On the Difference Between An Integer and Its Inverse Modulo n
On the Difference Between An Integer and Its Inverse Modulo n
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DOI：
10.1006/jnth.1995.1050
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发表时间：
1995-05
影响因子：
0.7
通讯作者：
Wenpeng Zhang
中科院分区：
文献类型：
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作者：
Wenpeng Zhang
设n > 2是一个整数，对于每个整数0 < x < n且（n，x）= 1，用同余式xx <$1（mod n）和0 < x < n定义x。设M（n，k）= ∑′n−1a=1（a − a）2k.本文的主要目的是研究M（n，k）的渐近性质，并证明对任意正整数k，我们有[公式]其中φ（n）是Euler函数，d（n）是除数函数，O（·）提供一个绝对常数.
Let n > 2 be an integer, and for each integer 0 < x < n with (n, x) = 1, define x by the congruence xx ≡ 1 (mod n) and 0 < x < n. Let M(n, k) = ∑′n−1a=1 (a − a)2k. The main purpose of this paper is to study the asymptotic behaviour of M(n, k), and prove for any positive integer k that we have [formula] where φ(n) is the Euler function, d(n) is the divisor function, and the O(·) provides an absolute constant.