By considering even functions (\(\hbox {mod}\ n\)), we generalize a recent Menon-type identity by Li and Kim, involving additive characters of the group \({\mathbb {Z}}_n\). We use a different approach, based on certain convolutional identities. Some other applications, including related formulas for Ramanujan sums, are discussed as well.

中文翻译：

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有关加性的Menon型恒等式

通过考虑偶数函数（\（\ hbox {mod} \ n \）），我们通过Li和Kim推广了最近的Menon型恒等式，其中涉及组\（{\ mathbb {Z}} _ n \）的加性。基于某些卷积身份，我们使用不同的方法。还讨论了其他一些应用程序，包括Ramanujan和的相关公式。