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.
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