English

Generalizations of Menon's arithmetic identity

Number Theory 2023-09-26 v3 Combinatorics

Abstract

Menon's identity is aAm(a1,m)=d(m)φ(m)\sum_{a \in A}^m (a-1,m) = d(m) \varphi(m), where AA is a reduced set of residues modulo mm. This paper contains elementary proofs of some generalizations of this result.

Cite

@article{arxiv.2111.05086,
  title  = {Generalizations of Menon's arithmetic identity},
  author = {Melvyn B. Nathanson},
  journal= {arXiv preprint arXiv:2111.05086},
  year   = {2023}
}

Comments

9 pages; minor improvements

R2 v1 2026-06-24T07:32:08.112Z