew Granvill问题的推广

On the Generalization of a Problem of Andrew Granville

设是一个整数，对任一０＜α＜ｎ且（ａ，ｎ）＝１，显然存在唯一的整数０＜α＜ｎ－１使得αα≡１（ｍｏｄｎ）．本文的主要目的是研究差式｜α－α｜在算术级数中的分布性质，并给出一个有趣的渐近公式．

Let be an integer number, for each integer 0 < α< n with (n, a) = 1, it is clear that there exists one and only one αwith 0 < α< n such that αα= 1(modn). The main purpose of this paper is to study the distribution behaviour of |a-a| (where αand αbelong to an arithmetical progression), and give an interesting asymptotic formula.