| 关于模N的原根与它的逆的差的偶数幂的分布及其整除性 |
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| 引用本文： | 崔志明,王辉. 关于模N的原根与它的逆的差的偶数幂的分布及其整除性[J]. 延安大学学报(自然科学版), 2001, 20(1): 11-13 |
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| 作者姓名： | 崔志明 王辉 |
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| 作者单位： | 1. 延安大学数学与计算机科学系,
2. 北京科技大学应用数学系, |
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| 摘 要： | 设模n≥3存在原根，对任一原根1≤α≤n-1且(α，n)＝1，显然存在唯一的原根1≤
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| 关 键 词： | 原根 同余方程 逆 整除性 渐近公式 |
| 文章编号： | 1004-602X(2001)01-0011-03 |
| 修稿时间： | 1997-06-16 |
On the even power of thedifference between the primitive root and its inverse modulo N and divisibility |
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| CUI Zhi-ming,WANG Hui. On the even power of thedifference between the primitive root and its inverse modulo N and divisibility[J]. Journal of Yan'an University(Natural Science Edition), 2001, 20(1): 11-13 |
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| Authors: | CUI Zhi-ming WANG Hui |
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| Affiliation: | CUI Zhi-ming,WANG Hui2 |
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| Abstract: | Let modulo n ≥ 3 contain a primitive root, and for each primitive root 1 ≤ a ≤ n - 1 with (a ,n)＝ 1 ,it is clear that there exists one and only one primitive root 1 ≤ α ≤ n - 1, so that αα ≡ 1 (modn) and iteger 1 ≤ k ＜ n with (k,n) ＝ 1. The main purpose of this paper, is to study the distribution properties of the even power of the difference between the primitive root and its inverse α modulo n and its divisibility, and to give an asymptotic formula for nΣa=1 |a-a|≤δn aэA k|a+a (a-a)2h. |
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| Keywords: | primitive root congruence equation inverse divisibility asymptotic formula |
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