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• W3206475467 abstract "Menon's identity states that for every positive integer $n$ one has $sum (a-1,n) = varphi(n) tau(n)$, where $a$ runs through a reduced residue system (mod $n$), $(a-1,n)$ stands for the greatest common divisor of $a-1$ and $n$, $varphi(n)$ is Euler's totient function and $tau(n)$ is the number of divisors of $n$. Menon's identity has been the subject of many research papers, also in the last years. We present detailed, self contained proofs of this identity by using different methods, and point out those that we could not identify in the literature. We survey the generalizations and analogs, and overview the results and proofs given by Menon in his original paper. Some historical remarks and an updated list of references are included as well." @default.
• W3206475467 created "2021-10-25" @default.
• W3206475467 creator A5050354606 @default.
• W3206475467 date "2021-10-14" @default.
• W3206475467 modified "2023-09-27" @default.
• W3206475467 title "Proofs, generalizations and analogs of Menon's identity: a survey" @default.
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• W3206475467 hasPublicationYear "2021" @default.
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