关于模N的原根的分布

On the distribution of the primitive root module N

设模n≥3存在原根,对任一原根1≤a≤n-1,且(a,n)=1,显然存在唯一原根1≤a≤n-1,使得a a≡1(modn),对给定的正整数1≤k≤n,且(k,n)=1及实数0<δ≤1,研究了模n的原根a与它的逆a及整除性,并给出关于∑na=1|a-a|≤δna∈Ak|a+amin(|a-a|,|n+a-a|)较强的渐近公式。

Let module n≥3contain a primitive root and for each primitive root 1≤a≤n-1 with （a,n） =1, it is clear that exists one and only one primitive root 1≤a≤n-1, so that a a≡1（mod n） and integer 1≤k≤n with （k,n）=1 and real 0〈δ≤ 1. The main purpose of this paper is to study the distribution of the primitive root and its inverse module n,and to give a sharper asymptotic formula for n∑a=1 ｜a-a｜≤δn a∈A k｜a＋a min（｜a-a｜,｜n＋a-a｜）