Divisibility rules for integers presented as permutations

2025/02/21 by Oliver, Thomas, Vernitski, Alexei
#FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.15559

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.

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