带有一个狄利克雷特征的Menon-Sury恒等式

Menon-Sury’s Identity with a Dirichlet Character

摘要: Li, Hu和Kim[1]运用整数剩余类环及其单位群的滤链证明了Menon-Sury恒等式的如下推广：

, 其中φ是欧拉φ函数， ，且χ是一个模n的导子为d的狄利克雷特征。在本文中，我们运用狄利克雷特征的正交性和初等计算去重新证明上述等式[2]。

Abstract: Li, Hu and Kim [1] proved the following generalization of the Menon-Sury identity by using the filtrations of the ring   Z_nand its unit group Z^*_n:

, where φ is Euler’s Totient function, , and χ is a Dirichlet character mod n with conductor d. In this paper, we re-prove the above identity based the orthogonality of Dirichlet characters and elementary calculations [2].

文章引用：陈曼. 带有一个狄利克雷特征的Menon-Sury恒等式[J]. 理论数学, 2019, 9(2): 188-194. https://doi.org/10.12677/PM.2019.92024

参考文献

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