Menon-type identities again: A note on a paper by Li, Kim and Qiao
Pentti Haukkanen, L\'aszl\'o T\'oth
TL;DR
This paper generalizes Menon-type identities involving multiple variables and gcd/lcm functions, introduces a new identity, and offers a simple proof method without characters.
Contribution
It provides broad generalizations of existing identities, includes a novel Menon-type identity for the lcm function, and simplifies proofs with a character-free approach.
Findings
Generalized Menon-type identities for multiple variables
New identity involving the lcm function
Simplified proof technique without characters
Abstract
We give common generalizations of the Menon-type identities by Sivaramakrishnan (1969) and Li, Kim, Qiao (2019). Our general identities involve arithmetic functions of several variables, and also contain, as special cases, identities for gcd-sum type functions. We point out a new Menon-type identity concerning the lcm function. We present a simple character free approach for the proof.
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