English

Divisibility rules for integers presented as permutations

Number Theory 2025-02-24 v1 Group Theory

Abstract

In this note, we represent integers in a type of factoradic notation. Rather than use the corresponding Lehmer code, we will view integers as permutations. Given a pair of integers n and k, we give a formula for n mod k in terms of the factoradic digits, and use this to deduce various divisibility rules.

Keywords

Cite

@article{arxiv.2502.15559,
  title  = {Divisibility rules for integers presented as permutations},
  author = {Thomas Oliver and Alexei Vernitski},
  journal= {arXiv preprint arXiv:2502.15559},
  year   = {2025}
}

Comments

4 pages

R2 v1 2026-06-28T21:52:53.792Z